WCSU 2021-2022 Graduate Catalog : MACRICOSTAS SCHOOL OF ARTS AND SCIENCES

MASTER OF ARTS IN MATHEMATICS

Master of Arts in Mathematics

Xiaodi Wang, Graduate Coordinator, HI 101L Phone: (203) 837-9355
wangx@wcsu.edu
Cathy DeSisto-Reynolds, Department Secretary, HI101 Phone: (203) 837-9299
reynoldsc@wcsu.edu
Fax: (203) 837-8393 

 

Faculty:   D. Burns; S. Christofi; B. Hall; S. Hayes; S. Lightwood; A. Lubell; P. Maida; C. Rocca; M. Shoushani, T. Trimble, X. Wang

 

Program Overview and Mission

The Master of Arts (M.A.) in Mathematics degree program provides students with an avenue to further in-depth study in theoretical or applied mathematics. Students may use this program as a first step toward a Ph.D. in Mathematics or Applied Mathematics, as a means of increasing their knowledge of mathematics to support their teaching, or as learning-centered tool to empower and enhance their skills and knowledge for careers in such diverse fields as actuarial science, scientific computing, machine learning, statistics, information security, 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 concepts and theories in Algebra, Analysis, Ordinary and Partial Differential Equations, and Applied Statistics. These include:

o theories of measure and integration,

o algebraic structures,

o families of ordinary and partial differential equations and properties of their solutions, and

o applications of statistical techniques and models.

· Be able to prove statements about fundamental concepts in the listed areas,

· Develop and apply problem solving techniques in applied and pure mathematics,

· Develop and use mathematical models in applied areas and analyze the outcomes of those models, with technology assistance when necessary,

· Demonstrate in depth knowledge in two areas of their choice. Possible demonstrations of this knowledge include:

o Data processing using modern techniques and algorithms such as multivariate statistical analysis or signal analysis

o Apply major theoretical, analytical, and computational techniques and concepts to analyze, construct, and solve ordinary and partial differential equations used in realistic models of practical importance

o Proving statements involving measure theory and Lebesgue integration

o Solving problems and demonstrating proofs involving field extensions, quotient structures, and Galois theory

o Demonstrating understanding of algebraic structures from a geometric standpoint

 

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 an applicant does not meet this requirement, s/he is required to complete appropriate courses that are prerequisites to graduate study in mathematics with a GPA of 3.0 or above, these must include at least six of the following seven classes:

o MAT 222: Introduction to Statistics,

o MAT 322: Probability

o MAT 272: Introduction to Linear Algebra,

o MAT 281: Calculus III,

o MAT 282: Ordinary Differential Equations,

o MAT 375: Algebraic Structures,

o MAT 383: Introduction to Analysis,

Which classes they complete will depend on their background and their educational goals.

· 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.

Possible partial financial support

· Pending availability of funds, students with a strong undergraduate STEM background and demonstrated communication skills, may apply to receive Graduate or Teaching Assistantships to teach Developmental Math Courses as a means of receiving partial financial support for the

MA program and earn teaching experience. Preference will be given to the strongest academically prepared candidate(s).

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:

· a two-hour exam based on two semesters (six credits) of study in algebra, analysis, statistics, or differential equations (analytical and numerical)

· a one-hour exam based on one semester (three credits) of study in algebra, analysis, statistics, or differential equations (analytical or numerical)

The exams must be complementary so that the student will be tested in areas of both pure and applied mathematics.

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

· repeat that particular section of the examination on the next examination date or

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

Passing of appropriate certification exams (such as Society of Actuaries and Certified Financial Analyst professional exams) which cover the appropriate material can be considered as a substitute for one of, but not both, exams.

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

The comprehensive examination approach must be planned and agreed upon by the student and the graduate coordinator.

Thesis

In lieu of the two-hour exam, exceptional students (Graduate GPA>=3.75) may complete a thesis. They will still take the one-hour exam and the content of that exam must be complementary to the thesis so

that the student has demonstrated facility with both applied and pure mathematics. Students who publish an article in a peer-reviewed journal may submit the article for consideration for their thesis.

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

Master of Arts in Mathematics

The M.A. in Mathematics requires completion of 30 semester hours including 4 required courses (12 SH), 4 additional courses from our regular offerings (12 SH), and 2 additional courses from our regular offerings, special topics, or independent study (6 SH).

The Master of Arts in Mathematics degree program must be planned and agreed upon by the student and the graduate coordinator.

REQUIRED (12 SH)  
MAT 507    Applied Statistics I 3 SH
MAT 512    Group Theory 3 SH
MAT 514    Measure Theory and Integration 3 SH
MAT 568    Partial Differential Equations 3 SH
Regular Offerings (12-18 SH)  
MAT 505    Mathematical Logic 3 SH
MAT 508    Applied Statistics II 3 SH
MAT 513    Modern Algebra II 3 SH
MAT 518   Complex Analysis 3 SH
MAT 522    Advanced Geometry 3 SH
MAT 528    Number Theory 3 SH
MAT 529    Historical Development of Mathematics 3 SH
MAT 569    Numerical Methods for Ordinary and Partial Differential and Partial Differential Equations (OPDEs) 3 SH
MAT 570    Applications of Machine Learning and Wavelets 3 SH 
MAT 571    Functional Analysis 3 SH
Other (0-6 SH)  
MAT 540    Topics in Mathematics 3 SH
MAT 598    Faculty-Developed Study 3 SH
MAT 599    Student-Developed Study 3 SH

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

2 + 1 HR Comprehensive Exam __     OR   1 HR Comprehensive Exam ___ AND  Thesis 3 to 6 S.H.__