WCSU Graduate Catalog 2019-2020 : MACRICOSTAS SCHOOL OF ARTS AND SCIENCES

MASTER OF ARTS IN MATHEMATICS

Master of Arts in Mathematics

Charles Rocca, Graduate Coordinator, WH 322A Phone: (203) 837-9360
roccac@wcsu.edu
Cathy DeSisto-Reynolds, Department Secretary, WH 321 Phone: (203) 837-9299
reynoldsc@wcsu.edu
Fax: (203) 837-8527 

 

Faculty:   D. Burns; S. Christofi; B. Hall; S. Hayes; S. Lightwood; A. Lubell; P. Maida; L. Novozhilova; C. Rocca; Michael Shoushani, Todd Trimble, X. Wang

 

Program Overview and Mission

The Master of Arts (M.A.) in Mathematics degree program provides students with an avenue for further in-depth study in theoretical or applied mathematics. Students may use this program as a first step toward a Ph.D. in Mathematics, as a means of increasing their knowledge of mathematics to support their teaching, or to enhance their skills and knowledge for careers in such diverse fields as actuarial science, statistics, cryptography, engineering, and computer science.

The mission of the M.A. in Mathematics program is to extend the knowledge of beginning mathematicians with depth and breadth in mathematics content, research, and applications.

Program Learning Goals and Objectives

 Upon the completion of the MA in Mathematics program, graduates will

  • Demonstrate knowledge of functional concepts and theories in Modern Algebra, Real Analysis, Complex Analysis, Numerical Analysis, and Applied Statistics. These include:
    • Functional series with both real and complex terms
    • Real and complex functions
    • Theory of Riemann integral
    • Algebraic Structures, such as groups, rings and fields
    • Theory of integration of complex functions
    • Theories of interpolation and approximation of functions and numerical solutions to transcendental, polynomial, and differential equations as well as to linear and non-linear systems of equations
    • Applications of statistical techniques for both discrete and continuous distributions
    • Verifications of assumptions appropriate for specific statistical models
  • Be able to use techniques for proving statements about the fundamental concepts in the listed areas
  • Develop and apply working skills in problem solving techniques involving the fundamental concepts and theoretical facts in the listed areas
  • Use/develop mathematical models in applied areas, solve them, and analyze the solutions with technology assistance when necessary.
  • Demonstrate in depth knowledge in two areas of their choice. Possible demonstrations of this knowledge include:
    • Data processing using modern techniques and algorithms such as multivariate statistical analysis or signal analysis
    • Proving statements involving measure theory and Lebesgue integration
    • Solving problems and demonstrating proofs involving field extensions, quotient structures, Galois theory, geometric or combinatorial group theory
    • Solving ordinary and partial differential equations both analytically and numerically
    • Proving statements in advanced Number Theory

Admission Requirements

The following are the requirements for admission into the M.A. in Mathematics program:

  • Bachelor’s degree in math  or math-related field,  with courses through Abstract Algebra
    • If applicant does not meet this requirement, s/he is required to take the appropriate courses that are prerequisites to graduate study in mathematics: Linear Algebra, Calculus III, Abstract Algebra, and earn a GPA 3.0 in these courses.
  • Undergraduate overall GPA 2.5 or better, and Undergraduate GPA in major math courses 2.5 or better if applicant does not meet this requirement, s/he must complete the GRE Quantitative, General Exam, with a score of 650 or better.
  • Special cases may be accepted by the department graduate committee.

Degree Requirements

Requirements for the degree of M.A. in Mathematics include:

     1. a minimum of 30 semester hours of course work as described below, and

     2. a culminating experience, which consists of a comprehensive examination and may include a thesis.

Comprehensive Examination

The comprehensive examination is a three-hour examination on the courses in the program completed by the student as follows:

     1. one hour on each of two one-year, six-credit MAT courses in the areas of algebra, analysis, numerical analysis, or statistics, with at least one being algebra or analysis;

     2. two half-hour exams in courses of student’s choice

     3. Exceptional students (GPA > 3.75) have the option of writing a thesis.  In such cases, the examination is a single one-hour exam in one of the areas of algebra, analysis, numerical analysis or statistics, and it must be in an area different from the thesis.

All course work must be completed prior to the semester in which students take the comprehensive examination. The total GPA must be 3.0 or better. Credit is not awarded for the comprehensive examination.

The written examination is given at a time agreed to by the student and graduate coordinator. It is the responsibility of students choosing to take the examination to notify their adviser no less than 2 months prior to the expected examination date. Successful fulfillment of the examination requirement necessitates a passing mark on each section of the examination. In the event the student fails to pass one section of the examination, the student may

    1. repeat that particular section of the examination on the next examination date or

    2. choose another option with the approval of the department graduate committee.

Thesis

The thesis is completed through MAT 592, Independent Thesis Research in Mathematics (up to six semester hours, as agreed to by the student, the thesis adviser, and Mathematics Department chair). The thesis is a scholarly work researched and solely written by the student under the guidance of a thesis adviser and thesis committee. The thesis proposal must be approved by the thesis committee and graduate school before registering for MAT 592. The thesis credits must be approved by the Mathematics Department.

The Master of Arts in Mathematics degree program, including the thesis and the comprehensive examination approach, must be planned and agreed upon by the student and the graduate adviser.

Master of Arts in Mathematics

The M.A. in Mathematics requires completion of 30 semester hours. (21 SH required credits as indicated – five courses required of all students plus two of the second semester classes in algebra, analysis, numerical analysis, or statistics. The remaining nine credits can be selected from those listed in agreement with the student’s faculty advisor and graduate coordinator.) Students exhibiting exceptional ability may choose the thesis option to complete their degree.

REQUIRED  
MAT 512    Modern Algebra I 3 SH
MAT 507    Applied Statistics I 3 SH
MAT 514    Real Analysis I 3 SH
MAT 518    Complex Analysis I 3 SH
MAT 526    Numerical Analysis I 3 SH
Plus 2 of the following  
MAT 513    Modern Algebra II 3 SH
MAT 515    Real Analysis II 3 SH
MAT 508    Applied Statistics II 3 SH
MAT 527    Numerical Analysis II 3 SH
ELECTIVES (9 SH)  
MAT 505    Logic 3 SH
MAT 508    Applied Statistics II 3 SH
MAT 513    Modern Algebra II 3 SH
MAT 515    Real Analysis II 3 SH
MAT 522    Topics in Advanced Geometry 3 SH
MAT 528    Number Theory 3 SH
MAT 529    Historical Development of Mathematics 3 SH
MAT 540    Topics in Mathematics 3 SH
MAT 598    Faculty-Developed Study 3 SH
MAT 599    Student-Developed Study 3 SH
MAD 513   Topics in Secondary School Mathematics Education 3 SH

A maximum of six S.H. may be taken at the 400-level with approval of coordinator.

Comprehensive Exam __     OR   Thesis 3 S.H.__