math masters vs phd

Stack Exchange Network

Stack Exchange network consists of 183 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Q&A for work

Connect and share knowledge within a single location that is structured and easy to search.

How should a mathematics major choose between doing a Masters or PhD?

I would really appreciate any advice or suggestions anyone might have. I am currently a senior mathematics major, about to graduate in May. For two years, I have planned on going for my PhD in pure mathematics (my highest interests have been in algebra, number theory, and discrete math). I applied to 8 PhD programs and 1 masters program, the masters program just for the heck of it. I was accepted into the masters program, but I was rejected from 6 PhD programs and wait-listed on the other two. Neither of these last two would I really want to go to, but I would be happy at either of them nonetheless.

Now, the masters program is at Ohio State and gives full tuition waiver plus a minimum monthly stipend of $1950, plus a significantly reduced health insurance bill. The program specifically is the Master of Mathematical Sciences with concentration in Computational Sciences. The department is super lenient as to which courses I can take outside of their main core courses, as long as my course plan fits the computational theme and as long as my advisor signs off.

So, my question is, should I go to the masters program or should I go to one of the PhD programs (if I'm even accepted; again, I'm still wait-listed)? Will finishing this MMS program at Ohio State help my chances of getting in to a top-notch PhD program in the future? How common is it (in mathematics) for mathematicians to earn a (non-"incidental") masters degree before pursuing their PhD?

Thanks! Let me know if you want any clarification or further information.

graduate-school

6 I think its important for you to understand why you were turned down by 6 PhD programs in mathematics. This could be because you've aimed way to high, or it could be because of some specific flaw in your application, but you haven't provided us with much information. – Brian Borchers Commented Mar 23, 2015 at 2:15
Hello, this is the OP. Thank you all for your feedback so far. I should add that I believe my most significant flaw in my application materials was my Subject GRE score. It was abysmal, but I don't want to release any specifics. My grades have been really good (overall GPA of 3.80 and math/CS GPA of 3.90), I went to an REU, and I have several pre-print papers (although not actually published as of yet). I should also add that I come from a small, liberal arts college that is not well known. – user32088 Commented Mar 23, 2015 at 2:35
1 If you're serious about a PhD, you should take the subject again. At least for the general GRE (only one I had to take), that is very common. If it's very low, you might hit cutoffs where faculty won't even see an otherwise strong application (at least in my old field). – gnometorule Commented Mar 23, 2015 at 2:42

3 Answers 3

I'm not in mathematics so take my answer for what it is. The fact that you were turned down by 6 PhD programs suggests that your applications probably weren't too strong. Maybe you had bad grades, bad test scores, bad recommendations, etc. Or you simply overestimated your application strength and applied to schools beyond your reach (i.e. top 15 schools).

Whatever it is, you need to overcome these shortcomings in your credentials. A Masters degree could be a great way to prove that you are grad school material, especially if you can demonstrate that you fit in academia by publishing article(s). This could be a jumping point to a decent PhD program. Generally, graduate programs would rather accept successful masters students over successful bachelors students, simply because good masters students already know the system and how to make it work.

1 I think this is generally good advice. However, a particular aspect of this that is discipline specific is that the OP wants to do a PhD in pure mathematics but has been accepted into an MS program in computational/applied mathematics. Having that master's degree isn't going to be particularly helpful in getting into a pure math PhD program. – Brian Borchers Commented Mar 23, 2015 at 2:13
1 @Brian Borchers. My plan as of now (if I go to Ohio State) is to plan my studies around algorithmic techniques in number theory or algebra. I'm hoping that focusing on either of these disciplines will help my application for a pure math PhD program. – user32088 Commented Mar 23, 2015 at 2:43
1 See the description of the MMS program's computational sciences track at Ohio State. It isn't a program that is designed for what you want to do, and it isn't clear to me that you'll be able to follow your interests within this program. math.osu.edu/grad/future/mms/computational-sciences – Brian Borchers Commented Mar 23, 2015 at 3:56
See also the list of required and elective courses: math.osu.edu/grad/current/mms/computational-sciences – Brian Borchers Commented Mar 23, 2015 at 4:04
That was the very first thing I did. Because it was not clear to me either, I contacted the director of graduate studies. He said that course plans centered around computational number theory and topological data analysis are especially encouraged. He also said that the department has been very lenient with elective course substitutions so long as they fit the computational theme and are approved by the advisor. – user32088 Commented Mar 23, 2015 at 5:10

At this point it seems like your choice is actually whether to go for the Masters or not. So, you can either wait another year and apply again with the same application as before, hoping that you'll be luckier and get admitted somewhere... or you can get a jump-start on graduate studies, study for a couple of years, write up a good thesis (by all means, you should do a thesis) and then if you still want to go for the PhD you will have solid grades in graduate-level courses, a fresh batch of recommendations, some publishable work and a new perspective on whether to continue studies or enter industries, all of which would make you look that much better in the eyes of admissions committees -- all for $0. Given that you want to end up with a PhD, it seems like a no-brainer to me. :)

I would recommend you start a program where you can begin your masters and then have the option to move on to a PhD (many programs have that option). I am just finishing my masters now in statistics and will not pursue a PhD anytime soon. Two reasons. One reason is because I want to work and make money. Second reason: I don't think I can stand being in school for another three years... in addition to more exams, thesis, and comp exams.

Maybe in the future I might change my mind. Or maybe an employer (like many do today) will help pay for me to pursue a PhD. You never know :)

4 The majority of this answer consists of information about yourself. Could you clarify how this information addresses the OP's question? – Pete L. Clark Commented Mar 23, 2015 at 1:20

You must log in to answer this question.

Not the answer you're looking for browse other questions tagged graduate-school education ..

Featured on Meta
Site maintenance - Mon, Sept 16 2024, 21:00 UTC to Tue, Sept 17 2024, 2:00...
User activation: Learnings and opportunities
Join Stack Overflow’s CEO and me for the first Stack IRL Community Event in...

Hot Network Questions

When I use \llap to overlap words, the space between the overlapped words and the rest of the text is too much: how do I fix it?
Is it true that before European modernity, there were no "nations"?
AWK search for multiple patterns in a file
Tensor product of intersections in an abelian rigid monoidal category
C++ std::function-like queue
Ubuntu 22.04.5 - Final Point Release
What factors cause differences between dried herb/spice brands?
Why was Panama Railroad in poor condition when US decided to build Panama Canal in 1904?
Why is steaming food faster than boiling it?
Will "universal" SMPS work at any voltage in the range, even DC?
Stuck as a solo dev
Is it a correct rendering of Acts 1,24 when the New World Translation puts in „Jehovah“ instead of Lord?
Why does counterattacking lead to a more drawish and less dynamic position than defending？
Why is resonance such a widespread phenomenon?
1950s comic book about bowling ball looking creatures that inhabit the underground of Earth
View undo history of Windows Explorer on Win11
Does such a manifold exist??
History of the migration of ERA from AMS to AIMS in 2007
How did people know that the war against the mimics was over?
What is the oldest open math problem outside of number theory?
Where is DC-3 parked at KOPF?
What properties of the fundamental group functor are needed to uniquely determine it upto natural isomorphism?
In Photoshop, when saving as PNG, why is the size of my output file bigger when I have more invisible layers in the original file?
How in the world do I fix this anciently old slop sink? I am okay even with a temporary fix

$Department of Mathematics$

University of Louisiana at Lafayette

Department of mathematics, ray p. authement college of sciences, search form.

News & Events
Department Facts
Awards & Recognition
Alumni & Friends
Professional Organizations
Job Openings
What can I do with a degree in math?
Undergraduate
Critical Courses
Major Checklist
Online Courses
Selected Syllabi
Placement & Credit
Financial Aid & Scholarships
Catalogs & Handbooks
Dates & Deadlines
Organizations & Associations
Career Opportunities
Student Survival Guide
Mathematics Make-up Exams
Activities for Undergraduates
Research Areas
Research News
Grants & Contracts
Conferences & Meetings
Seminars & Colloquia
Reliable Computing Journal
The Statistical Consulting Center

The great thing about math is that it applies to everything — from the health industry to the banking industry, from education to engineering, from logistics to neuroscience. Your math graduate degree will give you the analytical and problem-solving skills needed for any job after graduation, whether that’s working in academia or in the private or public sectors.

To figure out whether you should choose to pursue your math master’s or your PhD in mathematics, it’s a good idea to look at them side by side and see which program fits your personal goals.

Math Master’s Degree

Students who graduate with their master’s in math are equipped for a range of careers. Earning your master’s typically takes about two years, so you can return to the workforce sooner with a higher level of expertise than your peers.

With your math master’s, you can become a better high school teacher and opportunities to teach at the community college level can open to you. At either level, you’d be helping young students realize the excitement and complexity of your field. This is a great option if you’ve already earned an undergraduate education degree or teaching certification.

Another career option is conducting research for various industries and government agencies. You can work in robotics, health care, the financial sector, aviation, technology and more — the possibilities are vast. Mathematicians creatively and meticulously study and solve problems, and pretty much any industry can utilize that expertise.

And if you’re looking to learn even more, earning your master’s is a great prep for doctoral studies in math or if you’re not sure about your post-grad career options. Most of our math master’s students at UL Lafayette choose to pursue their master’s and PhD simultaneously or attend another university for their PhD in math.

PhD in Mathematics Degree

Typically, students who pursue a PhD in math choose a career in academia. A PhD is needed to teach at the university level, because you’re sharing your intense expertise with students, helping them do research and delve deeper into the field you love so much.

If you teach at a research university, you’ll teach high-level classes and you’ll have the opportunity to continue complex and speculative research. As a PhD student, you’ll begin to discover and invent new math, and you can continue doing just that as a professor, forging a path for yourself and your research.

Earning your PhD in math widens your academic career opportunities, and you get to spend your career as a student and then as a professor learning more about your passions.

There are also plenty of opportunities to work for private companies or governmental organizations. Many of our PhD in mathematics alumni work in medicine, engineering, and software development, applying the knowledge they gained in their PhD program to help solve complex, real-world problems.

Some of our recent UL Lafayette math PhD alumni include:

Peter Xiao, who holds 8 U.S. patents and is engineering director at CISCO;
Jie Yang, associate actuary at Humana, Inc.;
Sowmya Muniswamy, assistant professor at the Rashtriya Vidyalaya College of Engineering in Bangalore, India;
Dan Zhang, statistician at L2C, Inc.;
Jie Peng, assistant professor in the Department of Economics at St. Ambrose University;
Haochun Zhang, quantitative analyst at Pittsburgh National Corporation; and
Shuhua Hu, senior research scientist at the Center for Research in Scientific Computation at North Carolina State University.

Learn more about our graduate programs in math >>

Have a language expert improve your writing

Run a free plagiarism check in 10 minutes, generate accurate citations for free.

Knowledge Base
Applying to graduate school
Master’s vs PhD | A Complete Guide to the Differences

Master's vs PhD | A Complete Guide to the Differences

Published on November 27, 2020 by Lauren Thomas . Revised on May 10, 2024.

The two most common types of graduate degrees are master’s and doctoral degrees:

A master’s is a 1–2 year degree that can prepare you for a multitude of careers.
A PhD, or doctoral degree, takes 3–7 years to complete (depending on the country) and prepares you for a career in academic research.

A master’s is also the necessary first step to a PhD. In the US, the master’s is built into PhD programs, while in most other countries, a separate master’s degree is required before applying for PhDs.

Master’s are far more common than PhDs. In the US, 24 million people have master’s or professional degrees, whereas only 4.5 million have doctorates.

Master’s vs phd at a glance, which is right for you, length of time required, career prospects, costs and salaries, application process, other interesting articles, frequently asked questions about master's and phd degrees.

The table below shows the key differences between the two.

