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Course Criteria
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3.00 Credits
Designed for elementary-and middle-school mathematics teachers. Elementary calculus, beginning with sequences and series, proceeding to functions, limits, continuity, differentiation and integration. Focus on concepts and applications with a discovery and inquiry approach. Prerequisites: Four units of high school mathematics including Trigonometry, or MATH 120, or MATH 110 and MATH 125. Offered: Winter 3 hrs
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4.00 Credits
Vectors, solid analytic geometry, vector functions and multiple variable functions, partial derivatives, multiple integrals, line and surface integrals with applications. Prerequisite: MATH 220. Fall, Winter, Summer 4 hrs
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3.00 Credits
Vectors, matrices, linear equations, matrix algebra, determinants, vector spaces, linear transformations, vector spaces with an inner product. Prerequisite: MATH 250, or consent of instructor Offered: Fall, Winter 3 hrs
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3.00 Credits
Transition to advanced mathematics, elements of set theory and cardinality of sets, logic, mathematical proof techniques, induction, functions, elementary proofs in various subjects such as algebra, number theory, calculus, and others as time permits. Satisfies a state requirement for teacher certification. Prerequisite: MATH 220 3 hrs
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4.00 Credits
First order equations, linear second order differential equations, Taylor series and power series solutions, Laplace transforms, elementary systems of differential equations, numerical methods, and Fourier series and boundary value problems. Prerequisite: MATH 250. Fall, winter, summer. 4 hrs
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3.00 Credits
Congruences and residue classes. The theorems of Euler and Fermat. Primitive roots and indices. Quadratic residues. The Legendre and Jacobi symbols, the law of quadratic reciprocity. Number theoretic functions: the Euler phi-function, the Moebius inversion formula. Quadratic forms. The approximation of irrationals by rationals. Prerequisite: MATH 301 3 hrs
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3.00 Credits
Numerical sequences and completeness of the real numbers, numerical series, continuity and differentiation of real-valued functions of a real variable, integration and the fundamental theorem of calculus. Prerequisite: MATH 250 and MATH 301 3 hrs
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3.00 Credits
Separation of variables, boundary value problems, Fourier series and integrals, wave equation, heat equation, potential equation, problems in several dimensions, and Bessel's differential equation. Prerequisite: MATH 345. Offered: Winter. 3 hrs
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3.00 Credits
Complex numbers, complex differentiation, elementary functions, contour integration and the Cauchy integral formula, Taylor series and Laurent series, residue calculus and its applications, and special functions. Prerequisites: MATH 250, and one of MATH 300, MATH 301, or MATH 345, with MATH 301 recommended Offered: Fall 3 hrs
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3.00 Credits
Groups, rings, integral domains, fields and polynomial rings. Prerequisite: MATH 300 and MATH 301. 3 hrs
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