# Denver Masters in Mathematics Degrees

**Masters in Math** programs often immerse students in the study of pure mathematics or help them discover its application to other disciplines. Curriculums in Math Masters programs might explore numerous areas such as modeling, business analytics, data science, biological science and other related fields.

## Masters in Math: Overview

Masters in Math degree programs address how to find patterns in data or abstract logic, draw conclusions, test theories and model the real world. Students could learn through a blend of lectures and seminars, and may spend time independently as they work to solve problem sets.

The scope of a program could span basic graduate courses in mathematics and may offer students the chance to pursue more focused study in an area of interest. A Masters course of study may involve basic courses in real analysis, complex analysis and linear algebra, followed by other essential courses, such as:

- Probability
- Scientific computing
- Differential equations

Depending on their mathematical interests, students might then be able to take more advanced graduate courses in pure and applied mathematics.

### Masters in Mathematics Requirements

Admission to some Masters in Mathematics programs may be competitive, although requirements could vary between universities. Some schools may accept applicants based on overall college GPA, transcripts, general and subject GRE scores, and the information contained in the letters of recommendation.

While applicants to Math masters programs may not need an undergraduate degree specifically in a math major, some universities might require prospective students to have a strong math background. For this reason, some programs might expect that students be thoroughly familiar with subjects such as multivariable calculus, abstract linear algebra, analysis and differential equations.

Students should refer to

individual math schools to see what other material may be required to apply into specific programs.

### What Is Mathematics?

As one of the key STEM fields, mathematics is a broad discipline and serves as the technical foundation for science, engineering and technology. Masters in mathematics curriculums could therefore help students learn to use numerical, spatial and logical formulas to study and solve problems in these domains. ^{i}

### Masters in Applied Mathematics or Pure Mathematics?

Math Masters programs could involve a mix of pure mathematics and applied mathematics. A university may combine the two approaches, or focus on one aspect over the other.

Pure math degrees typically offer curriculums that are weighed with theory and abstract formulas. Courses often cover advanced topics in algebra, analysis and topology, and geometry. In addition to a wide range of courses, students may pursue research topics in the more theoretical aspects of mathematics.

Students who explore a Masters degree in pure mathematics might research and write their thesis under the supervision of a Math professor.

Applied math degrees typically use mathematics as a practical way to quantify and explain observed physical, social or business phenomena. Also, it is used to predict possible outcomes as with finances and weather forecasts. Through the use of mathematical methods and models, applied and computational mathematics could solve a variety of real-world issues.

Some Masters in Applied Mathematics programs may offer core courses in numerical analysis, applied analysis, and mathematical methods. Students in this type of program often study the applications of mathematics, with a strong emphasis on interdisciplinary research.

Research could delve into the many areas that sit on the crossroads of mathematics and the physical, life and engineering sciences. For this reason, learners in this type of program may have advisors from other departments.

DID YOU KNOW?

When asked about their education, 38% of Mathematicians reported they had a Masters degree.^{ii}

## Types of Masters in Mathematics Degrees

Masters in Math degrees could lead to a Master of Arts (MA) or Master of Science (MS) in Mathematics. Both these programs could take a full-time student about two years to complete and usually require coursework and a thesis. The MA and especially the MS degree often serve as a stepping stone towards the PhD.

### MA vs MS Math Programs

A MA degree in Mathematics might require more courses outside mathematics and may have a teaching option. This is often intended for secondary school teachers. By contrast, a MS in Math program might require more advanced mathematics courses. That said, one should refer to individual Math schools as they may differ in how they define their Masters in Math programs.

### Master of Arts in Mathematics

A Master of Arts (MA) in Mathematics could be formatted to align with common core state standards in K-8 mathematics. Students could therefore study a broad range of math courses as well as methods to teach them to middle school learners.

In some schools, a MA in Mathematics could require students to complete about 33 credits of required courses and electives. Elective topics might enable teachers to refine specific pedagogical skills—for instance, how to integrate technology into lesson design or teach to students with disabilities.

Core MA Math courses could be designed to encourage breadth of knowledge in foundational topics. Some examples are highlighted below.

- Numbers
- Algebra
- Geometry
- Mathematics in Science
- Data Analysis and Probability
- Mathematical Applications

Applicants to some MA programs may need to be certified teachers who have earned a baccalaureate degree in any subject area from an accredited college or university. Along with transcripts, schools may ask students to furnish letters of recommendation, Praxis Scores, GRE Scores, and/or copy of state teaching certificate.

### Master of Science in Mathematics

A Master of Science (MS) in Math Degree program could allow students to choose a few areas of mathematics to pursue, such as: applied mathematics, statistics, algebra or analysis.

To earn their Masters degree in Mathematics, students might need to complete about 34 credits of courses and a thesis. Additionally, some programs could require students to pass comprehensive exams.

Core MS Math courses could help students deepen their grasp of several content areas. Some sample topics are indicated below.

- Advanced Calculus
- Topology
- Number Theory
- Mathematical Statistics
- Numerical Linear Algebra
- Wavelets

Students may also have the chance to take electives in mathematical topics such as mathematical proofs, knot theory or logic. In some schools, electives could also include courses in math education.