	Master’s	PhD
Career prospects	Usually intended for a career outside of academia.	Prepares for a research career, ideally as a university professor.
Length of time	1–2 years	5–7 in the US (master’s degree included); 3–5 outside the US (after a separate master’s degree)
Structure	Mostly coursework, often with a semester-long or capstone project at the end.	2 years of coursework (in the US), followed by 3–5 years of preparing a dissertation, which should make a significant original contribution to current knowledge.
Cost	Varies by country, university and program; usually higher upfront cost with limited financial aid available.	Tuition fees are usually waived and a living stipend provided in exchange for being a teaching or research assistant.
Graduate salaries	Wage premium (compared to earnings with a high school education) is 23% on average.	Wage premium is 26% on average.

Receive feedback on language, structure, and formatting

Professional editors proofread and edit your paper by focusing on:

Academic style
Vague sentences
Style consistency

See an example

A PhD is right for you if:

Your goal is to become a professor at a university or some other type of professional researcher.
You love research and are passionate about discovering the answer to a particular question.
You are willing to spend years pursuing your research even if you have to put up with a lot of dead ends and roadblocks.

A master’s degree is the better choice if any of the following apply:

You want to continue studies in your field, but you’re not committed to a career as a professional researcher.
You want to develop professional skills for a specific career.
You are willing to pay a higher upfront cost if it means finishing with your degree (and thus being able to work) much faster.
You want the option to study part-time while working.

The length of time required to complete a PhD or master’s degree varies. Unsurprisingly, PhDs take much longer, usually between 3–7 years. Master’s degrees are usually only 1–2 years.

Length of a master’s

Master’s degrees are usually 2 years, although 1-year master’s degrees also exist, mainly in the UK.

Most of the degree consists of classes and coursework, although many master’s programs include an intensive, semester-long master’s thesis or capstone project in which students bring together all they’ve learned to produce an original piece of work.

Length of a PhD

In the US, a PhD usually takes between 5 and 7 years to complete. The first 2 years are spent on coursework. Students, even those who choose to leave without finishing the program, usually receive a master’s degree at this point.

The next 3–5 years are spent preparing a dissertation —a lengthy piece of writing based on independent research, which aims to make a significant original contribution to one’s field.

Master’s degrees tend to prepare you for a career outside of academia, while PhDs are designed to lead to a career in research.

Careers for master’s graduates

There are two types of master’s degrees: terminal and research-intensive. The career prospects are different for each.

Terminal master’s degrees are intended to prepare students for careers outside of academia. Some degrees, known as professional degrees, specifically prepare students for particular professions; these include the Master of Public Policy (MPP), Master of Business Administration (MBA), Doctor of Physical Therapy (DPT), Master of Fine Arts (MFA), and Master of Public Health (MPH) degrees.

Other master’s degrees, usually Master of Arts (MA) or Master of Sciences (MS or MSc) degrees, do not necessarily lead to a specific career, but are intended to be a final degree. Examples include an MS in Communications or MS in Data Analytics.

In research-intensive master’s programs, students take coursework intended to prepare them for writing an original piece of research known as the master’s thesis . Such programs are usually intended to prepare for further study in a doctoral program.

Careers for PhD graduates

As research degrees, PhDs are usually intended to lead to an academic career. A PhD can be thought of like an apprenticeship, where students learn from professional researchers (academics) how to produce their own research.

Most students aspire to become a university professor upon the completion of their degree. However, careers in academia are highly competitive, and the skills learned in a doctoral program often lend themselves well to other types of careers.

Some graduates who find they prefer teaching to producing research go on to be teachers at liberal arts colleges or even secondary schools. Others work in research-intensive careers in the government, private sector, or at think tanks.

Below are a few examples of specific fields and non-academic careers that are common destinations of graduates of those fields.

Computer Science
Lab Sciences

Many government jobs, including economists at a country’s central bank, are research-intensive and require a PhD. Think tanks also hire economists to carry out independent research.

In the private sector, economic consulting and technology firms frequently hire PhDs to solve real-world problems that require complex mathematical modeling.

Graduate students from the humanities are sometimes hired by museums, who can make use of their research and writing skills to curate exhibits and run public outreach.

Humanities PhDs are often well-suited to research and grant-writing roles at nonprofits. Since so much of research is funded by grants, PhD students often gain a lot of experience applying for them, which is a useful skill in the nonprofit sector.

There are a wide range of non-academic research jobs for lab scientists with doctorates in subjects like chemistry, biology, ecology and physics.

Many PhD graduates are hired by pharmaceutical companies that need to perform research to create and test their products. Government agencies, such as the Environmental Protection Agency (EPA), also hire lab scientists to work on research projects.

Job prospects after graduation vary widely based on the field. In fields like management, computer science, statistics, and economics, there’s little underemployment—even graduates from less well-known programs can easily find jobs that pay well and use the skills they’ve gained from the PhD.

However, in other fields, particularly in the humanities, many PhD graduates have difficulty in the job market. Unfortunately, there are far more PhD graduates than assistant professor roles, so many instead take on part-time and low-paid roles as adjunct instructors. Even non-academic careers can sometimes be difficult for PhDs to move into, as they may be seen as “overqualified” or as lacking in relevant professional experience.

Because career options post-PhD vary so much, you should take the time to figure out what the career prospects are in your field. Doctoral programs often have detailed “placement” records online in which they list the career outcomes of their graduates immediately upon leaving the program. If you can’t find these records, contact the program and ask for them—placement information should play an important role in your choice of PhD program.

Prevent plagiarism. Run a free check.

Although PhDs take far longer to complete, students often receive a living stipend in exchange for being a teaching or research assistant. Master’s degrees are shorter but less likely to be funded.

Both master’s degrees and PhDs lead to increased salaries upon graduation. While PhDs usually earn a bit more than those with a master’s degree, in some fields, the wages are identical, meaning that no financial benefit is gained from going on to a PhD.

Cost of a master’s

The upfront cost of a master’s degree is usually higher than a doctoral degree due to the lower amount of financial aid available. However, increased salaries also arrive faster than with a doctoral degree, because people graduate much earlier from a master’s program.

Some master’s students do receive stipends for their degrees, usually as compensation for being a teaching or research assistant. In addition, many people complete master’s degrees part time while working full-time, which allows them to fund their living costs as well as tuition.

The cost varies significantly by school and program. Public schools are usually cheaper than private ones. Some master’s degrees, such as MBAs, are notoriously expensive, but also result in much higher wages afterwards that make up for the high cost.

The master’s wage premium , or the extra amount that someone with a master’s degree makes than someone with just a high school diploma, is 23% on average. Many universities provide detailed statistics on the career and salary outcomes of their students. If they do not have this online, you should feel free to contact an administrator of the program and ask.

Cost of a PhD

PhDs, particularly outside the humanities, are usually (though not always) funded, meaning that tuition fees are fully waived and students receive a small living stipend. During the last 3–5 years of a PhD, after finishing their coursework (and sometimes before), students are usually expected to work as graduate instructors or research assistants in exchange for the stipend.

Sometimes students can apply for a fellowship (such as the National Science Foundation Graduate Research Program in the United States) that relieves them of any obligations to be a teaching or research assistant. Doctoral programs in the US tend to be better funded than in the rest of the world.

Sometimes, PhD degrees can be completed part-time, but this is rare. Students are usually expected to devote at least 40 hours a week to their research and work as teaching or research assistants.

The main cost of doctoral programs comes in the form of opportunity cost—all the years that students could be working a regular, full-time job, which usually pays much better than a graduate school stipend.

The average wage premium for PhDs is 26%, which is not much higher than the master’s degree premium.

In the US, the application process is similar for master’s and PhD programs. Both will generally ask for:

At least one application essay, often called a personal statement or statement of purpose .
Letters of recommendation .
A resume or CV .
Transcripts.
Writing samples.

Applications for both types of programs also often require a standardized test. PhDs usually require the Graduate Record Examination (GRE), which tries to measure verbal reasoning, quantitative, critical thinking , and analytical writing skills. Many master’s programs require this test as well.

Applying for a master’s

Master’s degrees programs will often ask you to respond to specific essay prompts that may ask you to reflect upon not just your academic background, but also your personal character and future career ambitions.

Northwestern University’s Kellogg Business School requires Master’s of Business Administration (MBA) applicants write two essays, one about a recent time they demonstrated leadership and the second about their personal values.

Who you should ask for your letters of recommendation varies by program. If you are applying to a research-intensive master’s program, then you should choose former professors or research supervisors. For other programs, particularly business school, current work supervisors may be a better choice.

Some professional master’s programs require a specific test. For example, to apply to law school, you must take the Law School Admissions Test, or LSAT. For business school, you must take either the GRE or the Graduate Management Admissions Test (GMAT).

Applying for a PhD

When applying for a PhD, your resume should focus more on your research background—you should especially emphasize any publications you’ve authored or presentations that you’ve given.

Similarly, your statement of purpose should discuss research that you’ve participated in, whether as an assistant or the lead author. You should detail what exactly you did in projects you’ve contributed to, whether that’s conducting a literature review, coding regressions, or writing an entire article.

Your letters of recommendations should be from former professors or supervisors who can speak to your abilities and potential as a researcher. A good rule of thumb is to avoid asking for recommendations from anyone who does not themselves have a PhD.

If you want to know more about college essays , academic writing , and AI tools , make sure to check out some of our other language articles with explanations, examples, and quizzes.

College essays

College essay examples
College essay format
College essay style
College essay length
Diversity essays
Scholarship essays

Academic writing

Writing process
Avoiding repetition
Literature review
Conceptual framework
Dissertation outline
Thesis acknowledgements
Burned or burnt
Canceled or cancelled
Dreamt or dreamed
Gray or grey
Theater vs theatre

A master’s is a 1- or 2-year graduate degree that can prepare you for a variety of careers.

All master’s involve graduate-level coursework. Some are research-intensive and intend to prepare students for further study in a PhD; these usually require their students to write a master’s thesis . Others focus on professional training for a specific career.

A PhD, which is short for philosophiae doctor (doctor of philosophy in Latin), is the highest university degree that can be obtained. In a PhD, students spend 3–5 years writing a dissertation , which aims to make a significant, original contribution to current knowledge.

A PhD is intended to prepare students for a career as a researcher, whether that be in academia, the public sector, or the private sector.

This depends on the country. In the United States, you can generally go directly to a PhD with only a bachelor’s degree, as a master’s program is included as part of the doctoral program.

Elsewhere, you generally need to graduate from a research-intensive master’s degree before continuing to the PhD.

This varies by country. In the United States, PhDs usually take between 5–7 years: 2 years of coursework followed by 3–5 years of independent research work to produce a dissertation.

In the rest of the world, students normally have a master’s degree before beginning the PhD, so they proceed directly to the research stage and complete a PhD in 3–5 years.

A master’s degree usually has a higher upfront cost, but it also allows you to start earning a higher salary more quickly. The exact cost depends on the country and the school: private universities usually cost more than public ones, and European degrees usually cost less than North American ones. There are limited possibilities for financial aid.

PhDs often waive tuition fees and offer a living stipend in exchange for a teaching or research assistantship. However, they take many years to complete, during which time you earn very little.

In the US, the graduate school application process is similar whether you’re applying for a master’s or a PhD . Both require letters of recommendation , a statement of purpose or personal statement , a resume or CV , and transcripts. Programs in the US and Canada usually also require a certain type of standardized test—often the GRE.

Outside the US, PhD programs usually also require applicants to write a research proposal , because students are expected to begin dissertation research in the first year of their PhD.

Cite this Scribbr article

If you want to cite this source, you can copy and paste the citation or click the “Cite this Scribbr article” button to automatically add the citation to our free Citation Generator.

Thomas, L. (2024, May 09). Master's vs PhD | A Complete Guide to the Differences. Scribbr. Retrieved September 9, 2024, from https://www.scribbr.com/graduate-school/masters-vs-phd/

Is this article helpful?

