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Course Criteria
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3.00 Credits
Statistical models, estimation, hypothesis testing, optimality, linear models, analysis of discrete data, and nonparametric methods. Prerequisite: MATH 350.
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3.00 Credits
Principles of enumeration, finite difference calculus, generating functions, finite difference equations, principle of Inclusion and Exclusion, introduction to the theory of combinatorial graphs, and applications to computer science. Prerequisites: MATH 151 and 160, or consent of instructor.
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3.00 Credits
A study of the foundations of real analysis, including the calculus of functions of one and several variables, infinite processes, convergence theory, and selected topics of advanced undergraduate analysis. Prerequisites: MATH 160 and 250. (360: fall semester, every year; 361: spring semester, odd years)
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3.00 Credits
Analytic function theory; power series, analytic continuation, conformal mapping, and applications. Prerequisite: MATH 160 and 250, or consent of instructor.
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3.00 Credits
Divisibility, Euclidean algorithm, fundamental theorem of arithmetic, congruences, Fermat's theorem, Euler's function, Chinese Remainder Theorem, Diophantine equations, primitive roots, quadratic residues, reciprocity law, and continued fractions. Prerequisites: MATH 160 and 250, or consent of instructor. (spring semester, even years)
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3.00 Credits
An introduction to groups, rings, integral domains, division rings, fields, vector spaces, and algebras, and applications of these systems to other branches of mathematics. Prerequisites: MATH 160 and 250, or consent of instructor. (spring semester, odd years)
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3.00 Credits
An introduction to an area of modern geometry. The specific topic will be chosen from the following: non-Euclidean geometry, differential geometry, projective geometry, or metric geometry, and historical references. Prerequisites: MATH 160 and 250, or consent of instructor. (fall semester, odd years)
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3.00 Credits
Metric spaces, topologies, subspaces, continuity, separation axioms, compactness, and connectedness. Prerequisites: MATH 160 and 250, or consent of instructor. (spring semester, even years)
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3.00 Credits
Abstract structure of logical arguments, theory of the propositional and predicate calculus, and selected topics in modern logic. Prerequisites: MATH 160 and 250, or consent of instructor.
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1.00 - 3.00 Credits
This course is intended for students who enjoy the challenge of mathematical problems. This course differs from other mathematics courses which are focused on the theory and applications of a single branch of mathematics. It emphasizes problem-solving techniques, creative thinking, and exposition of skills in different areas of mathematics such as algebra, calculus, geometry, and number theory. Prerequisite: MATH 151. (fall semester, every year)
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