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Upper Level MATH Courses


3 Credits

A study of theory and practice of mathematical proof and its foundations in symbolic logic and set theory. Applications to basic number theory and algebra.
Prereq:  MATH270

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MATH310-MATH FOUNDATIONS FOR PRIMARY TEACHERS II

3 Credits

A course aimed at improving problem-solving and basic mathematical skills while exploring geometric and algebraic concepts and the fundamentals of logical thinking. Open only to Primary Education majors.

Prereq: MATH110 or MATH140

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MATH320-NUMERICAL METHODS

3 Credits

A course aimed at examining various numerical approximation techniques: location of roots, interpolation, numerical differentiation, numerical integration, and solutions of systems of linear equations.

Prereq:  MATH270

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MATH340-GEOMETRY

3 Credits
A survey of Euclidean geometry with an introduction to non- Euclidean geometries. Additional topics include transformations and tessellations, constructions and analytical geometry.
Prereq: MATH300

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MATH350-INTRODUCTION TO NUMBER THEORY

3 Credits

This course provides an overview of the theory of real numbers (especially integers). Topics covered include divisibility, math- ematical induction, prime numbers, numerical functions, the algebra of congruence classes, the number theory of real numbers and Diophantine equations.

Prereq:  MATH300

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MATH360-PROBABILITY THEORY AND MATHEMATICAL STATISTICS I

3 Credits

A foundation for advanced work in Mathematics, Statistics and Probability Theory. Topics include laws of probability, combination probability; properties of set functions; random variables, functions of random variables; universal and multivariate distributions; random walks and Markov chains.

Prereq:  MATH259 and MATH270

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MATH370-ABSTRACT ALGEBRA I

3 Credits

This is the first of two courses in Abstract Algebra. Topics covered are: methods of proof; congruence; groups; homomorphism; rings; fields; integral domains; quotient groups; and polynomials in F[x] and their factorization.

Prereq:  MATH251

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MATH380-ADVANCED CALCULUS

3 Credits

This course is an intense study of the foundation of calculus. The topics include the real number system, continuity, differentiation, Riemann integration and sequences and series of real numbers. Students are exposed to the knowledge and technical expertise necessary for advanced studies in analysis and topology.
Prereq:  MATH280

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MATH390-DISCRETE MATHEMATICS/COMBINATORICS

3 Credits

This course comprises a study of the fundamentals of discrete mathematics and basic problems and techniques of combinatorics. Topics include basic counting principles, permutations and combi- nations, the principles of inclusion and exclusion, The Pigeonhole Principle, basic graph theory, trees and circuits, generating functions and recurrence relations and a survey of problems that illustrate the three main concerns of combinatorics.

Prereq:  MATH300

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MATH400-HISTORY AND DEVELOPMENT OF MATHEMATICS

3 Credits

A survey of the historical development of Mathematics over the centuries from origins in Egypt and Mesopotamia to the twentieth century. Research projects and presentations are integral components of the course.

Prereq:  MATH270

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MATH410-REAL ANALYSIS I

3 Credits

This is the first of two courses in Real Analysis. Topics covered are number systems; real Euclidean n-space; cardinal numbers; open, closed, compact and connected sets; sequences and series in Rn; Hausdorff spaces; metric spaces; continuity; uniform continuity; and equicontinuity.

Prereq:  MATH380

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MATH411-REAL ANALYSIS II

3 Credits

This is the second of two courses in Real Analysis for mathematics majors. Topics covered include derivatives, mapping theorems, the Riemann-Stieltjes integral, Lebesgue measure, measurable functions, the Lebesgue integral, Lp spaces, mean convergence and applications to Fourier series.

Prereq:  MATH410

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MATH420-THEORY OF COMPLEX VARIABLES

3 Credits

This course begins with the algebra and geometry of the complex number system and covers three major areas of complex calculus - differentiation, integration and infinite series. It also explores the relationships among properties of each of these areas.

Prereq:  MATH300

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MATH430-INTRODUCTION TO TOPOLOGY

3 Credits

This course introduces students to Point-Set Topology. The topics covered include open and closed subsets or “R”; topological spaces; homeomorphisms and embeddings; connectivity; closure and limit points; and compact sets.

Prereq:  MATH300

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MATH450-ADVANCED DIFFERENTIAL EQUATIONS

3 Credits

This course extends the theory of differential equations introduced in MATH 274 and explores additional solution techniques. Topics include systems of second order linear differential equations and eigenvalues; Fourier, Bessel and Legendre Series; the heat, wave, and Laplace equations; partial differential equations and boundary-value problems.

Prereq:  MATH251 and MATH274

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MATH470-ABSTRACT ALGEBRA II

3 Credits

The is the second of two courses in Abstract Algebra. Topics covered are: direct products; the Sylow Theorems, arithmetic in integral domains; field extensions; Galois theory; lattices and Boolean algebra.

Prereq:  MATH370

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