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Course Criteria
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3.00 Credits
Prerequisite: MATH 235 and MATH 236. This course studies selected topics from vector calculus, line and surface integrals, Fourier series and integrals, and partial differential equations. The emphasis is on engineering applications. Offered in the fall semester and in the spring on demand. 3 cr.
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3.00 Credits
Prerequisite: MATH 262 and CS 284, or permission of the instructor. This is a study of the mathematical background and methods needed in computer science especially in the specification, design, analysis, and verification of algorithms. Topics include predicate calculus, solution of recurrences, generating functions, finite state machines and formal languages, and introduction to computability and complexity. Offered in alternate fall semesters. 3 cr.
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3.00 Credits
Prerequisite: MATH 262 or MATH 282 or permission. A linear program (LP) calls for the optimization of a linear function subject to linear inequality constraints. This course studies the theory and applications of LPs. Topics include modeling using LPs, polyhedra, the simplex method, duality, parametric and sensitivity analysis, LP software, and applications to game theory, network flows, and statistics. Students will also read and report on recent journal articles describing applications of linear programming to the solution of real-world problems. Offered on demand. 3 cr.
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3.00 Credits
Prerequisite: MATH 262 or MATH 282 or permission. This is an examination of various topics in geometry. Topics selected depend on the interests of the instructor and the needs of the students involved. Possible topics include finite geometries, Euclid's Elements (Book I), advanced topics in Euclidean geometry, Euclidean constructions and impossible constructions, transformations of the plane, non-Euclidean geometry, and projective geometry. Offered in alternate spring semesters. 3 cr.
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3.00 Credits
Prerequisite: MATH 235. This is a calculusbased course in the theory of probability. Topics include sample spaces, combinatorics, axioms and rules of probability, conditional probability and independence, discrete and continuous random variables, mathematical expectation, and the moment generating function. Offered in alternate fall semesters. 3 cr.
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3.00 Credits
Prerequisite: MATH 372. This course and the prerequisite are intended to prepare students to take the actuarial exam on probability and statistics. Topics include sampling distributions of certain statistics, confidence intervals, tests of hypotheses, regression and correlation, goodness of fit tests, and Bayesian estimation. Offered in alternate spring semesters. 3 cr.
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3.00 Credits
Prerequisite: MATH 262 or MATH 282 or permission. The course will discuss creative problems from all areas of mathematics. Students will learn problem-solving techniques, will combine some of the seemingly disparate parts of their mathematics background, and will gain an appreciation of new areas of mathematics, by looking at some of the fundamental questions that illustrate the key ideas. There will be emphasis on student presentation and analysis of solutions, and students will learn how to present mathematical arguments while developing their mathematical creativity. Offered in alternate fall semesters. 3 cr.
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3.00 Credits
Prerequisite: MATH 262 or MATH 282 or permission. This is the study of integers and their properties. The course provides a simple account of classical number theory as well as some of its historical background including divisibility; gcds; prime factorization; congruencies; theorems of Wilson, Fermat, and Euler; pseudoprimes; multiplicative functions; and primitive roots. Other topics include recent applications of the classical subject area in cryptology and computer science. Offered in alternate spring semesters. 3 cr.
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3.00 Credits
Prerequisite: MATH 262 or MATH 282 or permission. Combinatorics concerns the mathematical theory of counting. This course emphasizes enumeration, but existence and construction issues will also be discussed. Topics include bijective functions, the pigeonhole principle, the theory of distributions, Stirling numbers, partition numbers, inclusion-exclusion, generating functions, recurrence relations, and Polya theory. Further topics will be selected from: partially ordered sets, combinatorial designs, Ramsey theory, and the applications of combinatorics to graph theory. Offered in alternate fall semesters. 3 cr.
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3.00 Credits
Prerequisite: MATH 262 or MATH 282 or permission. This is an introduction to graph theory and its applications through a modeling process. Topics include degrees, isomorphic graphs, trees, connectivity, traversability, matchings, planarity, coloring, digraphs, Ramsey Numbers, networks, and distance. Offered in alternate fall semesters. 3 cr.
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