Lauren Thomas

Other students also liked, when to apply for graduate school | month-by-month timeline, how to write a statement of purpose | example, how to write a graduate school resume | template & example, get unlimited documents corrected.

✔ Free APA citation check included ✔ Unlimited document corrections ✔ Specialized in correcting academic texts

Directories

Colorado School of Mines Graduate School Insights

Should you get a graduate degree in mathematics?

Should you get a master’s or doctoral degree.

Data science students working on white board

A master’s in mathematics alone will qualify you to work in fields such actuarial science, computer science, and data science, all of which report high earnings and high job satisfaction . Master’s degrees also offer a lot of potential for degree specialization .

A doctoral degree qualifies you for all of the above, as well as working in academia, whether that’s teaching, research or a combination of the two.

Another thing to consider is how much time you’re willing to invest in getting your applied mathematics and statistics graduate degree . For reference, the doctoral program at Mines requires 72 credit hours (one class usually counts for three credit hours). If you’re taking on a recommended course load of 15 credit hours (five classes) each semester, then it’ll take a little over three years for you to get your doctorate. And this doesn’t take into account the time you’ll spend conducting research and writing your thesis.

The master’s program, on the other hand, requires 30 credit hours, or two years for a full-time student. Mines also offers a non-thesis option, which favors coursework over original research.

Many people working toward their master’s do so online and part time. A 2016 survey found that 31% of students enrolled in a master’s program were taking courses online .

Cost is another consideration for many seeking their master’s in mathematics. At Mines, the annual cost of attendance for 2021-2022 is $41,013 for Colorado residents, $62,325 for students from outside the state and $40,003 for online students.

What you’ll need to start a graduate program in mathematics

An undergraduate degree – You don’t specifically need an undergraduate degree in pure math to move on to a graduate program. People who get advanced degrees in math come from a variety of educational backgrounds, with one constant: a bachelor’s.

An above-average GPA – Mines’ program requires a GPA of 3.0 or better on a 4.0 scale.

Math research experience – If you have unique, mathematical research experience, it’ll help set you apart from other candidates . In fact, many programs outright require you to have some kind of research under your belt. The more the better, as there’s a strong chance your program will require you to publish before you can get your diploma. This is not as vital for non-thesis master’s programs.

A GRE score of 151 or higher – Graduate Record Examinations are tests you take prior to getting into grad school that determine your placement. Mines requires a 151 for its applied mathematics and statistics program , but each school is different. The absolute lowest we’ve seen is 145. Generally speaking, the higher the GRE score (especially for math programs) the better off you’ll be in grad school.

Time to devote to the program – Graduate programs require significant time commitments. That said, it is possible to get a graduate degree and work at the same time.

Letter(s) of recommendation – For many graduate programs you’ll need a solid letter of recommendation (or three) from faculty who know you well.

A statement of purpose – Almost every graduate program will require you to communicate to them why exactly you’re seeking a graduate degree in math, and why you’ve landed on their university.

Why a graduate degree in mathematics is worth the cost

People with master’s degrees in mathematics hold a variety of positions – and nearly all of them pay exceptionally well. This is also true for those who hold PhDs in mathematics. Mines’ master’s graduates report an average starting salary of $88,500. A master’s in mathematics alone puts you in the top 75% of earners.

Job prospects for math graduate students are good. Like, seriously good. Demand for graduates with advanced degrees in mathematics has shot up. By 2027, mathematics and statistics jobs are expected to increase by 33% by 2027 , according to the Bureau of Labor Statistics, and these are among the highest-paying jobs in STEM fields.

Graduate degree holders are equipped to work in any number of fields, but often find work in industries such as:

Actuarial Sciences
Health care
Cryptography

STEM graduates in general have enjoyed strong job prospects for years. STEM jobs are expected to grow 13% by 2027 , and with a graduate degree, your employability is even higher, as is your job satisfaction, making your degree even more robust. The U.S. Bureau of Labor Statistics projects employment of mathematicians and statisticians to grow 33 percent from 2019 to 2029, much faster than the average for all occupations —about 5,100 openings on average per year, the result of increased use of statistical analysis to make business, health care and policy decisions. Much of this grown will be among statisticians in research development, consulting and computer systems design.

Job Satisfaction

Those with advanced degrees in applied mathematics and statistics report some of the highest job satisfaction in the market. In fact, according to the Jobs Rated Almanac report for 2019 , jobs requiring more than a bachelor’s in mathematics have the highest satisfaction overall. Data scientist (which requires a master’s in math or higher) ranked number one, with statistician (also requires a master’s or higher) coming in second place. Mathematician ranked eighth, with actuary coming in 10th, both of which require a graduate degree.

Satisfaction is rated on a number of factors, including employability, environment, emotional factors, physical factors, salary and more. Math majors find quick work in office environments, usually with high pay and high career mobility (meaning there’s plenty of advancement opportunities).

Mines Grad Programs

$Woman doing calculus on whiteboard$

Applied Mathematics and Statistics

Go beyond the numbers and use your analytical skills to solve problems in a variety of fields

Data Science

A strong, balanced master's program that prepares students for careers or further study

Computer Science

Master's and doctoral degrees limited only by your imagination

Electrical Engineering

The top EE program in Colorado, offering master's degrees, a PhD and graduate certificates, including data science for signals and systems

Electrical engineering jobs for graduates

Making some sense of the electrical engineering job market >What do electrical engineering jobs look like, and how do you get one? And how much...

How to add a master’s or graduate certificate in data science to your science or engineering degree

The world is awash in data, and companies in every single industry—from retail and health care to manufacturing and finance and beyond—are looking...

How does data science apply to health care, manufacturing and many other fields?

To demonstrate how exciting and varied data science is, here are a few examples of the research being conducted at Colorado School of Mines: 1. A...

Graduate School

Mathematics

General information, program offerings:, director of graduate studies:, graduate program administrator:.

The Department of Mathematics graduate program has minimal requirements and maximal research and educational opportunities. It differentiates itself from other top mathematics institutions in the U.S. in that the curriculum emphasizes, from the start, independent research. Our students are extremely motivated and come from a wide variety of backgrounds. While we urge independent work and research, a real sense of camaraderie exists among our graduate students. As a result, the atmosphere created is one of excitement and stimulation and mentoring and support. There also exists a strong scholarly relationship between the department and the Institute for Advanced Study (IAS), located a short distance from campus. Students can contact IAS members as well as attend the IAS seminar series.

Students are expected to write a dissertation in four years but may be provided an additional year to complete their work if deemed necessary. Each year, our graduates are successfully launched into academic positions at premier mathematical institutions and industry.

Program Offerings

Program offering: ph.d..

The department offers a broad variety of research-related courses as well as introductory (or “bridge”) courses in several areas, which help first-year students strengthen their mathematical background. Students also acquire standard beginning graduate material primarily through independent study and consultations with the faculty and fellow students.

Language(s)

Students must satisfy the language requirement by demonstrating to a member of the mathematics faculty a reasonable ability to read ordinary mathematical texts in one of the following three languages: French, German, or Russian. Students must pass the language test by the end of the first year and before standing for the general exam.

Additional pre-generals requirements

Seminars The department offers numerous seminars on diverse topics in mathematics. Some seminars consist of systematic lectures in a specialized topic; others present reports by students or faculty on recent developments within broader areas. There are regular seminars on topics in algebra, algebraic geometry, analysis, combinatorial group theory, dynamical systems, fluid mechanics, logic, mathematical physics, number theory, topology, and other applied and computational mathematics. Without fees or formalities, students may also attend seminars in the School of Mathematics at the IAS.

The department also facilitates several informal seminars specifically geared toward graduate students: (1) Colloquium Lunch Talk, where experts who have been invited to present at the department colloquium will give introductory talks, which allows graduate students to understand the afternoon colloquium more easily; (2) Graduate Student Seminar (GSS), which is organized and presented by graduate students and helps in creating a vibrant mathematical interaction among the graduate students; and, (3) What’s Happening in Fine Hall (WHIFH) seminar, where faculty members present talks in their own research areas specifically geared towards graduate students. Reading seminars are also organized and run by graduate students.

General exam

Beyond needing a strong knowledge of three more general subjects (algebra, and real and complex analysis), first-year students are set on the fast track of research by choosing two advanced research topics as part of their general exam. The two advanced topics are expected to come from distinct major areas of mathematics, and the student’s choice is subject to the approval of the department. Usually, by the second year, students will begin investigations of their own that lead to the doctoral dissertation.

General Exam in Mathematical Physics For a mathematics student interested in mathematical physics, the general exam is adjusted to include mathematical physics as one of the two special topics.

Qualifying for the M.A.

The Master of Arts (M.A.) degree is considered an incidental degree on the way to full Ph.D. candidacy. It is earned once a student successfully passes the language requirement and the general exam, and the faculty recommends it. It may also be awarded to students who, for various reasons, may leave the Ph.D. program, provided that the following requirements are met: passing the language requirement as well as the three general subjects (algebra, and real and complex analysis) of the general exam, and receiving department approval.

During the second, third, and fourth years, graduate students are expected to either grade or teach two sections of an undergraduate course, or the equivalent, each semester. Although students are not required to teach to fulfill department Ph.D. requirements, they are strongly encouraged to do so at least once before graduating. Teaching letters of recommendation are necessary for most postdoctoral applications.

Post-Generals requirements

Selection of a Research Adviser Upon completion of the general exam, the student is expected to choose a thesis adviser.

Dissertation and FPO

Two to three years is usually necessary for the completion of a suitable dissertation. Upon completion and acceptance of the dissertation by the department and Graduate School, the candidate is admitted to the final public oral examination. The dissertation is presented and defended by the candidate.

The Ph.D. is awarded after the candidate’s doctoral dissertation has been accepted and the final public oral examination sustained.

Igor Rodnianski

Associate Chair

János Kollár

Director of Graduate Studies

Lue Pan (associate)
Chenyang Xu

Director of Undergraduate Studies

Jennifer M. Johnson (associate)
Michael Aizenman
Noga M. Alon
Manjul Bhargava
Sun-Yung A. Chang
Maria Chudnovsky
Fernando Codá Marques
Peter Constantin
Mihalis Dafermos
Charles L. Fefferman
David Gabai
June E. Huh
Alexandru D. Ionescu
Nicholas M. Katz
Sergiu Klainerman
Peter Steven Ozsváth
Peter C. Sarnak
Paul Seymour
Amit Singer
Christopher M. Skinner
Allan M. Sly
Zoltán Szabó
Paul C. Yang
Shou-Wu Zhang

Assistant Professor

Bjoern Bringmann
Matija Bucic
Marc Aurèle Tiberius Gilles
Jonathan Hanselman
Susanna Haziot
Ana Menezes
Ravi Shankar
Jacob Shapiro
Jakub Witaszek
Ruobing Zhang

Associated Faculty

John P. Burgess, Philosophy
René A. Carmona, Oper Res and Financial Eng
Bernard Chazelle, Computer Science
Hans P. Halvorson, Philosophy
William A. Massey, Oper Res and Financial Eng
Frans Pretorius, Physics
Robert E. Tarjan, Computer Science
Ramon van Handel, Oper Res and Financial Eng
Louis Esser
Sepehr Hajebi
Kimoi Kemboi
Dmitry Krachun
Anubhav Mukherjee
Sung Gi Park
Semon Rezchikov
Joshua X. Wang
Mingjia Zhang

University Lecturer

Jennifer M. Johnson

Senior Lecturer

Jonathan M. Fickenscher
Mark W. McConnell
Fraser M. Binns
Tatyana Chmutova
Tatiana K. Howard
Justin Lacini
Tristan J. Leger
Jennifer Li
Andrew O'Desky
Stan Palasek
John T. Sheridan
Sahana Vasudevan
David Villalobos
Liyang Yang
Bogdan Zavyalov

Visiting Professor

Bhargav B. Bhatt
Alex Kontorovich

Visiting Lecturer with Rank of Professor

Camillo De Lellis
Helmut H. Hofer
Aaron Naber
Akshay Venkatesh

For a full list of faculty members and fellows please visit the department or program website.

