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Course Criteria
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3.00 Credits
Goal To study the algebraic properties of groups and rings by means of a rigorous axiomatic approach, focusing on the use of logic and on various methods of proof. Content A study of groups, subgroups, rings, ideals, domains, unique factorization domains, and ideal domains. Taught Fall. Alternate years. Prerequisite MAT 210. Credit 3 hours.
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3.00 Credits
Goal To continue the study of algebraic properties of rings and fields. To expand understanding and use of various methods of proof. To prepare students for graduate level mathematics. Content A study of fields, modules, and Galois theory. Taught Spring. Alternate years. Prerequisite MAT 311. Credit 3 hours.
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3.00 Credits
Goal To examine the properties of Euclidean geometry. To survey the properties of non-Euclidean geometry. Content A rigorous study of the properties of Euclidean geometry and an introduction to the elementary properties of non-Euclidean geometries. Taught Offered occasionally. Prerequisites MAT 205 and 206. Credit 3 hours.
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3.00 Credits
Goal To study and extend the concepts of linear algebra in a more rigorous manner. Content Theory of linear transformations, vector spaces, and eigenvalues and eigenvectors; Cayley-Hamilton Theorem, diagonalization, similar matrices. Taught Spring. Alternate years. Prerequisites MAT 208, MAT 210. Credit 3 hours.
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3.00 Credits
Goal To provide an opportunity to examine in greater depth an area of higher mathematics. Content An in-depth examination of an area in advanced mathematics. The topics covered will vary from time to time and a student may take no more than two such special topics courses. Representative special topics include graph theory, combinatorics, history of mathematics, and fractal geometry. Taught Offered occasionally. Prerequisite Permission of instructor. Credit 3; 3 hours.
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3.00 Credits
Goal To examine more intensively topics presented in the calculus sequence, focusing on the roles of rigorous proof and logic. Content A study of the algebraic and topological properties of the ordered field of real numbers, sets, functions, limits, continuity, differentiation, and integration. Taught Fall. Alternate years. Prerequisite MAT 205-208. Credit 3 hours
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3.00 Credits
Goal To extend the concepts and techniques presented in MAT 401. To extend the calculus sequence to functions of several variables. To prepare students for graduate level mathematics. Content A study of the analytical properties of functions of several real variables, including differentiation, the inverse function theorem, integration, simplexes, and chains. Taught Spring. Alternate years. Prerequisites MAT 210 and 401. Credit 3 hours.
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3.00 Credits
Goal To provide an opportunity for students to make connections between mathematics and other disciplines. To enable each student to analyze and adopt a particular model and to present her results in a public forum. Content An introduction to mathematical modeling and computer simulation of real-world phenomena, with special attention paid to the initial formulation of the model, the computer implementation of the model, and the interpretation of the mathematical or numerical results. The topics covered will include optimization models, dynamic models, and probability models while real-world phenomena will be drawn from such disciplines as biology, economics, chemistry, physics, political science, psychology, and sociology. Taught Spring. Alternate years. Prerequisites MAT 205-208, MAT 210, MAT 300, PHY 121, or permission of the instructor. Credit 3 hours. This course may be taken to fulfill the requirement for the senior integrative experience in Physics.
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3.00 Credits
Goal To provide a capstone experience for mathematics majors and to further prepare students for graduate level study by exploring topics in set theory and metric spaces from contemporary, historical, and philosophical viewpoints. Content Rigorous development of the real number system. Dedekind cuts, Cantorian set theory, transfinite numbers, Axiom of Choice, well-ordering principle, Zorn's Lemma, Russell's paradox, basic properties of metric spaces, andfractal geometry. Taught Spring. Alternate years. Prerequisites MAT 311 or 401. Credit 3 hours; S-course.
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3.00 Credits
Goal To study basic mathematical theory, methods, and techniques in probability and statistics, and to examine applications. Content A calculus-based treatment of discrete and continuous probability distributions and their applications, including the binomial, hypergeometric, Poisson, uniform, geometric, and normal distributions. Hypothesis testing and chi-square tests. Taught Fall. Alternate years. Prerequisite MAT 206. Credit 3 hours. This course may be taken to fulfill the requirement for the senior integrative experience in Physics.
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