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Course Criteria
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4.00 Credits
Lecture, 3 hours; discussion, 1 hour. Prerequisite(s): MATH 009B with a grade of "C-" orbetter or MATH 09HB with a grade of "C-" or better orequivalent. Introduction to first-order equations, linear second-order equations, and Laplace transforms, with applications to the physical and biological sciences. Courses numbered MATH 100-109 do not meet upper-division mathematics requirements.
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4.00 Credits
Lecture, 3 hours; discussion, 1 hour. Prerequisite(s): sophomore, junior, or senior standing. Examines contemporary instructional strategies relating to mathematics education. Includes thinking skills and problem solving strategies applicable to number theory, logic patterns and functions, statistics, probability, and geometry and algebra. Cross-listed with EDUC 104.
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4.00 Credits
Lecture, 3 hours; discussion, 1 hour. Prerequisite(s): CS 010; CS 011/MATH 011; MATH 009C or MATH 09HC. Study of discrete mathematical structures with emphasis on applications to computer science. Topics include asymptotic notation, generating functions, recurrence equations, elements of graph theory, trees, algebraic structures, and number theory. Cross-listed with CS 111.
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4.00 Credits
Lecture, 3 hours; discussion, 1 hour. Prerequisite(s): MATH 009A or MATH 09HA; CS 010 or MATH 009B or MATH 09HB. Introduction to the basic concepts of finite and structural mathematics with emphasis on applications to computer science. Topics include axiomatic systems, combinatorics, propositional and predicate calculi, graph theory, trees, state diagrams, networks, induction, elementary enumeration, and recurrence relations.
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5.00 Credits
Lecture, 3 hours; discussion, 2 hours. Prerequisite(s): concurrent enrollment in or completion of MATH 010A. Study of matrices and systems of linear equations, determinants, Gaussian elimination and pivoting, vector spaces, linear independence and linear transformation, orthogonality, eigenvalues, and eigenvectors. Also examines selected topics and applications. Integrates numerical linear algebra and extensive computer use with these topics. Credit is awarded for only one of MATH 113 or MATH 131.
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4.00 Credits
Lecture, 3 hours; discussion, 1 hour. Prerequisite(s): MATH 010A; MATH 113 or MATH 131 (may be taken concurrently). Introduction to classical optimization, including unconstrained and constrained problems in several variables, Jacobian and Lagrangian methods, and the Kuhn-Tucker conditions. Covers the basic concepts of linear programming, including the simplex method and duality, with applications to other subjects.
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4.00 Credits
Lecture, 3 hours; discussion, 1 hour. Prerequisite(s): MATH 010A. Games in extensive, normal, and characteristic form as models of conflict and/or cooperation. Two-person zero-sum games, minimax theorem, relation to linear programming. Non-zero-sum games, Nash equilibrium theorem, bargaining, the core, Shapley value. Economic market games.
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4.00 Credits
Lecture, 3 hours; discussion, 1 hour. Prerequisite(s): CS 111/MATH 111. A study of elements of combinatorics theory. Topics include chromatic polynomials, enumerating partitions of sets and integers, asymptotic enumeration, Polya theory, and Ramsey theory.
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4.00 Credits
Lecture, 3 hours; discussion, 1 hour. Prerequisite(s): concurrent enrollment in or completion of MATH 010A. An introduction to vector spaces, matrices, and linear transformations. Credit is awarded for only one of MATH 113 or MATH 131.
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4.00 Credits
Lecture, 3 hours; discussion, 1 hour. Prerequisite(s): MATH 113 with a grade of "C-" or better or MATH 131 with a grade of"C-" or better or equivalent. Further study of topics inlinear algebra, including eigenvalues. Exploration of Hermitian and unitary matrices, positive definite matrices, and canonical forms.
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