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Course Criteria
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4.00 Credits
4 hours, 4 credits. Introduction to the ideas and methods of probability and statistical inference for students in mathematics and the sciences. Topics include confidence intervals, tests of significance, chi-square tests of goodness-of-fit and independence, regression analysis, and analysis of variance. Students will be introduced to a standard computer statistical package. PREREQ: MAT 176.
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4.00 Credits
4 hours, 4 credits. Basic probability theory. Combinatorial problems, distributions, expectation, law of large numbers and central limit theorem, Bernoulli processes, and Markov chains. Other topics from probability and statistics. PREREQ: MAT 176.
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3.00 Credits
3 hours, 3 credits. The syllabus of this course is continued in MAT 336. Calculus of variations, Lagrange's and Hamilton's formulations for mechanics, wave and heat equations, boundary-value problems, and solutions by separation of variables and special functions. Fourier series and integrals. PREREQ: MAT 226.
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3.00 Credits
3 hours, 3 credits. Continuation of MAT 335. Existence and uniqueness theorems for initial value problems in ordinary differential equations. Green's function, and eigenvalue problems; control theory. PREREQ: MAT 335.
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3.00 Credits
3 hours, 3 credits. The nature of mathematical proof, basic logic, and set theory. A rigorous construction of the natural numbers within set theory, of the rational numbers, and of the real numbers via Dedekind cuts or their equivalent. PREREQ: MAT 226 or MAT 314.
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4.00 Credits
4 hours, 4 credits. Study of the historical development of mathematics from ancient to modern times, including the contributions of underrepresented groups and diverse cultures. PREREQ: MAT 313.
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4.00 Credits
4 hours, 4 credits. Geometric theory from an axiomatic viewpoint motivated by Euclidean geometries and additional non-Euclidean examples. Emphasis on the relationship between proof and intuition. PREREQ: MAT 314.
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4.00 Credits
4 hours, 4 credits. Euclidean and non-Euclidean geometries approached from the points of view of axiomatics and transformation groups. PREREQ: MAT 314.
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3.00 Credits
3 hours, 3 credits. An introduction to the mathematical theory of games of strategy. Matrix games. Optimal strategies for zero-sum two-person games. Convex sets in Euclidean n-space, systems of linear inequalities, linear programming, and the simplex method. N-person games and non-zero-sum games. PREREQ: One course in linear algebra.
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4.00 Credits
4 hours, 4 credits. Conditions for optimization, classical inventory problems. Linear programming and its applications, including the transportation problem. Use of software packages for linear programming calculations. Probability, expectation, and risk. Portfolio selection. Stochastic processes and queues. Computer simulation of stochastic processes. PREREQ: MAT 174 (or 175), 301, and CIS 211. Note: Primarily for students in the Computing and Management major; not to be counted toward the Mathematics major.
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