Permanent Courses

Courses listed below are graduate-level courses that have been approved by the program’s faculty as well as the Curriculum Subcommittee of the Faculty Committee on the Graduate School as permanent course offerings. Permanent courses may be offered by the department or program on an ongoing basis, depending on curricular needs, scheduling requirements, and student interest. Not listed below are undergraduate courses and one-time-only graduate courses, which may be found for a specific term through the Registrar’s website. Also not listed are graduate-level independent reading and research courses, which may be approved by the Graduate School for individual students.

COS 522 - Computational Complexity (also MAT 578)

Mat 500 - effective mathematical communication, mat 515 - topics in number theory and related analysis, mat 516 - topics in algebraic number theory, mat 517 - topics in arithmetic geometry, mat 518 - topics in automorphic forms, mat 519 - topics in number theory, mat 520 - functional analysis, mat 522 - introduction to pde (also apc 522), mat 525 - topics in harmonic analysis, mat 526 - topics in geometric analysis, mat 527 - topics in differential equations, mat 528 - topics in nonlinear analysis, mat 529 - topics in analysis, mat 531 - introduction to riemann surfaces, mat 547 - topics in algebraic geometry, mat 549 - topics in algebra, mat 550 - differential geometry, mat 555 - topics in differential geometry, mat 558 - topics in conformal and cauchy-rieman (cr) geometry, mat 559 - topics in geometry, mat 560 - algebraic topology, mat 566 - topics in differential topology, mat 567 - topics in low dimensional topology, mat 568 - topics in knot theory, mat 569 - topics in topology, mat 572 - topics in combinatorial optimization (also apc 572), mat 577 - topics in combinatorics, mat 579 - topics in discrete mathematics, mat 585 - mathematical analysis of massive data sets (also apc 520), mat 586 - computational methods in cryo-electron microscopy (also apc 511/mol 511/qcb 513), mat 587 - topics in ergodic theory, mat 589 - topics in probability, statistics and dynamics, mat 595 - topics in mathematical physics (also phy 508), mat 599 - extramural summer research project, phy 521 - introduction to mathematical physics (also mat 597).

Department of Mathematics

Mathematics phd program.

The Ph.D. program in the Department of Mathematics provides students with in-depth knowledge and rigorous training in all the subject areas of mathematics. A core feature is the first-year program, which helps bring students to the forefront of modern mathematics. Students work closely with faculty and each other and participate fully in both research and student-run seminars.

Questions? Email [email protected]

The firm deadline for applications for Autumn 2025, is December 5, 2024.
The (general and advanced) GRE tests are no longer accepted. Please do not submit these scores.

-->

» » Graduate PhD Program

The Department of Mathematics offers a program leading to the degree of Doctor of Philosophy.

The PhD program is an intensive course of study designed for the full-time student planning a career in research and teaching at the university level or in quantitative research and development in industry or government. Admission is limited and highly selective. Successful applicants have typically pursued an undergraduate major in mathematics.

In the first year of PhD studies, students must pass written examinations in the areas of the basic . In the second year an oral examination on two selected topics must be passed. Subsequent years are devoted to seminars, research, and the preparation of a dissertation. Students are required to serve as a teaching assistant or instructor for four years beginning with the second year of study. All students must serve as a primary instructor for at least one semester; all others semesters students will serve as a teaching assistant. En route to the Ph.D., students will earn three degrees: a Master of Arts (after year one), a Master of Philosophy (after year four), and the Doctorate of Philosophy (after a successful thesis defense).

There are also allied doctoral programs in , , and .

The Mathematics Department is housed in a comfortable building containing an excellent , computing and printing facilities, faculty and graduate student offices, a lounge for tea and conversation, and numerous seminar and lecture rooms.

The department has a broad fellowship program designed to help qualified students achieve the PhD degree in the shortest practicable time. Each student admitted to the PhD program is appointed a fellow in the Department of Mathematics for a period of five years, contingent on good progress. A fellow receives a stipend for the nine-month academic year and is exempt from payment of tuition.

A fellow in the Department of Mathematics may hold a fellowship from a source outside Columbia University. When not prohibited by the terms of the outside fellowship, the University supplements the outside stipend to bring it up to the level of the University fellowship. Candidates for admission are urged to apply for fellowships for which they are eligible (e.g., National Science Foundation, Ford and Hertz Foundations).

All students admitted to the PhD program become fellows in the Department and are exempt from tuition. Students may be responsible for certain : a student activity fee and transcript fee.

Students in the PhD program are entitled to affordable University housing near the Department in Morningside Heights. This makes it possible to live comfortably in the University neighborhood on the fellowship stipend.

The PhD program in mathematics has an enrollment of approximately 60 students. Typically, 10-12 students enter each year. While students come from all over the world, they form an intellectually cohesive and socially supportive group.

New York City is America’s major center of culture. Columbia University’s remarkably pleasant and sheltered , near the Hudson River and Riverside Park, is situated within 20-30 minutes of Lincoln Center, Broadway theaters, Greenwich Village, and major museums. Most department members live within a short walk of the University.

Since receiving its charter from King George II in 1754, Columbia University has played an eminent role in American education. In addition to its various faculties and professional schools (such as Engineering, Law, and Medicine), the University has close ties with nearby museums, schools of music and theology, the United Nations, and the city government.

The application deadline is typically early December for admission the following September. Precise details on requirements and deadlines can be found . Applicants must submit all required documents by the posted deadline. Students whose undergraduate degree was not from an English-speaking country must also submit scores from the TOEFL or IELTS. Applications must be filed .

Graduate School of Arts and Sciences
Columbia University
Office of Student Affairs
107 Low Library, MC 4304
New York, NY 10027
212-854-6729

Michael Harris
Director of Graduate Studies
Department of Mathematics
Columbia University
2990 Broadway
509 Mathematics, MC 4406
New York, NY 10027

Ph.D. Program

Degree requirements.

In outline, to earn the PhD in either Mathematics or Applied Mathematics, the candidate must meet the following requirements.

Take at least 4 courses, 2 or more of which are graduate courses offered by the Department of Mathematics
Pass the six-hour written Preliminary Examination covering calculus, real analysis, complex analysis, linear algebra, and abstract algebra; students must pass the prelim before the start of their second year in the program (within three semesters of starting the program)
Pass a three-hour, oral Qualifying Examination emphasizing, but not exclusively restricted to, the area of specialization. The Qualifying Examination must be attempted within two years of entering the program
Complete a seminar, giving a talk of at least one-hour duration
Write a dissertation embodying the results of original research and acceptable to a properly constituted dissertation committee
Meet the University residence requirement of two years or four semesters

Detailed Regulations

The detailed regulations of the Ph.D. program are the following:

Course Requirements

During the first year of the Ph.D. program, the student must enroll in at least 4 courses. At least 2 of these must be graduate courses offered by the Department of Mathematics. Exceptions can be granted by the Vice-Chair for Graduate Studies.

Preliminary Examination

The Preliminary Examination consists of 6 hours (total) of written work given over a two-day period (3 hours/day). Exam questions are given in calculus, real analysis, complex analysis, linear algebra, and abstract algebra. The Preliminary Examination is offered twice a year during the first week of the fall and spring semesters.

Qualifying Examination

To arrange the Qualifying Examination, a student must first settle on an area of concentration, and a prospective Dissertation Advisor (Dissertation Chair), someone who agrees to supervise the dissertation if the examination is passed. With the aid of the prospective advisor, the student forms an examination committee of 4 members. All committee members can be faculty in the Mathematics Department and the chair must be in the Mathematics Department. The QE chair and Dissertation Chair cannot be the same person; therefore, t he Math member least likely to serve as the dissertation advisor should be selected as chair of the qualifying exam committee . The syllabus of the examination is to be worked out jointly by the committee and the student, but before final approval, it is to be circulated to all faculty members of the appropriate research sections. The Qualifying Examination must cover material falling in at least 3 subject areas and these must be listed on the application to take the examination. Moreover, the material covered must fall within more than one section of the department. Sample syllabi can be reviewed online or in 910 Evans Hall. The student must attempt the Qualifying Examination within twenty-five months of entering the PhD program. If a student does not pass on the first attempt, then, on the recommendation of the student's examining committee, and subject to the approval of the Graduate Division, the student may repeat the examination once. The examining committee must be the same, and the re-examination must be held within thirty months of the student's entrance into the PhD program. For a student to pass the Qualifying Examination, at least one identified member of the subject area group must be willing to accept the candidate as a dissertation student.

Publications Home — Over 100 years of publishing excellence

Book Author Resources
Submit a Book Proposal
AMS Rights, Licensing, Permissions
Open Math Notes
Frequently Asked Questions
Member Journals
Research Journals
Translation Journals
Distributed Journals
Open Access Journals
Guidelines and Policies
Journal Author Resources

Librarian Resources

eBook Collections
COUNTER Usage Statistics
My Subscriptions
Subscription Information
Licensing Information

Mathematical Reviews/MathSciNet®

MathSciNet ®
Reviewer Home
MathSciNet ® Subscriptions

Membership Home — Welcome to your membership center

Membership choices.

Join the Society
Renew your Membership
Gift a Membership

Individual Membership

Member Benefits
Member Directory
Reciprocating Societies
Members in Developing Countries

Institutional Membership

Domestic Institutions
International Institutions
Two-Year Institutions
Graduate Student Chapter Program

Other Member Types

Corporate Memberships
Associate Memberships

Meetings & Conferences Home — Engage with colleagues and the latest research

National meetings.

Joint Mathematics Meetings
Upcoming JMMs
Previous JMMs
Special Lectures
Professional Enhancement Programs (PEPs)

Sectional Meetings

Upcoming Sectionals
Previous Sectionals
Presenting Papers
Hosting Sectionals

Other Meetings, Conferences & Workshops

Mathematics Research Communities
Education Mini-conference
International Meetings
Mathematics Calendar
Short Courses
Workshop for Department Chairs and Leaders

Meetings Resources

Suggest a Speaker
AMS Meetings Grants
Submitting Abstracts
Welcoming Environment Policy
MathSafe – supporting safe meetings

News & Outreach Home — Explore news, images, posters, and mathematical essays

News from the ams.

AMS News Releases
Feature Stories
Information for Journalists
In Memory Of

Math Voices

Feature Column
Math in the Media
Column on Teaching and Learning

Explorations

Recognizing Diverse Mathematicians
AMS Posters
Mathematics & Music
Mathematical Imagery
Mathematical Moments

Professional Programs Home — Resources and opportunities to further your mathematical pursuits

Professional development.

Employment Services
Mathjobs.org
BEGIN Career Initiative
Mathprograms.org
Mathematical Opportunities Database
Research Seminars

Institutional Information and Data

Annual Survey of the Mathematical and Statistical Sciences
CBMS Survey
Other Sources of Data
Directory of Institutions in the Mathematical Sciences
Professional Directory

Grants & Support

AMS-Simons Grants for PUI Faculty
Travel Grants
Fellowships & Scholarships
Epsilon Fund
Child Care Grants

Awards & Recognition

AMS Prizes & Awards
Fellows of the AMS

Education Home — Resources to support advanced mathematics teaching and learning

For students.

Information for Undergraduate and High School Students
Research Experiences for Undergraduates (REUs)
Considering Grad School
Find Grad Programs
Applying to Grad School
What do Mathematicians Do?

For Teachers

Teaching Online
Teaching Resources
Inclusive Classrooms
Assessing Student Learning
Education Webinars

For Department Leaders & Mentors

Information for Department Leaders
paraDIGMS (Diversity in Graduate Mathematical Sciences)

Government Relations Home — Advocating for the mathematical sciences

Elevating mathematics in congress.

