# Vermont Math Graduate Programs & Math Graduate Degrees

Mathematics Graduate programs award math degrees at the masters and doctorate and certificate levels. Graduate math degrees might help students hone their skills and knowledge in a specific area, from algebra and advanced calculus to mathematical statistics and numerical analysis.

There are also math graduate programs designed to help current teachers pursue licensure to teach math at the middle school, collegiate, or university levels. These programs tend to highlight instructional methods and research, in addition to various pure and applied math courses.

DID YOU KNOW?

A Mathematician is one of the top 5 fastest growing careers with a graduate degree in 2016. Learn more about Mathematician salary and employment outlook.

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## Mathematics Graduate Programs: Types of Math Degrees

The field of mathematics, and mathematics graduate programs, might be divided into two basic categories: pure (theory and abstract) mathematics and applied (practical application) mathematics. A typical mathematics degree program might involve a mix of both, as these areas often overlap, especially when it comes to professional practice.^{i} However some graduate math schools might offer pure or applied mathematics as separate degrees. You could look for a program with the focus that mirrors your own interests and goals.

### Pure Mathematics Graduate Programs

Pure mathematics graduate programs are theoretical. Theoretical mathematicians might identify, research and resolve unexplained issues in math. Students of pure math could study abstract concepts and formulas to prove or disprove theories, and solve math-related problems to boost knowledge about the field. Areas of pure mathematics generally draw from the topics that follow.

- Algebra
- Calculus and analysis
- Geometry and topology
- Combinatorics
- Number theory

### Applied Mathematics Graduate

### Programs

Applied math graduate programs could discuss how math theories and techniques could be used to solve practical problems in business, engineering, computer programming, the sciences and other fields. Applied mathematicians often use analytical methods such as mathematical modeling and data analysis. Some of the areas of applied mathematics are as follows.

- Computational mathematics
- Differential equations
- Mathematical physics
- Information theory
- Game theory
- Probability and statistics
- Operations research

## Masters in Mathematics Programs

Masters in Mathematics programs are typically two year courses of study that could lead to either a Master of Arts (MA) or Master of Science (MS) degree in math. Applicants to most programs need a strong foundation in mathematics, mathematics education or a related area. These degree programs typically build on students’ ability to write mathematical proofs and a familiarity with Calculus.

Some masters in mathematics programs may be designed for elementary, middle school and special education teachers who want to meet their state requirements to teach mathematics at the middle school level. Or, to upgrade their mathematical skills. For this type of masters degree in mathematics, students may need to have a bachelors degree in any subject area from an accredited college or university, Praxis and GRE scores, and a state teaching certificate.

### Master of Arts in Mathematics

In some math graduate schools, the Master of Arts track is intended as a platform for students who might want to pursue a PhD in Mathematics. As a result, coursework for this degree might be narrower in scope than the MS, but also more advanced.

Some MA in math programs require students to complete a masters thesis and about 30 credits of approved courses. The courses themselves might cover topics such as real and complex analysis, abstract algebra and foundations of computational mathematics. These courses could form the core of the student's program and provide the basis for comprehensive exams. Where a thesis is involved, it could be based on a student’s original contributions, which may lead to some suitable material for a future dissertation.

### Master of Arts in Mathematical Foundations

A Master of Arts in Mathematical Foundations program is designed for teachers who want to pursue a math educator certification with their state or regional education board. Some programs of this nature offer graduate study in mathematics to those who do not have a math background. Through their coursework, students might develop a better grasp of math topics and methods to teach and engage K-8 students. Math courses might cover a broad array of topics from numbers and algebra to geometry and sciences math. Students might also take courses in math applications, along with courses in curriculum and instruction.

### Master of Science in Mathematics

A Master of Science in Mathematics program could be broader in its scope of math coursework (pure and applied). While this might vary, the MS is often intended mainly for students who seek expansive and intensive preparation either to teach in a junior college or pursue a career in industry. Most MS in Mathematics programs require about 30 credits of approved courses and, in some schools, a thesis. When a thesis is required, it could draw content from a student’s area of interest. Students might also undergo oral and/or written exams and may have to defend the thesis in a seminar format.

Coursework in a MS degree in mathematics could include core first and second year topics, which students may be able to choose from their school’s list of approved subjects. First year topics could include areas such as numerical analysis, graph theory and stochastic processes. In their second year, students might wrap up any elective and concentration course requirements. Areas of emphasis might include topics from discrete mathematics (e.g. cryptography), dynamical systems (e.g. partial differential equations), or scientific computing (e.g. numerical analysis).

DID YOU KNOW?

Mathematicians typically need at least a master’s degree in mathematics.

^{i}When surveyed, 60% of Math Teachers at the Postsecondary level stated they had a doctoral degree.^{ii}

## PhD in Mathematics Programs

A PhD in Mathematics is the highest degree in math and is typically needed to conduct research or teach in a college or university.^{i} PhD Math programs are research-focused and students usually choose an area in which to anchor their studies. Broad areas might include Geometry and Topology, Number Theory and Representation Theory, and Algebraic Geometry. Specific areas are usually defined by faculty within a university’s math department.

