# General Mathematics Concentration

The Master of Science in Mathematics with Concentration in General Mathematics program is designed both to provide advanced skills and knowledge for persons seeking positions in industry, government, or teaching at the community college level, and to provide professional development to persons currently in such positions. Qualified graduates are also prepared to enter directly into at least the second year of a Ph.D. program in mathematics, applied mathematics, or statistics, depending on the particular course of study.

#### Additional Admission Requirements

In addition to the general requirements for admission to the Graduate School, the following are required for the concentration in General Mathematics:

- Applicants must present evidence of the satisfactory completion of at least 27 credit hours of mathematics approved by the department Graduate Committee.
- It is recommended that the student have a basic knowledge of at least two of the areas of algebra, real analysis, and topology.

#### Concentration Requirements

The M.S. in Mathematics with Concentration in General Mathematics degree requires successful completion of at least 30 credit hours of graduate work approved by the department Graduate Committee, including: MATH 5143 and MATH 5144 or their equivalents; at least one course each from two of the groups I, II, III, V, and VI below; and at least 15 credit hours in 7000-level courses. No credit shall be given for 6000-level math courses other than mathematical finance courses in group V. With the approval of the department Graduate Committee, a 3 credit hour 6000-level course in another department of a theoretical nature or a 3 credit hour 6000-level mathematical finance course may be applied toward the 15 credit hours in the 7000-level courses. Candidates for the degree concentration must demonstrate, to the satisfaction of the department Graduate Committee, competence on general knowledge in at least three of six groups of courses listed below. This may be accomplished by (a) successful performance on a written or oral comprehensive examination or (b) successful completion of courses in these areas.

##### Group I – Applied Mathematics

- MATH 5165 – Numerical Linear Algebra (3)
- MATH 5172 – The Finite Element Method (3)
- MATH 5173 – Ordinary Differential Equations (3)
- MATH 5174 – Partial Differential Equations (3)
- MATH 5176 – Numerical Methods for Partial Differential Equations (3)
- MATH 7172 – Partial Differential Equations (3)
- MATH 7176 – Advanced Numerical Analysis (3)
- MATH 7177 – Applied Optimal Control (3)
- MATH 7273 – Advanced Finite Element Analysis (3)

##### Group II – Probability-Statistics

- STAT 5123 – Applied Statistics I (3)
- STAT 5124 – Applied Statistics II (3)
- STAT 5126 – Theory of Statistics I (3)
- STAT 5127 – Theory of Statistics II (3)
- STAT 7027 – Topics in Statistics (3)
- STAT 7122 – Advanced Statistics I (3)
- STAT 7123 – Advanced Statistics II (3)
- STAT 7127 – Linear Statistical Models (3)
- STAT 7133 – Multivariate Analysis (3)
- STAT 7135 – Statistical Computation (3)
- STAT 7137 – Survival Analysis (3)
- STAT 7139 – Time Series Analysis (3)
- MATH 5128 – Applied Probability I (3)
- MATH 5129 – Applied Probability II (3)
- MATH 7120 – Probability Theory I (3)
- MATH 7121 – Probability Theory II (3)
- MATH 7125 – Stochastic Processes I (3)

##### Group III – Algebra-Topology

- MATH 5163 – Modern Algebra (3)
- MATH 5164 – Abstract Linear Algebra (3)
- MATH 5181 – Introduction to Topology (3)
- MATH 7163 – Modern Algebra I (3)
- MATH 7164 – Modern Algebra II (3)
- MATH 7181 – Topology I (3)
- MATH 7182 – Topology II (3)

##### Group IV – Analysis

- MATH 5143 – Analysis I (3)
- MATH 5144 – Analysis II (3)
- MATH 7141 – Complex Analysis I (3)
- MATH 7143 – Real Analysis I (3)
- MATH 7144 – Real Analysis II (3)
- MATH 7148 – Functional Analysis (3)

##### Group V – Mathematical Finance

- MATH 6202 – Derivatives II: Partial Differential Equations for Finance (3)
- MATH 6203 – Stochastic Calculus for Finance I (3)
- MATH 6204 – Numerical Methods for Financial Derivatives (3)
- MATH 6205 – Financial Computing (3)
- MATH 6206 – Stochastic Calculus for Finance II (3)

##### Group VI – Computer Science

All 5000- and 6000-level ITCS courses

#### Assistantships

A number of graduate assistantships are available each year (with nationally-competitive stipends) for qualified applicants. A limited number of fellowship awards can be applied to supplement these stipends for especially qualified students.

#### Thesis

Completion of a thesis is optional. With the approval of the department Graduate Committee, a candidate may receive up to six of the 15 hours required at the 7000 level for the writing of a master’s thesis on an approved topic. This thesis may be original work, work of an expository nature, or the mathematical formulation and solution of a particular industrial or business problem suggested by the career interests of the student. A candidate may receive no more than six of the hours required at the 7000 level for course and thesis work in another department. If the thesis option is selected, the candidate will be required to defend their thesis in an oral examination.

#### Comprehensive Examination

A candidate must perform satisfactorily on a written or oral comprehensive examination over their program of study. The thesis defense is the comprehensive examination for those students who select the thesis option.