Our Mission
Letters, Statements, & Legislation
Congressional Briefings

Legislative Priorities

Federal Issues of Concern
Federal Budget Process

Get Involved

Advocacy Resources
Take Action

DC-Based Fellowships

Congressional Fellowship
Mass Media Fellowship
Catalyzing Advocacy in Science & Engineering (CASE) Fellowship

Giving to the AMS — Your gifts make great things happen for mathematics Make a Gift

What you can support.

The 2020 Fund
Next Generation Fund
Birman Fellowship for Women Scholars
JMM Child Care Grants
MathSciNet for Developing Countries

Create a Legacy

Make a Tribute Gift
Create a Permanent Fund
Establish a Prize, Award or Fellowship
Bequests and Charitable Estate Planning

Honoring Your Gift

Donor Stories
Donor Wall of Honor
Thomas S. Fiske Society
AMS Contributors Society
AMS Gardens

Giving Resources

AMS Development Committee
AMS Gift Acceptance Policy

About the AMS — Advancing research. Connecting the mathematics community.

Our organization.

Executive Staff
Equity, Diversity, & Inclusion
Jobs at AMS
Customer Service

Our Governance

Board of Trustees
Executive Committee

Governance Operations

Calendar of Meetings
Policy Statements & Guidelines

On March 21 st , the AMS website will be down for regularly scheduled maintenance from 5:00am–8:00am

Find Graduate Programs in the Mathematical Sciences offers comparative information on graduate programs in the mathematical sciences for prospective graduate students and their advisers. This web service provides only an overview of the programs offered; departments should be contacted directly for more detailed information. Currently 276 graduate programs are listed.

All listings (alpha order) All listings by state

Institution name

Program type, masters programs (check all that apply), phd specialties (check all that apply), financial support available, gre required, online options available, skills training resources (check all that apply), number of phds awarded in the last year, enrollments, canadian province, list or edit your graduate program in the mathematical sciences.

Add new listing
Edit existing listing

Find Graduate Programs Find the right graduate program in the mathematical sciences

Find Graduate Programs (FGP) in the Mathematical Sciences offers comparative information on over 500 graduate programs in the mathematical sciences in the US and Canada. This web service provides only an overview of the programs offered; departments should be contacted directly for more detailed information. Currently 741 graduate programs are listed.

Bridge / Postbaccalaureate Programs

Masters Programs

Doctoral Programs

Certificate Programs

In the wake of the pandemic, many mathematical sciences departments have made at least short-term changes in their requirements regarding the GRE for individuals applying for admission to graduate programs. The Google doc USA/Canada Math PhD Programs: GRE requirements and Qualifying Exams , curated by Brown University graduate student Emily Winn, provides a list of those current requirements.

$The Department of Mathematics | Home$

Graduate Degree Requirements

Graduate Handbook

The following information is a snapshot of all Master of Arts, Master of Science, and Ph.D. in Mathematics requirements from the University of Arizona Catalog. For full details on these requirements, please see the Mathematics Graduate Program handbook.

Master of Arts vs Master of Science in Mathematics

The Master of Science in Mathematics program requires a plan of study, professional development requirement, a thesis and examinations, and 30 units of approved graduate credit with differing parameters.

See the Mathematics Graduate Handbook for more specific details.

Admission Requirements

$Master of Arts in Mathematics$

Master of Arts (M.A.)

While both degrees require a Master's thesis, the Master of Arts degree requires more courses outside mathematics and has a teaching option intended for secondary school teachers. This degree often serves as a stepping stone towards the PhD but not as strongly as the Master of Science.

$Test$

Master of Science (M.S.)

While this degree also requires a thesis, the Master of Science degree requires a greater number of more advanced mathematics courses (technically those which are not co-convened). This degree often serves as a stepping stone towards the PhD but not as strongly as the Master of Science. The M.A. but especially the Master of Science often serve as a stepping stone towards the PhD.

Doctor of Philosophy (PhD) in Mathematics

The Doctor of Philosophy degree usually requires about five years to complete. Ph.D. requirements are far more in depth than those of the Masters programs. You can find more detailed information in the Graduate Handbook. Aside from generalized course requirements, all Ph.D. students are required to select a supporting minor, find a graduate faculty advisor, complete professional development requirements, complete a dissertation, and successfully defend the dissertation. Course requirements include 36 units of graduate credit in the major with an additional 18 units of dissertation ( MATH920 ).

Catalog Requirements

$PhD in Mathematics$

Doctor of Philosophy (PhD)

This is the degree for you if you plan to pursue a career in academic research, university teaching, or high-level research in industry or a government laboratory. The most important requirement is a dissertation which represents a substantial new contribution, of publishable quality, to the mathematical sciences. In fact, the point of the PhD degree is to prepare you to make and publish exactly this sort of contribution.

$wildcat-statue$

Our Support Center is a hub of quick information for everyone. Whether you're a current student, future student, Mathematics Department member, donor, or a curious member of U of A, you can find the information you're looking for below!

Support Center

Department of Mathematics

$students at chalkboard$

Prospective Graduate Student FAQ
Graduate Board Oral Exam
Graduate Courses
Qualifying Exams
Recent PhD Theses
Graduate Awards

The goal of our PhD program is to train graduate students to become research mathematicians. Each year, an average of five students complete their theses and go on to exciting careers in mathematics both inside and outside of academia.

Faculty research interests in the Johns Hopkins University Department of Mathematics are concentrated in several areas of pure mathematics, including analysis and geometric analysis, algebraic geometry and number theory, differential geometry, algebraic topology, category theory, and mathematical physics. The department also has an active group in data science, in collaboration with the Applied Math Department .

The Department values diversity among its members, is committed to building a diverse intellectual community, and strongly encourages applications from all interested parties.

A brief overview of our graduate program is below. For more detailed information, please use the drop down menu above.

Program Overview

All students admitted to the PhD program receive support that includes a stipend, full tuition, and additional benefits. Students making satisfactory progress are guaranteed this support for five years. A sixth year of support is generally possible for students who are on track to complete their Ph.D. and would benefit from the additional year. Ph.D. students at JHU are unionized , and their stipends and benefits are specified in the union’s collective bargaining agreement; here is a summary .

PhD candidates take two or three courses per semester over the first several years of the program. These are a mix of required and intermediate-level graduate courses, independent studies, and special topics classes offered by our faculty.

By the beginning of their second year, students are asked to demonstrate competency in algebra and in analysis by passing written qualifying exams in these two broad areas. Students are then expected to choose an advisor, who will supervise their dissertation and also administer an oral qualifying exam to be taken in the second or third year. More specifics about all these requirements are described on the requirements page .

All graduate students are invited to attend weekly research seminars in a variety of topic areas as well as regular department teas and a weekly wine and cheese gathering attended by many junior and senior members of the department. A graduate student lunch seminar series provides an opportunity for our students to practice their presentation skills to a general audience.

Teaching experience is regarded as an important part of the graduate program, and graduate students are required to teach during their program, most frequently as a teaching assistant for undergraduate courses. First-year students are exempted from TAing, in preparation for the qualifying exams, and each student at the dissertation-writing stage is offered an additional semester free of teaching.

Each student receives a travel allowance to enable them to attend conferences for which limited funding is available, or to visit researchers at other institutions.

Welcome to the Math PhD program at Harvard University and the Harvard Kenneth C. Griffin Graduate School of Arts and Sciences.

Learn more about Harvard’s Math community and our statement on diversity and inclusion.

The Harvard Griffin GSAS Office of Equity, Diversity, Inclusion & Belonging offers diversity resources and student affinity groups for graduate students.

The Harvard University Office for Gender Equity has dedicated GSAS Title IX resource coordinators who work with and support graduate students.

open. The application deadline is December 15, 2021. -->

The pure math PhD admissions application is open. The application submission deadline is December 15, 2024.

For information on admissions and financial support , please visit the Harvard Kenneth C. Griffin Graduate School of Arts and Sciences.

Harvard Griffin GSAS is committed to ensuring that our application fee does not create a financial obstacle. Applicants can determine eligibility for a fee waiver by completing a series of questions in the Application Fee section of the application. Once these questions have been answered, the application system will provide an immediate response regarding fee waiver eligibility.

Note for Harvard College Undergraduates

Since it is better for a student’s mathematical development to learn mathematics at different institutions so as to be exposed to a broader range of mathematical perspectives, ordinarily applications for the mathematics PhD program from Harvard College undergraduates are not considered. If exceptional circumstances warrant an application from a Harvard undergraduate, an advisor or mentor of that student should seek approval from the Director of Graduate Studies before the student submits an application.

Mathematical Sciences

Mellon college of science, ph.d. programs, doctor of philosophy in mathematical sciences.

Students seeking a Ph.D. in Mathematical Sciences are expected to show a broad grasp of mathematics and demonstrate a genuine ability to do mathematical research. The Doctor of Philosophy in Mathematical Sciences is a traditional research degree, and its requirements are representative of all doctoral programs.

After being admitted to graduate status by the Department, a student seeking a Ph.D. must be admitted to candidacy for this degree by fulfilling the appropriate program requirements.

The most important requirement for the Ph.D. degree is timely completion and public defense of an original Ph.D. thesis. The Ph.D. thesis is expected to display depth and originality and be publishable by a refereed journal.

Doctor of Arts in Mathematical Sciences

The Doctor of Arts degree shares all requirements and standards with the Ph.D., except with regard to the thesis. The D.A. thesis is not expected to display the sort of original research required for a Ph.D. thesis, but rather to demonstrate an ability to organize, understand, and present mathematical ideas in a scholarly way, usually with sufficient innovation and worth to produce a publishable work. Whenever practical, the department provides D.A. candidates with the opportunity to use materials developed to teach a course. While a typical Ph.D. recipient will seek a position that has a substantial research component, the D.A. recipient will usually seek a position where research is not central.

Doctor of Philosophy in Algorithms, Combinatorics, and Optimization (ACO)

This program is administered jointly by the Department of Mathematical Sciences, the Department of Computer Science, and the Tepper School of Business. It focuses on discrete mathematics and algorithmic issues arising in computer science and operations research, particularly the mathematical analysis of these issues. The participating units evaluate applicants separately. The requirements for this degree and information on participating faculty are available at the ACO page .

Doctor of Philosophy in Pure and Applied Logic (PAL)

This is an interdisciplinary program with faculty from the Department of Mathematical Sciences, the Department of Philosophy, and the School of Computer Science. The participating units evaluate applicants separately and set their own program requirements. Students who have been admitted to the PAL program, and who complete the requirements for the Ph.D. in Mathematical Sciences with a thesis in the area of logic, can choose to receive either a Ph.D. in Pure and Applied Logic or a Ph.D. in Mathematical Sciences. The choice of which degree to receive is usually based on the intended career path.

Requirements
Financial Aid & Employment Policies
MCS Graduate Education
CMU Graduate Education
2024-2025 Mathematical Sciences Graduate Handbook
Archived Mathematical Sciences Graduate Handbooks
CMU Graduate Student Handbook

$Rales Fellows logo$

The CMU Rales Fellow Program is dedicated to developing a diverse community of STEM leaders from underrepresented and underresourced backgrounds by eliminating cost as a barrier to education. Learn more about this program for master's and Ph.D. students. Learn more

Apply Now [GRAD]
Apply Now [UNDERGRAD]
TA and Grader Positions
Computing Support
Computational Finance

$NYU Courant Department of Mathematics$

Admission Policies
Financial Support
Ph.D. in Atmosphere Ocean Science
M.S. at Graduate School of Arts & Science
M.S. at Tandon School of Engineering
Current Students

Ph.D. Program in Mathematics

Degree requirements.

A candidate for the Ph.D. degree in mathematics must fulfill a number of different departmental requirements.

NYU Shanghai Ph.D. Track

The Ph.D. program also offers students the opportunity to pursue their study and research with Mathematics faculty based at NYU Shanghai. With this opportunity, students generally complete their coursework in New York City before moving full-time to Shanghai for their dissertation research. For more information, please visit the NYU Shanghai Ph.D. page .

