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Course Criteria
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3.00 Credits
A course in ordinary differential equations utilizing concepts and techniques from Calculus I, II, and Linear Algebra. Emphasis is on solution to higher order linear equations. First order topics include: separation of variables, exact equations, integrating factors, and homogenous and nonhomogenous systems with applications to networks. Higher order topics include: a detailed study of solutions to second order linear equations by reduction of order, variation of parameters, and series solutions; linear independence of solutions, the Wronskian, general solution to linear homogenous and nonhomogenous equations, and linear equations with constant coefficients. Special topics include: nonlinear equations, Laplace transform method, and numerical methods of solution. It is recommended that MATH 3305 be taken prior to MATH 3307. Pre: MATH 2215 or higher except MATH 2326/MATH 3301.
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3.00 Credits
This course is designed to improve students' problem solving skills for solving both traditional and nontraditional mathematics problems. Reasoning, communicating mathematics, mathematical representations, and connections between various mathematical topics will be emphasized. Pre: MATH 3301.
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3.00 Credits
To provide students with a solid background in set theory and to develop mathematical sophistication in general, this is a course in which covers ZF (Zermelo Frankel Axioms) and ZFC (ZF + the Axiom of Choice), DeMorgan's laws, Power Set, Set Algebra, Zorn's Lemma and other equivalent versions of AC, equivalence relations, well orderings and partial orderings, bijections, Russell's paradox, confinal maps, mathematical induction, transfinite induction, ordinals and cardinals, ordinal and cardinal arithmetic, the Continuum Hypothesis, and the Constructible Universe. Pre: MATH 3301.
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3.00 Credits
An introduction to algebra as a deductive system. Topics include: complex numbers; well ordering; groups; cyclic groups; permutation groups; rings; equivalence relations; polynomial rings; division algorithm; unique factorization; zeros of polynomials. Pre: MATH 3305 or higher
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3.00 Credits
An introduction to the theory of real analysis. Topics include: completeness of the real numbers; basic topology of the real numbers; continuous functions and compactness; sequences and series; limits; derivatives; mean value theorems; the Riemann integral; Taylor's formula; power series; uniform convergence. Pre: MATH 3307 or higher
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3.00 Credits
Discrete and continuous probability with applications. Topics include: finite sample spaces; combinations and permutations; conditional probability; independent events; discrete random variables; continuous random variables; functions of random variables; higher-dimensional random variables; expectation; variance; correlation coefficient; generating function; reproductive properties; sequences of random variables; law of large numbers; central limit theorem. Pre: MATH 2215 or higher except MATH 2326/MATH 3301.
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3.00 Credits
Introduction to probability and probability distributions including techniques for finding expected values and variance of discrete and continuous variables. Certain distributions and their properties are examined to establish their application to applied statistical methods. The course provides a calculus-based foundation to probability and statistics. Pre: MATH 2214 or higher except MATH 2326/MATH 3301.
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3.00 Credits
The purpose of numerical analysis is two-fold: (1 credit) to find acceptable approximate solutions when exact solutions are either impossible or impractical, and (2 credits) to devise alternate methods of solution better suited to the capabilities of computers. Topics for this course include: elements of error analysis, real roots of an equation, polynomial approximation by finite difference and least square methods, interpolation, quadrature, numerical solution of ordinary differential equations, and numerical solutions of systems of linear equations. Students should expect to program a computer and use a graphing calculator. Pre: MATH 3305, MATH 3307 (can be taken concurrently), and CSCI 2911.
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1.00 - 3.00 Credits
See Internships page 393.
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1.00 - 3.00 Credits
See Internships page 393.
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