Math PhD students may build both general knowledge of the major areas of modern mathematics (algebra, analysis, and geometry), as well as a detailed command of more focused, advanced topics. Since many programs encourage it, students may be able to do original research in their area of study.** **Some students may also develop the ability to teach effectively courses in mathematics at the college level.

Doctorate degree in mathematics requirements could include a period of residency, coursework, examinations, teaching, and a dissertation. Coursework depends on the school and how well a student is prepared. Advanced students may skip some or all first-year courses and applicants with a bachelors degree are often encouraged to have at least one year in abstract algebra and analysis. Other required material could include GRE scores on the mathematics subject test, transcripts, letters of referral and TOEFL scores when applicable. Some schools recommend that reference letters be from past math teachers.

Some of the possible topics in a Math PhD program might include real analysis, algebra, and geometry-topology. As a student progresses through their program, they might move onto advanced courses and take part in research seminars. Dotted throughout, students may take exams on the course material. Upon satisfactory performance in exams, a student may be admitted to candidacy for their PhD and begin research for their doctoral dissertation. The dissertation usually consists of original scholarly work which may be assessed by a doctoral committee and orally defended by the candidate.

## Graduate Certificates in Mathematics

Graduate Certificates in Mathematics are shorter-term programs that may be taken as part of, or in addition to, a masters degree. Some certificates entail about 18 credits, which could be the number of courses that a regional or state education board requires for teachers to pursue certification to teach advanced math. Applicants to these types of programs may need a teacher’s license and undergrad courses in Linear Algebra, Calculus III, Abstract Algebra, Real Analysis, Geometry, and Statistics.

## Related Math Graduate Programs for Math Majors

There are many other degrees in related areas that could branch out of mathematics graduate programs, as computational skills are used in many fields outside of formal mathematics. Per the BLS, “people with a degree in mathematics or who develop mathematical theories and models are not formally known as mathematicians. Instead, they work in related fields and professions.” ^{i} Those who pursue a career in the computer systems design and related services industries may be known as computer systems analysts and computer programmers. In the world of finance, math professionals might be known as quantitative analysts, data scientists and statisticians.^{i }

### Master of Science in Data Science

A Master of Science in Data Science program might prepare students to analyze and protect vast amounts of digitally-stored data using mathematical concepts.^{i }

Core courses in a MS Data Science program might stress research design and the critical analysis of data based on theoretical models. Moreover, students might gain a solid grasp of the limits of data, legal and privacy issues, and ethical and socially responsible practices and decisions. Possible core topics might draw from the examples below.

- Statistical methods
- Data mining
- Machine learning

In addition to their core courses, students might be able to select an area of emphasis. A concentration is a series of extra courses that are planned-out to help students understand the practical applications of their courses to a specific industry. The following are some examples of the type of focal areas one might find in a Data Science masters program.

**Social Science Analytics**: A focus on social science analytics might narrow in on the application of data science to social science research and policy development. Learners might develop their grasp of things such as social trends, poll data and research design, among other topics.**Business Analytics:**An emphasis in business analytics might explore how data science is applied to business management and decisions. Students might learn how to use demographic trends, census information, and other databases to forecast market developments and manage risk.**Cybersecurity**: Students who focus their courses around cybersecurity might learn how to apply data science knowledge and skills to cyber intelligence and computer forensic practices. Coursework could discuss leadership and strategy for adapted to the cyberspace realm.**Financial Crime**: A focus in financial crime might help students learn to apply their data science knowledge and skills in areas such as fraud analysis and financial investigations. This area might interest students who wanted to develop their ability to manage corporate and technological resources to combat economic crime.

## Why Consider a Graduate Math Program?

Mathematics graduate programs may help students build their ability to use math to solve problems alongside chemists, engineers, industrial designers and others. Many programs encourage students to think critically, and engage with logic and reasoning to identify the strengths and weaknesses of alternative explanations, conclusions or approaches to problems. ^{i}

### Math Careers: An Outlook

The BLS projects a 28 percent rise in employment for mathematical science occupations to the year 2024. This includes a 21 percent increase among mathematicians specifically. Per their forecast, those with a graduate degree in math, strong quantitative and data analysis skills, and a background in a related discipline (e.g. business, computer science or statistics) may have an edge.^{i} Learn more about Mathematician salary and employment outlook.^{iii}

### Online or On-Campus?

Many mathematics graduate programs offer a choice of learning formats. Online math graduate programs might be purely digital with no physical meetings, although they could make use of online chats in place of in-person office hours. Other programs may be available in a hybrid format which brings together web conference software and regular lectures. By contrast, a campus program may offer a fully on site program, replete with formulas jotted on blackboards, lively discussion and interaction. Whichever format fits your needs, you could refine your search for a graduate degree in math with that in mind.

### Find Mathematics Graduate Programs

Start your search for mathematics graduate programs right here. Use the on-page menu to compare math programs at the certificate, masters and doctoral levels. Look for graduate math schools by location and delivery method (online, campus). Each search leads to a variety of paid programs for you to read about. Find a masters degree in math or a PhD in math you want to apply to? Great! Use the forms we provide to contact schools directly and right away! Take your next step now.

[i] bls.gov/ooh/math/mathematicians.htm | [ii] onetonline.org/link/summary/25-1022.00 | [iii] bls.gov/emp/ep_table_103.htm

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