Sample course schedules (Years 1 and 2) for students with a primary interest in:

Year I - Fall Term	Year I - Spring Term
Linear Algebra	Topology II
Differential Geometry I	Differential Geometry II
Real Variables	Ordinary Differential Equations
Complex Variables	Functional Analysis I

Year II - Fall Term	Year II - Spring Term
Advanced Topics in Geometry: Isometric Immersions Before and After Nash	Advanced Topics in Geometry: Randomness and Complexity
Advanced Topics in Geometry: High Dimensional Expanders and Ramanujan Complexes	Advanced Topics in Geometry: Topics in Geometric Nonlinear Functional Analysis
Harmonic Analysis	Advanced Topics in Geometry: Analysis and Geometry of Scalar Curvature
Advanced Topics in PDE: Resonances in PDEs	Advanced Topics in PDE: Analytic Aspects of Harmonic Maps

Applied Math (Math Biology, Scientific Computing, Physical Applied Math, etc.)

Year I - Fall Term	Year I - Spring Term
Linear Algebra	Applied Stochastic Processes
PDE I	Asymptotic Analysis
Fluid Mechanics	Continuum mechanics
Numerical Methods I	Numerical Methods II

Year II - Fall Term	Year II - Spring Term
Neurophysiology and Neuronal Networks	Data Analysis
Complex fluids	Mathematical Physiology
Real Variables	Geophysical Fluid Dynamics
Computational Fluid Dynamics	Nonlinear Optimization

Additional information for students interested in studying applied math is available here .

Probability

Year I - Fall Term	Year I - Spring Term
Stochastic Calculus	Probability: Limit Theorems II
Probability: Limit Theorems I	Applied Stochastic Analysis
Real Variables	Advanced Topics in Probability: Random Graphs
Complex Variables	Advanced Topics in Math Biology:Stochastic Problems in Cellular Molecular and Neural Biology

Year II - Fall Term	Year II - Spring Term
Advanced Topics in Probability: Ergodic Theory of Markov Processes	Advanced Topics in Geometry: Randomness and Complexity
Advanced Topics in Probability: Motion in Random Media	Advanced Topics in Probability: Random Matrices
Advanced Topics in Applied Math: Quantifying Uncertainty in Complex Turbulent Systems	Advanced Topics in Probability: Markov Chain Analysis
Derivative Securities	Advanced Topics in Numerical Analysis: Monte Carlo Methods

PDE/Analysis

Year I - Fall Term	Year I - Spring Term
Linear Algebra	Topology II
PDE I	Ordinary Differential Equations
Real Variables	PDE II
Complex Variables	Functional Analysis I

Year II - Fall Term	Year II - Spring Term
Differential Geometry I	Algebra II
Harmonic Analysis	Advanced Topics in PDE: Extreme Problems for Elliptic Eigenvalues
Advanced Topics in Analysis: Calculus of Variations	Advanced Topics in Analysis: Dynamics of the Nonlinear Schroedinger Equation
Probability: Limit Theorems I	Probability: Limit Theorems II

The Written Comprehensive Examination

The examination tests the basic knowledge required for any serious mathematical study. It consists of the three following sections: Advanced Calculus, Complex Variables, and Linear Algebra. The examination is given on three consecutive days, twice a year, in early September and early January. Each section is allotted three hours and is written at the level of a good undergraduate course. Samples of previous examinations are available in the departmental office. Cooperative preparation is encouraged, as it is for all examinations. In the fall term, the Department offers a workshop, taught by an advanced Teaching Assistant, to help students prepare for the written examinations.

Entering students with a solid preparation are encouraged to consider taking the examination in their first year of full-time study. All students must take the examinations in order to be allowed to register for coursework beyond 36 points of credit; it is recommended that students attempt to take the examinations well before this deadline. Graduate Assistants are required to take the examinations during their first year of study.

For further details, consult the page on the written comprehensive exams .

The Oral Preliminary Examination

This examination is usually (but not invariably) taken after two years of full-time study. The purpose of the examination is to determine if the candidate has acquired sufficient mathematical knowledge and maturity to commence a dissertation. The phrase "mathematical knowledge" is intended to convey rather broad acquaintance with the basic facts of mathematical life, with emphasis on a good understanding of the simplest interesting examples. In particular, highly technical or abstract material is inappropriate, as is the rote reproduction of information. What the examiners look for is something a little different and less easy to quantify. It is conveyed in part by the word "maturity." This means some idea of how mathematics hangs together; the ability to think a little on one's feet; some appreciation of what is natural and important, and what is artificial. The point is that the ability to do successful research depends on more than formal learning, and it is part of the examiners' task to assess these less tangible aspects of the candidate's preparation.

The orals are comprised of a general section and a special section, each lasting one hour, and are conducted by two different panels of three faculty members. The examination takes place three times a year: fall, mid-winter and late spring. Cooperative preparation of often helpful and is encouraged. The general section consists of five topics, one of which may be chosen freely. The other four topics are determined by field of interest, but often turn out to be standard: complex variables, real variables, ordinary differential equations, and partial differential equations. Here, the level of knowledge that is expected is equivalent to that of a one or two term course of the kind Courant normally presents. A brochure containing the most common questions on the general oral examination, edited by Courant students, is available at the Department Office.

The special section is usually devoted to a single topic at a more advanced level and extent of knowledge. The precise content is negotiated with the candidate's faculty advisor. Normally, the chosen topic will have a direct bearing on the candidate's Ph.D. dissertation.

All students must take the oral examinations in order to be allowed to register for coursework beyond 60 points of credit. It is recommended that students attempt the examinations well before this deadline.

The Dissertation Defense

The oral defense is the final examination on the student's dissertation. The defense is conducted by a panel of five faculty members (including the student's advisor) and generally lasts one to two hours. The candidate presents his/her work to a mixed audience, some expert in the student's topic, some not. Often, this presentation is followed by a question-and-answer period and mutual discussion of related material and directions for future work.

Summer Internships and Employment

The Department encourages Ph.D. students at any stage of their studies, including the very early stage, to seek summer employment opportunities at various government and industry facilities. In the past few years, Courant students have taken summer internships at the National Institute of Health, Los Alamos National Laboratory, Woods Hole Oceanographic Institution, Lawrence Livermore National Laboratory and NASA, as well as Wall Street firms. Such opportunities can greatly expand students' understanding of the mathematical sciences, offer them possible areas of interest for thesis research, and enhance their career options. The Director of Graduate Studies and members of the faculty (and in particular the students' academic advisors) can assist students in finding appropriate summer employment.

Mentoring and Grievance Policy

For detailed information, consult the page on the Mentoring and Grievance Policy .

Visiting Doctoral Students

Information about spending a term at the Courant Institute's Department of Mathematics as a visiting doctoral student is available on the Visitor Programs page.

Graduate Program

Our graduate program is unique from the other top mathematics institutions in the U.S. in that it emphasizes, from the start, independent research. Each year, we have extremely motivated and talented students among our new Ph.D. candidates who, we are proud to say, will become the next generation of leading researchers in their fields. While we urge independent work and research, there exists a real sense of camaraderie among our graduate students. As a result, the atmosphere created is one of excitement and stimulation as well as of mentoring and support. Furthermore, there exists a strong scholarly relationship between the Math Department and the Institute for Advanced Study, located just a short distance from campus, where students can make contact with members there as well as attend the IAS seminar series. Our program has minimal requirements and maximal research and educational opportunities. We offer a broad variety of advanced research topics courses as well as more introductory level courses in algebra, analysis, and geometry, which help first-year students strengthen their mathematical background and get involved with faculty through basic course work. In addition to the courses, there are several informal seminars specifically geared toward graduate students: (1) Colloquium Lunch Talk, where experts who have been invited to present at the Department Colloquium give introductory talks, which allows graduate students to understand the afternoon colloquium more easily; (2) Graduate Student Seminar (GSS), which is organized and presented by graduate students for graduate students, creating a vibrant mathematical interaction among them; and, (3) What’s Happening in Fine Hall (WHIFH) seminar where faculty give talks in their own research areas specifically geared towards graduate students. Working or reading seminars in various research fields are also organized by graduate students each semester. First-year students are set on the fast track of research by choosing two advanced topics of research, beyond having a strong knowledge of three more general subjects: algebra, and real and complex analysis, as part of the required General Examination. It is the hope that one, or both, of the advanced topics will lead to the further discovery of a thesis problem. Students are expected to write a thesis in four years but will be provided an additional year to complete their work if deemed necessary. Most of our Ph.D.'s are successfully launched into academic positions at premier mathematical institutions as well as in industry .

Chenyang Xu

Jill leclair.

Menu Close
Search

Applied and Computational Mathematics Master's Program Online

An online master's degree in applied and computational mathematics from Johns Hopkins University complements your knowledge with principles that can be applied to almost every discipline of science, engineering, industry, and technology—from defense technology and business to public policy and biomedicine.

Request Info
View Info Session

LIVE Lab at the Applied Physics Laboratory

Applied and Computational Math Program Overview

Johns Hopkins Engineering for Professionals online applied and computational mathematics master’s is one of the premier graduate degree options in our top-ranked online engineering master’s program and a leading computational mathematics master’s program in the industry. The advanced-level curriculum teaches students the key steps to incorporate design and mathematical algorithms into modern technologies.

Choose from highly relevant courses like Statistical Methods and Data Analysis, Real Analysis, and Matrix Theory to support your subject-matter interests. Whether you work to develop prototypes in manufacturing or create models to predict long-term climate change, the coursework emphasizes applied and theoretical aspects of the field, so you can:

Gain high demand skills to advance in industries that rely on mathematical modeling and computational science
Solve probability problems, including finding properties of distribution functions
Apply statistical software confidently
Interpret and solve simple regression models
Understand the distinction between axioms, definitions, and theorems
Learn on your terms and select a flexible course schedule in a format that works best for you

Master’s Degree Focus Areas

A focus area can be selected but is not required for the computational mathematics master’s .

Applied Analysis : Bring together mathematical topics such as differential equations, dynamical systems, approximation theory, number theory, topology, and Fourier analysis.
Information Technology and Computation : Apply a range of tools—such as neural networks, cryptography, and data mining—to solve business and organizational problems.
Operations Research : Employ techniques such as optimization and game theory across the employment spectrum in industries such as education, transportation, and public services.
Probability and Statistics : Measure randomness and how to collect, analyze, and interpret numerical data in such a way as to obtain useful information.
Simulation and Modeling : Learn to approximate a process or system over time with commonly used analytical tools like Monte Carlo Methods, Markov Chains, and queuing theory.

FOCUS AREA REQUIREMENTS

We offer three Applied and Computational Mathematics degree options; you can earn a Master of Science in Applied and Computational Mathematics, a Post-Master’s Certificate, or a Graduate Certificate.

Applied and Computational Mathematics Courses

Get details about course requirements, prerequisites, focus areas, and electives offered within the program. All courses are taught by subject-matter experts who are executing the technologies and techniques they teach. Selected undergraduate-level courses are also offered to provide mathematical background for the program. These 100- and 200-level courses are not for graduate credit. Some students may find one or more of these courses useful as a refresher or to fill gaps in their prior education.

Student Thesis and Research Papers/Projects

Learn about the requirements for completing research or a thesis in Applied and Computational Mathematics.

Self-assessment Math Placement Exams

Assessment examinations are available for Precalculus, Calculus 1, Calculus 2, and Calculus 3/Multivariable Calculus. Each assessment exam is an advisory tool to help you and your academic advisor gauge your preparedness for mathematics at a proper level here at EP. The exam is not a means to “pass out” of a particular course, and a waiver will not be granted solely based on an exam score.

Program Contacts

James spall.

Amanda Harwell

Andrew marshall, tuition and fees.