Applicants to some MS Mathematics programs may need a strong background in math, with undergraduate calculus and experience in writing mathematical proofs. Or, an undergraduate degree could be required preferably in mathematics, mathematics education, or an area with a significant mathematics coursework.

### Concentrations for MS Math Programs

Some Math graduate schools may offer areas of emphasis so that students might tailor their studies to mirror career goals and interests. Typically, concentration courses are stacked onto a series of compulsory Masters in Math courses. Some examples are described below.

*Algebra and Topology:* A Masters focus in algebra and topology explores two pillars of pure mathematics in depth. Students might be introduced to a host of techniques and concepts that are central to modern math.

This type of program could offer courses in Algebra, Topology, Geometry, Number Theory, and Logic and Computation—as well as their interactions with other research areas such as mathematical physics and computer science.

*Applied Stochastics*: A Masters with a focus in applied stochastics could help students describe randomness in nature and society to give data a predictive power. With its emphasis in pure math, students may fine-tune their grasp of functional analysis, partial differential equations, geometry of metric spaces and number theory.

*Mathematical Foundations of Computer Science*: A Masters focus in Mathematical Foundations of Computer Science could explore the work of Gödel, Church, Turing, Kleene and others. Students may take courses from different disciplines and may learn to use computers to help solve math problems with a discrete component.

Curriculums could cover both areas in depth. For instance, mathematics courses might zero in on algebra, general topology, logic, number theory and combinatorics. The computer science courses might concentrate on formal methods, type theory, category theory, co-algebra and theorem proving.

*Mathematical Physics*: A Masters in Mathematical Physics could discuss the work of Christiaan Huygens and Isaac Newton. Students might study to develop expertise in areas like functional analysis, geometry, and representation theory with research in, for example, quantum physics.

Some students might want to further explore areas such as quantum gravity and non-commutative geometry.

*Science in Society*: A Masters in Math with a focus in science could enable students to build a bridge between scientific expertise and societal practices. Required courses could cover issues related to climate change policy, genetic modification, big data and privacy.

*Pathology*: A MS in Pathology could be planned-out to help students refine their skills in analysis as they problem solve within the wide range of the basic medical sciences. Particular emphasis may be placed on the basic disciplines of cellular and molecular biology, biochemistry, and immunology. Students may spend time in class and in the laboratory as they research within the biomedical sciences.

*Pharmacology:* A MS in Pharmacology could highlight research methods into the action of drugs at the systemic, cellular and sub-cellular levels. Coursework could cover topics such as quantitation of responses, statistical analysis and methods to interpret data.

*Science, Management, Innovation*: A focus in Science, Management, Innovation could delve into how innovation is managed in company strategies, how government designs policy and how that interacts with societal challenges. Coursework could help students apply models and concepts from strategy, marketing and innovation management to entrepreneurship.

*Applied and Computational Math*: A MS in Applied and Computational Math could prepare graduates to apply mathematical models and methods to study various problems that arise in industry and business.

Coursework could place an emphasis on the development of computable solutions that might be implemented. Further concentrations could include discrete mathematics, dynamical systems, and scientific computing.

*Business Analytics:* A MS in Business Analytics might equip students with the analytical and business skills needed to translate data statistics and analysis into action. Courses in quantitative methods for management and data mining may be stacked onto key business topics such as financial theory.

Through their curriculum, students could gain a solid grasp of modern computational techniques and statistical methods used to balance risk with structured decisions. A course in data mining could help students learn to construct decision trees, find association rules, classification and clustering.

*Data Science*: A MS in Data Science could enable students to analyze and leverage big data to gain insights that might foster innovative ideas and solutions in a variety of fields. Core courses might stress research design and may entail critical evaluation of data through theoretical models.

Core data science courses could explore statistical methods, data mining, machine learning and data visualization. Students might, from this base, further refine their degree plan through an area of emphasis in one of the following areas.

- Social Science Analytics – how data science could be applied to social science research and policy development
- Business analytics – how data science is applied to business management and decisions
- Cybersecurity – the application of data science and computer forensics
- Financial Crime – how data science and skills could be used to combat economic crime

### What Might I Do with a Masters in Mathematics?

The wide reach of math applications could translate to different potential career paths for Masters in Math Graduates. Essentially, mathematicians conduct research in fundamental math or they apply math techniques to science, management and other fields.

Per the Bureau of Labor Statistics, mathematicians typically need at least a Masters in Math, and sometimes a doctorate for careers in the private sector.^{iii }Overall, employment of mathematicians is projected to grow 33 percent from 2016 to 2026, which is considered faster than average.^{iv}

O*Net lists several careers that Mathematicians have reported, a few examples of which are listed below.^{ii}

- Computational Scientist
- Cryptographer
- Research Scientist
- Emerging Solutions Executive

### On-Campus or Online Masters in Mathematics?

Do you prefer closer contact with professors and classmates? Would you enjoy earning a Masters degree in Math abroad? Are you a working professional who prefers to earn a Masters in Mathematics online?

### Get Matched for Free to Master's in Mathematics Programs

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[i] bls.gov/careeroutlook/2014/spring/art01.pdf | [ii] onetonline.org/link/summary/15-2021.00 | [iii] bls.gov/ooh/math/mathematicians-and-statisticians.htm#tab-4 | [iv] bls.gov/ooh/math/mathematicians-and-statisticians.htm#tab-6

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