WCSU Graduate Catalog 2023-2024

Mathematics

 

MAT 505 Mathematical Logic    3 SH

An introduction to mathematical logic, including sentential logic and first-order logic. Soundness, completeness, and compactness of sentential and first-order logic. Expressing properties of various mathematical structures with first-order languages. Applications of compactness. Prerequisite: MAT 375 or equivalent

MAT 507 – 508 Applied Statistics I, II    3 SH each

Topics will be taken from both descriptive and inferential statistics. These include estimation, hypothesis testing, simple- and multiple-regression analysis, analysis of variance, and one or more multivariate techniques such as factor, cluster, discriminant, or principal components analysis. Applications from a range of subject areas from the behavioral to the physical sciences will be given. Computer statistical packages will be used throughout both semesters. Prerequisite: MAT 120 or equivalent.

MAT 512 Group Theory
   3 SH 

Groups are one of the fundamental mathematical objects that help us to understand how and why things work as they do in mathematics. They are significant in their own right, but are also important in applications of mathematics to physics, chemistry, and information security. As such, students can greatly benefit from a clear understanding of their properties and structures. Prerequisite: MAT 375: Algebraic Structures, or equivalent.

MAT 513 Rings, Fields, and Galois Theory
   3 SH 

In this course, we examine rings, fields, field extensions, and vector spaces. Using these, we will study the Fundamental Theorem of Galois Theory in order to why some polynomials admit general solutions while others do not. Along the way we will also examine, rational, irrational, transcendental, constructible, and non-constructible numbers. Prerequisite: MAT 512: Group Theory or equivalent.

MAT 514 Measure Theory and Integration     3 SH 

A first graduate course in Real Analysis. General theory of measure and Lebesgue integration, and Lp-spaces. Prerequisite: MAT 383 or equivalent

MAT 518 Complex Analysis I    3 SH

Complex number systems and properties of such, continuity, differentiability, analyticity, line integration, and power series. Residues and poles, conformal mapping, analytic continuation and the well-known classical theorems associated with the theory of complex analysis.

MAT 522 Advanced Geometry     3 SH

A second course in geometry focusing on axiomatic systems and non-Euclidean geometric systems. Topics covered include finite geometry, affine geometry, transformational geometry, analytic geometry, hyperbolic geometry and projective geometry. Proof and explanation are emphasized throughout. Prerequisite: Admission to MA program in Mathematics, MAT 207 and MAT 3xx or equivalent. Offered spring semester in odd years. Prerequisites: Admission to the MA Program in Mathematics, MAT 207 and MAT 3xx Axiomatic Geometry (or equivalent) or permission of the instructor.

MAT 528 Number Theory     3 SH

This course will give a broad overview of the fundamental ideas in number theory and examine a handful of applications.

MAT 529 Historical Development of Mathematics    3 SH

In this course we will examine significant moments in the development of key areas of mathematics. Particular emphasis will be placed on understanding contributions from a variety of cultures and time periods, as well as from significant individuals. Prerequisite: Successful completion of at least one 200-level math class or Equivalent, this course is not open to students who have completed MAT 429.

MAT 540 Topics in Mathematics    3 SH

This course offers an opportunity for students to pursue in greater depth topics introduced in other courses or topics not included in other courses. The topic varies from year to year and from student to student. Typical subjects might include mathematical models, combinatorics, field theory, algebraic topology, decision theory, and harmonic analysis or applications.

MAT 568 Partial Differential Equations    3 SH

This course is a comprehensive introduction to solution methods for partial differential equations. Advanced solution methods for ordinary differential equations, primarily for use in constructing solutions to partial differential equations, will also be discussed. Students will be introduced to a variety of partial differential equations of various orders and types. Fundamental analytical solution methods for partial differential equations will be discussed. Students will also be exposed to the occurrence and use of partial differential equations in various real-world applications. Appropriate technology will be used throughout the course as an aid in visualizing solutions, and to reinforce material learned in the course. Prerequisite(s): MAT 281 and MAT 282 with a grade of C or better. MAT 383 highly recommended.

MAT 569 Numerical Methods for Ordinary and Partial Differential Equations (OPDEs)    3 SH

The course will cover the development, analysis, and application of efficient and stable numerical methods to ordinary and partial differential equations that arise in a wide range of science, including meteorology; business; and engineering applications. Prerequisite(s): MAT 281 and MAT 282 with a grade of C or better.

MAT 570 Applications of Machine Learning and Wavelets    3 SH

The study of various transforms and their use in wavelet analysis and machine learning. This course will provide a foundation for wavelet analysis and machine learning techniques. The purpose of this course is to prepare students to apply relevant tools from wavelet analysis and machine learning to a variety of real-world problems and to prepare them to apply these tools for future use in their career, for instance, in graduate school / industry. Prerequisite(s): MAT 332 with a grade of C or better.

MAT 571 Functional Analysis    3 SH

This course provides a thorough introduction to the foundations of functional analysis in normed linear spaces. The course will include a treatment of both Banach and Hilbert spaces. Fundamental theorems including but not limited to the “Big theorems” of functional analysis such as the Hahn-Banach theorem, Baire category theorem, uniform boundedness theorem, open mapping theorem, and closed graph theorem as well as their applications will be discussed. Linear operators including bounded, compact, and self-adjoint operators will be defined and their spectral properties will be explored. Prerequisite(s): MAT 272 and MAT 383 with a grade of C or better.

MAT 591 Independent Thesis Research in Mathematics/Mathematics Education    0-6 SH

This course is designed for students fulfilling the thesis requirements for the M.A. in Mathematics degree. The submitted topic and outline for the thesis must be approved by the adviser, the department graduate committee, and the Dean of Arts and Sciences prior to registration for the course. The student will be required to work independently on the thesis research and writing. Credit for the thesis will be awarded upon the submission of one copy of the approved final draft of the thesis and thesis abstract. Prerequisite:s ED 501 and permission of the department and the Dean of Arts and Sciences.

MAT 592 Independent Thesis Research in Mathematics    0-6 SH

This course is designed for the student fulfilling the requirements for the Master of Arts in Mathematics. The student must submit an acceptable thesis topic and outline in mathematics, and the student will be required to work independently on the thesis research and writing in consultation with the thesis advisor. Credit for the thesis will be awarded upon the submission of one copy of the approved thesis and abstract. Prerequisite: permission of the thesis adviser and the Dean of Arts and Sciences.

MAT 598 Faculty-Developed Course

This experimental course is offered by the Mathematics Department as a means of determining its value to the total department program or in response to a particular request from a group of students.

MAT 599 Student-Developed Study

This vehicle is designed to provide the student with an opportunity to develop his/her own learning experience. A student will design a project and secure a faculty sponsor. The vehicle may be utilized more than once. Prerequisite: written permission of faculty sponsor and department. Registration through the Division of Graduate Studies Office is required.