Did you know that 78 percent of our enrolled students’ tuition is covered by employer contribution programs? Find out more about the cost of tuition for prerequisite and program courses and the Dean’s Fellowship.

Why Hopkins?

Build on your applied and computational mathematics degree by engaging with all the rest Johns Hopkins has to offer.

two employees at the Applied Physics Laboratory

Expert Faculty - Study with faculty who are practicing scientists and notable professionals with corporations and government entities, including the Johns Hopkins Applied Physics Lab, NASA, Raytheon, and the U.S. Department of Defense. Exceptional one-on-one mentoring sets you on a course to be a confident, knowledgeable leader. Learn More

Beyond Rankings: We Help You Fulfill Your Vision - We are proud to be ranked among the top online graduate engineering schools by U.S. News & World Report . But we’re about more than just numbers and rankings—we’re focused on making sure you flourish as a learner and engineer. Learn More

Network and Connect - Your knowledge is stronger with a network. In the applied and computational mathematics program, you will make career-advancing connections with accomplished scientists and engineers who represent a variety of disciplines across many industries. Learn More

“ I enjoyed the flexibility of attending part-time, the personableness of the instructors in the program, and the content of the courses. ”

Applied and Computational Mathematics FAQs

I don't have an engineering background, can i still apply to this program.

Yes. If we are otherwise willing to accept the student, we will determine which prerequisites are still needed as part of the review process. You will then be admitted provisionally until those courses have been successfully completed.

What is the difference between computational mathematics vs computer science?

Generally speaking, computation mathematics refers to the mathematics that fuels a computer’s ability to solve complex equations, while computer science refers to the science that goes into building and innovating the computer itself. A computer science master’s program will focus more on the building and operations of computers while a computational mathematics master’s program leans more into the mathematics that computers use.

What can I do with an applied and computational mathematics degree?

Applied and computational mathematics jobs can range from genetic and healthcare research to software engineering and machine learning and over into statistics or actuarial science. You can also pursue careers in industries like medical research, international banking, and software development—just to name a few.

Academic Calendar

Find out when registration opens, classes start, transcript deadlines and more. Applications are accepted year-round, so you can apply any time.

Related News

A New Groundbreaking Method to Match Celestial Objects Across Telescopes

Applied and Computational Mathematics
Faculty News

Amitabh Basu's approach promises to improve the accuracy of celestial object matching.

Mike Synder smiles for a photo, wearing an Orioles pullover, standing beyond left field in Camden Yards. The field is behind him.

Numbers Game: Alums Help Orioles Rise to the Top

Alumni News

EP graduate Mike Snyder applied his math and analytics background as Director of Pro Scouting for the playoff Orioles.

A man works in a room with various screens projected on walls, including see-through panels.

5 Careers in Applied Mathematics

Interested in pursuing an advanced career in applied mathematics? Learn which industries and occupations are available to you with JHU EP.

Primary (Specialist Mathematics full-time) PGCE

London, Bloomsbury

This is the programme information for 2024 entry

If you require details of this year's programme, Primary (Specialist Mathematics full-time) PGCE (2025), click here

On this specialist Primary PGCE programme, students learn to teach all the primary curriculum subjects but there is an added emphasis on learning to teach mathematics by considering both mathematics as a subject in its own right, but also its links to other subject areas.

UCL works in partnership with around 200 primary schools, enabling students to fully prepare to be a primary teacher. We welcome a wide range of students each year to our Primary PGCE programmes and traditionally under-represented groups are particularly encouraged to apply. Our cohorts are typically very diverse, reflecting school communities across London.

UK tuition fees (2024/25)

Overseas tuition fees (2024/25), programme starts, applications accepted.

Applications closed

Start teaching

IOE, UCL's Faculty of Education and Society, has been ranked 1st for Education in the QS World University Rankings by Subject since 2014.

Entry requirements

First degree

A minimum of a lower second-class UK Bachelor's degree or an overseas qualification of an equivalent standard.

No specific subjects required.

English Language, Science (one from Combined Science, Biology, Chemistry or Physics) at grade 4 or above and Mathematics at grade 5. We do not accept "applied" or "additional" GCSE subjects. Applicants who do not offer a GCSE in English Language or Science may demonstrate an equivalent standard by completing a test via Equivalency Testing or A Star Equivalency and achieving at least a grade 4, we require grade 5 in Mathematics. For Mathematics, equivalency tests in Mathematics Foundation or Mathematics Higher with grade 5 are accepted. For Science, equivalency tests in either Combined Science or Biology with grade 4 are accepted. BTEC, Functional Skills or Access course qualifications are not accepted in place of GCSEs.

School experience

We recommend that you aim to gain some experience in a classroom prior to interview.

Skills tests

Trainees will be assured against a set of fundamental Mathematics and English skills by the end of their teacher training.

Relevant experience and background

Applicants whose degree qualifications are below a lower second-class standard may be admitted if they can demonstrate an appropriate academic background at Master's level and above and/or significant postgraduate experience in the relevant field.

Country-specific information, including details of when UCL representatives are visiting your part of the world, can be obtained from the International Students website .

International applicants can find out the equivalent qualification for their country by selecting from the list below. Please note that the equivalency will correspond to the broad UK degree classification stated on this page (e.g. upper second-class). Where a specific overall percentage is required in the UK qualification, the international equivalency will be higher than that stated below. Please contact Graduate Admissions should you require further advice.

The English language level for this programme is: Level 2

Further information can be found on our English language requirements page.

This programme is suitable for international students on a Student visa - study must be full-time, starting September.

DBS and occupational health

If you are made an offer you will be required to successfully complete Occupational Health and Disclosure Barring Service (DBS) Enhanced Disclosure checks. The Occupational Health Check is £90, and depending on your DBS requirements, there may be an additional fee of £15.00 if you can submit your DBS Enhanced Disclosure check via a UK Post Office. These checks are required to ensure you meet the Department for Education’s requirements for physical and mental health to teach, as well as assessing your suitability for access to children and vulnerable adults. More details can be found on the Entry requirements page.

About this course

Our Primary PGCE develops effective, confident teachers whose classroom practice is informed by an advanced knowledge of educational theory, and who will continue to learn and reflect throughout their careers. We will help students to acquire the skills and expertise to support children’s learning, prepare them to teach in an inclusive urban environment, provide professional development in all national curriculum subjects, with a strong focus on mathematics, and ensure that students show a concern for professional values and demonstrate the positive attitudes and behaviour expected from pupils.

Who this course is for

The Primary PGCE (Specialist Mathematics full-time) programme is suited to those wishing to gain Qualified Teaching Status (QTS) for teaching in a UK maintained (state-funded) school and who have fulfilled the appropriate entry requirements.

What this course will give you

Students on the Primary PGCE programme benefit enormously from the complementary skills and expertise of staff in partnership schools and at IOE, UCL's Faculty of Education and Society.

The schools offer placements for teaching experience, and their teachers serve as tutors, mentors and joint assessors for our student teachers. IOE tutors have extensive experience of teaching, school management, inspection, research and consultancy.

Primary PGCE mathematics students spend time across the Foundation stage, Key Stage 1 and 2, and they gain experience of teaching across Key Stage 1 and Key Stage 2. Students will learn to teach all the primary curriculum subjects, with mathematics as a speciality.

The teacher you want to be

The Primary PGCE programme aims to provide a springboard into a rewarding career as a skilled teacher and future educational leader. It also lays the foundations for researching, writing and further study in education

The tools of a great educator

Understanding of theory and subject or phase pedagogy
Creating a successful climate for learning, including behaviour management
Planning and teaching classes that engage pupils
Using assessment to inform planning
Working with the wider school community, including parents

Employability

Graduates of the Primary PGCE programme are highly employable and sought after by schools and colleges in London and beyond. Almost all graduates secure their first teaching post by the time they finish the PGCE programme.

Graduates of the programme have great career prospects, some are working as classroom teachers and mentors to PGCE students, while others have jobs as maths subject leaders. Many have taken on further leadership roles within their schools, some of our graduates are now Headteachers, and many have developed their careers as subject specialist mathematics teachers, Special Educational Needs Co-ordinators and lead teachers in the classroom.

Accreditation

Students who successfully complete this programme will be recommended for Qualified Teacher Status (QTS).

The programme is taught through a mix of face-to-face and online sessions, (including lectures, presentations, discussions, and classroom group tasks), and a practical teaching element based in three schools. Students are required to read widely and to carry out written assignments in their own time.

Throughout the year, students will also participate in specific activities at IOE and in school that focus on important areas of our curriculum. These activities (totalling 20 days with at least 10 days in school) will help students to better understand links between theory and practice. They will also involve feedback from experts so that progress is supported in these pivotal areas. These days form part of the 130 days of teaching practice.

Students are assessed through assignments, presentations, audits, feedback and tutorials. A final assessment is based on a range of evidence including observations of teaching, assignments, subject knowledge development, professional conduct and responses to self-study.

University sessions run 9.00am - 4.30pm daily. During school placements you will be expected to attend at least 30 mins prior to the start of the school day and leave at least 30 after the school day ends.

Students will have readings and additional self-directed study to complete in addition to these contact hours.

This Programme is run over a period of 36 weeks.

You will undertake two Masters level modules (level 7), one Professional Practice module at level 6 and three school placements. The Masters Level modules are worth a total of 60 Masters credits on completion.

When you are not undertaking face-to-face teaching at IOE, you will be undertaking at least 130 days of teaching practice in various Partnership Schools.

Your three placements would be:

School Experience 1 in Autumn & Spring Terms (organised by UCL)
School Experience 2 in Spring Term (a one week placement organised by UCL)
School Experience 3 in Summer Term (organised by UCL).

Throughout the year, you will also participate in specific activities at IOE and in school that focus on important areas of our curriculum. These activities (totalling 20 days with at least 10 days in school) will help you to better understand links between theory and practice. They will also involve feedback from experts so that your progress is supported in these pivotal areas. These days form part of your 130 days of teaching practice.

Compulsory modules

Please note that the list of modules given here is indicative. This information is published a long time in advance of enrolment and module content and availability are subject to change. Modules that are in use for the current academic year are linked for further information. Where no link is present, further information is not yet available.

Upon successful completion of 60 credits and the Professional Practice module, you will be awarded a PGCE in Primary (Specialist Mathematics full-time).

School placements

As part of the programme students will spend time on placements at primary schools, during which time their teaching experience will be supported by a tutor and mentor. Students will spend at least 130 days on placements.

During placement periods you should be prepared to travel to and from each school placement. It should be noted that there is variation in how accessible schools are, and whether they have parking facilities.

We ensure your placement will provide fulfilling and valuable experiences through:

A dedicated team who will identify the best schools for your placements
Support and guidance from your university tutor and your school-based mentor
School experience that allows you to progress at an appropriate pace for you
Reasonable travel times from your home to your school

Making the most of your placement

Teaching is a demanding profession and student teachers can feel nervous about school placements or anxious about the workload. Your tutor and school-based mentor will help you navigate your school experience, ensuring that you have the input you need. Empathetic feedback and discussion about your developing professional practice will support you to be successful.

Accessibility

Details of the accessibility of UCL buildings can be obtained from AccessAble accessable.co.uk . Further information can also be obtained from the UCL Student Support and Wellbeing Services team .

Online - Open day

Graduate Open Events: Learn to Teach with IOE

Are you interested in a career in teaching? Join our virtual events to find out more about Teacher Training at UCL, including admissions and student funding information.

Graduate Open Events: PGCE Primary Teacher Training

Fees and funding, fees for this course.

Fee description	Full-time
Tuition fees (2024/25)	£9,250
Tuition fees (2024/25)	£25,900

The tuition fees shown are for the year indicated above. Fees for subsequent years may increase or otherwise vary. Where the programme is offered on a flexible/modular basis, fees are charged pro-rata to the appropriate full-time Master's fee taken in an academic session. Further information on fee status, fee increases and the fee schedule can be viewed on the UCL Students website: ucl.ac.uk/students/fees .

