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MAT 337: Introductory Modern Algebra II
3.00 Credits
University of North Carolina Wilmington
Prerequisite: MAT 336. Elementary properties of rings, integral domains, ideals, homomorphisms, quotient rings and fields. Rings of polynomials and factorization of polynomials over a field; unique factorization domains; Eisenstein's irreducibility criterion; field extensions; the isomorphism extension theorem; the primitive element theorem; geometric constructions by ruler and compass; introduction and illustrations of Galois theory.
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MAT 337 - Introductory Modern Algebra II
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MAT 345: Modern College Geometry
3.00 Credits
University of North Carolina Wilmington
Prerequisite: MAT 275 or consent of instructor. Use of elementary methods in advanced study of the triangle and circle, special emphasis on solving original examples, comparison of Euclidean and non-Euclidean and projective geometries.
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MAT 345 - Modern College Geometry
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MAT 346: Historical Development of Mathematics
3.00 Credits
University of North Carolina Wilmington
Corequisite: MAT 275 or consent of instructor. Development of mathematics from earliest systems to present century. Personalities involved with the contributions of each. A problem-study approach to give the student some training in research.
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MAT 346 - Historical Development of Mathematics
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MAT 361: Differential Equations
3.00 Credits
University of North Carolina Wilmington
Prerequisite: MAT 261. Theory, methods of solution, and applications of ordinary differential equations with emphasis on first order equations and linear equations. Additional topics from power series solutions, Laplace transforms, linear systems, and numerical methods.
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MAT 361 - Differential Equations
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MAT 365: Vector Calculus
3.00 Credits
University of North Carolina Wilmington
Prerequisite: MAT 261 and 335. A thorough study of differential and integral calculus of vector-valued functions of a vector variable. Jacobians, inverse and implicit function theorems, change of variables in multiple integrals; theorems of Green, Gauss, and Stokes; applications.
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MAT 365 - Vector Calculus
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MAT 367: Principles in Applied Mathematics
3.00 Credits
University of North Carolina Wilmington
Prerequisite: MAT 261; MAT 335 recommended. Fourier series and orthogonal functions; Fourier and Laplace transforms; elementary applications to differential equations and boundary value problems. Introduction to complex variables and residue theory.
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MAT 367 - Principles in Applied Mathematics
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MAT 375: Combinatorics
3.00 Credits
University of North Carolina Wilmington
Prerequisite: MAT 275 or CSC 133. Techniques for counting configurations of objects. Recurrence relations; principle of inclusion-exclusion; graphs, trees, and circuits. Additional topics chosen from Polya's Theorem, generating functions, and network flows.
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MAT 375 - Combinatorics
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MAT 395: Problem Solving in Mathematics
1.00 Credits
University of North Carolina Wilmington
Prerequisite: MAT 261. Introduction to various mathematical problems and methods. Examples selected from mathematics journals, the national Putnam Exam, and the VPI Regional Math Contest. Students present solutions in a public seminar. Solutions to journal problems are submitted for publication. Participation in problem competitions is encouraged. One hour each week. May be repeated once for credit.
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MAT 395 - Problem Solving in Mathematics
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MAT 411-412: Real Analysis
3.00 Credits
University of North Carolina Wilmington
Prerequisite: MAT 311 and 335. Advanced study of convergence, continuity, differentiation and integration in metric space. The real number system, basic topology, sequences and series; continuity, uniform continuity, theories of integration with an introduction to Lebesgue measure and related convergence theorems.
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MAT 411-412 - Real Analysis
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MAT 415: Introduction to Complex Variables
3.00 Credits
University of North Carolina Wilmington
Prerequisite: MAT 311 and 367 or 411. First study of functions of a complex variable. Algebra of complex numbers, elementary functions with their mapping properties; analytic functions; power series; integration, Cauchy's Theorem, Laurent series and residue calculus; elementary conformal mappings and boundary value problems.
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MAT 415 - Introduction to Complex Variables
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