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MATH 441: Introduction to Probability
3.00 Credits
California State University-San Marcos
Discrete and continuous probability spaces, axiomatic formulation, combinatorics, conditional probability and independence, standard discrete and continuous probability distributions (including uniform, Bernoulli, binomial, Poisson, geometric, normal, and exponential), random variables, expectation and variance, joint distributions, limit theorems. Emphasis on modeling. Simple proofs required. Additional topics may include random walks, branching processes, and generating functions. Enrollment Requirement: MATH 162 with a grade of C (2.0) or better. Co/prerequisite: MATH 260.
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MATH 441 - Introduction to Probability
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MATH 442: Introduction to Mathematical Statistics
3.00 Credits
California State University-San Marcos
Data analysis and inferential statistics: random samples, estimation, sufficient statistics, confidence intervals, hypothesis tests, curve fitting, linear regression, least squares, goodness of fit. Covers both theory and applications, with emphasis on applications. Simple proofs required. Prerequisite: MATH 441 with a grade of C (2.0) or better.
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MATH 442 - Introduction to Mathematical Statistics
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MATH 464: Numerical Analysis and Computing
3.00 Credits
California State University-San Marcos
Computer arithmetic, solution of a single algebraic equation, solution of systems of equations interpolating polynomials, numerical integration, numerical solution of ordinary differential equations; error analysis and computational effort of numerical algorithms. Combines theoretical ideas with hands-on laboratory experience. Also offered as CS 464. Students may not receive credit for both. Enrollment Requirement: CS 111 and MATH 162.
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MATH 464 - Numerical Analysis and Computing
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MATH 470: Introduction to Abstract Algebra
3.00 Credits
California State University-San Marcos
An introduction to the theory of groups, rings, and fields, with abstract ideas reinforced by concrete and important examples, such as permutation groups, polynomial rings, and finite fields. The power of the axiomatic systems introduced will be illustrated via several applications to concrete and classical problems. Prerequisite: MATH 378 with a grade of C (2.0) or better.
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MATH 470 - Introduction to Abstract Algebra
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MATH 472: Introduction to Graph Theory
3.00 Credits
California State University-San Marcos
Fundamental concepts of undirected and directed graphs, trees, connectivity and traversability, planarity, colorability, networks, matchings; emphasis on modern applications. Prerequisite: MATH 350 or 370 with a grade of C (2.0) or better.
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MATH 472 - Introduction to Graph Theory
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MATH 474: Introduction to Combinatorics
3.00 Credits
California State University-San Marcos
Introduction of the basic tools of combinatorics and their applications. Permutations, combinations, occupancy problems, generating functions, recurrences, inclusion/ exclusion, graph theory, pigeonhole principle, experimental design, coding theory. Prerequisite: MATH 350 or 370 with a grade of C (2.0) or better.
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MATH 474 - Introduction to Combinatorics
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MATH 480: Introduction to Optimization
3.00 Credits
California State University-San Marcos
Modern study of linear programming with an emphasis on model formulation, solution, and interpretation of software output. Applications in work-scheduling, diet, capital budgeting, blending, production process, transportation, assignment, transshipment, and flow problems. Programming methods include the simplex method and its specialized variations, Big M Method, goal programming, and integer programming. Theoretical aspects include optimality conditions, sensitivity analysis, and duality. Requires using industry-standard software to strengthen the ideas and concepts. Also offered as CS 480. Students may not receive credit for both. Prerequisite: MATH 374.
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MATH 480 - Introduction to Optimization
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MATH 490: Senior Seminar
3.00 Credits
California State University-San Marcos
Presentation and discussion of selected areas of mathematics in order to supplement available offerings. Sample areas include differential forms, complex variables, partial differential equations, a second course in analysis, abstract algebra, or discrete math. May be repeated twice as course content changes, with consent of the program, for a maximum of nine (9) units of credit from MATH 490 and 491. Enrollment Requirement: Twelve (12) units of upper-division mathematics. Other requirements to be determined by instructor.
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MATH 490 - Senior Seminar
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MATH 491: Senior Seminar with Lab
3.00 Credits
California State University-San Marcos
Presentation and discussion of selected areas of mathematics in order to supplement available offerings. Sample areas include mathematical modeling and a second course in numerical analysis, optimization or statistics. This course meets for four hours per week. May be repeated for a maximum of nine (9) units of credit for MATH 490 and 491. Enrollment Requirement: Twelve (12) units of upper-division mathematics. Other requirements to be determined by instructor.
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MATH 491 - Senior Seminar with Lab
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MATH 495: Internship in Mathematics
1.00 - 3.00 Credits
California State University-San Marcos
Faculty-sponsored academic internship in business, industrial, government, research firm, or university labs and centers. Enrollment restricted to students who have obtained consent of instructor.
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MATH 495 - Internship in Mathematics
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