Additional costs

Students are responsible for funding their travel to and from placements.

For more information on additional costs for prospective students please go to our estimated cost of essential expenditure at Accommodation and living costs .

Funding your studies

For a comprehensive list of the funding opportunities available at UCL, including funding relevant to your nationality, please visit the UCL Scholarships and Funding website .

IOE-Clarke Scholarships

Deadline: 3 May 2024 Value: Tuition fees, return flights and stipend (1 year) Criteria Based on both academic merit and financial need Eligibility: EU, Overseas

IOE-ISH Centenary Masters Scholarships

Deadline: 3 May 2024 Value: Tuition fees and accommodation (1 year) Criteria Based on both academic merit and financial need Eligibility: EU, Overseas

Application and next steps

Students are advised to apply as early as possible due to competition for places. Those applying for scholarship funding (particularly overseas applicants) should take note of application deadlines.

Got questions? Get in touch

Learning and Leadership

[email protected]

UCL is regulated by the Office for Students .

Prospective Students Graduate

Graduate degrees
Taught degrees
Taught Degrees
Applying for Graduate Taught Study at UCL
Research degrees
Research Degrees
Funded Research Opportunities
Doctoral School
Funded Doctoral Training Programmes
Applying for Graduate Research Study at UCL
Teacher training
Teacher Training
Early Years PGCE courses
Primary PGCE courses
Secondary PGCE courses
Further Education PGCE programme
How to apply
The IOE approach
Teacher training in the heart of London
Why choose UCL?
Entrepreneurship
Inspiring facilities and resources
Careers and employability
Your global alumni community
Your wellbeing
Postgraduate Students' Association
Your life in London
Accommodation
Funding your Master's

IMAGES

Masters vs PhD: Which is Right For You?
Differences between Masters vs PhD
PhD vs Masters
Masters Vs PhD: The Difference Between Masters & PhD/Doctorates 2024+
Masters vs. Phd (Applied math/stats) for Work in Industry. Comparison
Master’s vs. Ph.D.: What’s the Difference and Which One to Choose

VIDEO

Master's vs. PhD: Navigating the Educational Landscape
Choose the Right Masters Degree!
Inverse Trigonometric Function| Class 12th Boards| Complete NCERT| From very basic
PhD information in malayalam || Dr Jisha || Difference in mode of study || Masters Vs PhD || PhD
JEE-Advanced problem from sequence and series| Class-11th and 12th| AP and GP
🧠💡 Kid Math Masters: Take on These Mind-Blowing Challenges! Can You Solve Them All?🧠💡 #MathForKids

COMMENTS

How should a mathematics major choose between doing a Masters or PhD?
I would really appreciate any advice or suggestions anyone might have. I am currently a senior mathematics major, about to graduate in May. For two years, I have planned on going for my PhD in pure mathematics (my highest interests have been in algebra, number theory, and discrete math). I applied to 8 PhD programs and 1 masters program, the ...
PhD or Master's in Math? That is the Question
A math master's or PhD is required to teach at an advanced level, and a graduate degree in math is recommended for most high-level positions in government and industry. The great thing about math is that it applies to everything — from the health industry to the banking industry, from education to engineering, from logistics to neuroscience.
Should I pursue an MA/MS before PhD in Mathematics?
Yes, a masters sounds like a better option, based on what you're saying. Also a lot of PhD students have a MA already, so it's not uncommon to do an MA first and then decide from there. Some universities offer a one-year masters - I would look into that option. 1. Reply.
Guide To Graduate Study
Guide to Graduate Studies. The PhD Program. The Ph.D. program of the Harvard Department of Mathematics is designed to help motivated students develop their understanding and enjoyment of mathematics. Enjoyment and understanding of the subject, as well as enthusiasm in teaching it, are greater when one is actively thinking about mathematics in ...
Best Mathematics Programs in America
Yale University. New Haven, CT. #8 in Mathematics (tie) Save. 4.6. A graduate degree in mathematics can help students hone their skills in a specialty area, from algebra and number theory to ...
Master's vs PhD
The two most common types of graduate degrees are master's and doctoral degrees: A master's is a 1-2 year degree that can prepare you for a multitude of careers. A PhD, or doctoral degree, takes 3-7 years to complete (depending on the country) and prepares you for a career in academic research. A master's is also the necessary first ...
Should you get a graduate degree in mathematics?
Mines requires a 151 for its applied mathematics and statistics program, but each school is different. The absolute lowest we've seen is 145. Generally speaking, the higher the GRE score (especially for math programs) the better off you'll be in grad school. Time to devote to the program - Graduate programs require significant time ...
Mathematics
Overview. The Department of Mathematics graduate program has minimal requirements and maximal research and educational opportunities. It differentiates itself from other top mathematics institutions in the U.S. in that the curriculum emphasizes, from the start, independent research. Our students are extremely motivated and come from a wide ...
Masters Vs PhD: The Difference Between Masters & PhD/Doctorates 2024+
Because a PhD takes longer to complete, it usually costs more money. The flip side to this is that a PhD may yield a higher salary upon completion. Therefore it may be worth the increased cost long-term. Whichever graduate degree you decide to pursue, you'll have expenses, such as tuition, fees, books, and others.
Mathematics PhD Program
Mathematics PhD Program. The Ph.D. program in the Department of Mathematics provides students with in-depth knowledge and rigorous training in all the subject areas of mathematics. A core feature is the first-year program, which helps bring students to the forefront of modern mathematics. Students work closely with faculty and each other and ...
Department of Mathematics at Columbia University
Office of Student Affairs. 107 Low Library, MC 4304. New York, NY 10027. 212-854-6729. [email protected]. For information on the department and program: Michael Harris. Director of Graduate Studies. Department of Mathematics.
Ph.D. Program
In outline, to earn the PhD in either Mathematics or Applied Mathematics, the candidate must meet the following requirements. During the first year of the Ph.D. program: Take at least 4 courses, 2 or more of which are graduate courses offered by the Department of Mathematics. Pass the six-hour written Preliminary Examination covering calculus ...
AMS :: Find Graduate Programs
Edit existing listing. Find Graduate Programs (FGP) in the Mathematical Sciences offers comparative information on over 500 graduate programs in the mathematical sciences in the US and Canada. This web service provides only an overview of the programs offered; departments should be contacted directly for more detailed information.
Graduate Degree Requirements
Master of Arts vs Master of Science in Mathematics. The Master of Science in Mathematics program requires a plan of study, professional development requirement, a thesis and examinations, and 30 units of approved graduate credit with differing parameters. See the Mathematics Graduate Handbook for more specific details. Admission Requirements.
Masters vs. Phd (Applied math/stats) for Work in Industry ...
Life is more than pick this and do that to get a higher paying the job. The point is that a masters and PhD might lead to similar paying jobs. But if you love math and want to continue your work in it, getting a PhD is a solid option. If you're just doing grad school to make more money, then maybe leave with a masters.
Graduate
Graduate. The goal of our PhD program is to train graduate students to become research mathematicians. Each year, an average of five students complete their theses and go on to exciting careers in mathematics both inside and outside of academia. Faculty research interests in the Johns Hopkins University Department of Mathematics are ...
Harvard Mathematics Department Graduate Information
The pure math PhD admissions application is open. The application submission deadline is December 15, 2024. For information on admissions and financial support, please visit the Harvard Kenneth C. Griffin Graduate School of Arts and Sciences.. Harvard Griffin GSAS is committed to ensuring that our application fee does not create a financial obstacle. . Applicants can determine eligibility for ...
Ph.D. Programs
Students who have been admitted to the PAL program, and who complete the requirements for the Ph.D. in Mathematical Sciences with a thesis in the area of logic, can choose to receive either a Ph.D. in Pure and Applied Logic or a Ph.D. in Mathematical Sciences. The choice of which degree to receive is usually based on the intended career path.
Ph.D. in Mathematics
The Ph.D. program also offers students the opportunity to pursue their study and research with Mathematics faculty based at NYU Shanghai. With this opportunity, students generally complete their coursework in New York City before moving full-time to Shanghai for their dissertation research. For more information, please visit the NYU Shanghai Ph ...
Graduate Program
Our graduate program is unique from the other top mathematics institutions in the U.S. in that it emphasizes, from the start, independent research. Each year, we have extremely motivated and talented students among our new Ph.D. candidates who, we are proud to say, will become the next generation of leading researchers in their fields. While we ...
MATH-PHD Program
Program Overview. The Department of Mathematics offers programs leading to the degrees of Bachelor of Science (BS), Master of Science (MS), and Doctor of Philosophy (PhD) in Mathematics, and also participates in the program leading to the MS and PhD degree programs offered through the Institute for Computational & Mathematical Engineering.
MS in Applied & Computational Mathematics
Applied and Computational Math Program Overview. Johns Hopkins Engineering for Professionals online applied and computational mathematics master's is one of the premier graduate degree options in our top-ranked online engineering master's program and a leading computational mathematics master's program in the industry. The advanced-level curriculum teaches students the key steps to ...
Ph.D. Program
Ph.D. Program. The degree of Doctor of Philosophy in Applied Mathematics and Computational Science is conferred in recognition of marked ability and high attainment in advanced applied and computational mathematics, including the successful completion of a significant original research project. The program typically takes four to five years to ...
Primary (Specialist Mathematics full-time) PGCE
On this specialist Primary PGCE programme, students learn to teach all the primary curriculum subjects but there is an added emphasis on learning to teach mathematics by considering both mathematics as a subject in its own right, but also its links to other subject areas. UCL works in partnership with around 200 primary schools, enabling students to fully prepare to be a

Stack Exchange Network

How should a mathematics major choose between doing a Masters or PhD?

3 Answers 3

You must log in to answer this question.

Hot Network Questions

University of Louisiana at Lafayette

You are here

Math Master’s Degree

PhD in Mathematics Degree

Have a language expert improve your writing

Master's vs PhD | A Complete Guide to the Differences

Table of contents

Receive feedback on language, structure, and formatting

Length of a master’s

Length of a PhD

Careers for master’s graduates

Careers for PhD graduates

Prevent plagiarism. Run a free check.

Cost of a master’s

Cost of a PhD

Applying for a master’s

Applying for a PhD

Cite this Scribbr article

Is this article helpful?

Lauren Thomas

Should you get a graduate degree in mathematics?

What you’ll need to start a graduate program in mathematics

Why a graduate degree in mathematics is worth the cost

Job Satisfaction

Mines Grad Programs

Applied Mathematics and Statistics

Data Science

Computer Science

Electrical Engineering

Related Articles

Electrical engineering jobs for graduates

How to add a master’s or graduate certificate in data science to your science or engineering degree

How does data science apply to health care, manufacturing and many other fields?

Graduate School

Mathematics

Program Offerings

Language(s)

Additional pre-generals requirements

General exam

Qualifying for the M.A.

Post-Generals requirements

Dissertation and FPO

Associate Chair

Director of Graduate Studies

Director of Undergraduate Studies

Assistant Professor

Associated Faculty

University Lecturer

Senior Lecturer

Visiting Professor

Visiting Lecturer with Rank of Professor

Permanent Courses

COS 522 - Computational Complexity (also MAT 578)

Department of Mathematics

Ph.D. Program

Detailed Regulations

Course Requirements

Preliminary Examination

Qualifying Examination

Publications Home — Over 100 years of publishing excellence

Librarian Resources

Mathematical Reviews/MathSciNet®

Membership Home — Welcome to your membership center

Individual Membership

Institutional Membership

Other Member Types

Meetings & Conferences Home — Engage with colleagues and the latest research

Sectional Meetings

Other Meetings, Conferences & Workshops

Meetings Resources

News & Outreach Home — Explore news, images, posters, and mathematical essays

Math Voices

Explorations

Professional Programs Home — Resources and opportunities to further your mathematical pursuits

Institutional Information and Data