MATH 300      Linear Algebra I
Linear equations, matrix algebra, real vector spaces, linear transformations, determinants, eigenvalues and eigenvectors, orthogonality, and applications. Prerequisite: MATH 250, or Math 220 and Comp-Sci 191, or consent of the instructor.
Credits: 3 hours
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MATH 301      On Solid Ground: Sets And Proofs
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
Credits: 3 hours
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MATH 345      Ordinary Differential Equations
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.
Credits: 4 hours
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MATH 402      Advanced Analysis I
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
Credits: 3 hours
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MATH 406      Partial Differential Equations
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.
Credits: 3 hours
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MATH 407      Introduction To Complex Variables
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.
Credits: 3 hours
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MATH 410      Modern Algebra
Groups, rings, integral domains, fields and polynomial rings. Prerequisite: MATH 300 and MATH 301.
Credits: 3 hours
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MATH 412      Advanced Analysis II
Topics in advanced analysis such as sequences and series of functions, power series and elementary functions, Fourier series, metric spaces, analysis in Euclidean spaces, or advanced integration. Prerequisite: MATH 402 or consent of instructor.
Credits: 3 hours
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MATH 414      Mathematics For Secondary Teachers: Algebra And Analysis
Designed for secondary-school teachers. Examine high school mathematics from a higher point of view. Real and complex numbers, functions, algebraic structures of equations, integers and polynomials, number system structures; analyses of alternate approaches, extensions, and applications of mathematical ideas, discussion of historical contexts and connections between ideas that may have been studied separately in different courses, relationships of ideas studied in secondary-school to those students may encounter in later study. When taken for graduate credit as MATH 5514, an extra project is required. Prerequisites: MATH 300 and 301.
Credits: 3 hours
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MATH 420      Linear Algebra II
The topics of Math 300 are expanded and presented in the context of vector spaces over a field, with rigorous justification. Vector spaces and linear transformations, determinants, eigenvalues and eigenvectors, inner product spaces and orthogonality. Prerequisites: Math 300 and Math 301
Credits: 3 hours
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MATH 424      Mathematics For Secondary Teachers: Geometry
Designed for secondary-school teachers. Examine high school mathematics from a higher point of view. Congruence, distance and similarity, trigonometry, area and volume, axiomatics and Euclidean geometry; analyses of alternate approaches, extensions, and applications of mathematical ideas, discussion of historical contexts and connections between ideas that may have been studied separately in different courses, relationships of ideas studied in secondary-school to those students may encounter in later study. When taken for graduate credit as MATH 5524, an extra project is required. Prerequisite: MATH 300 and 301.
Credits: 3 hours
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MATH 430      Numerical Analysis I
Error analysis, solutions of equations of one variable, interpolation and polynomial approximation, numerical integration and differentiation, numerical solutions of initial-value problems. Prerequisite: MATH 250
Credits: 3 hours
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MATH 440      Numerical Analysis II
Direct and iterative methods for solving linear systems, introduction to approximation theory, approximating eigenvalues and eigenvectors, solution of systems of nonlinear equations. Prerequisites: MATH 300 and MATH 430, or consent of instructor.
Credits: 3 hours
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MATH 444      Modern Geometries
Modern axiomatic development of Euclidean geometry and neutral geometry, followed by examination of non-Euclidean geometries; geometric transformations, and other geometries as time permits. Satisfies a state requirement for teacher certification. Prerequisites: MATH 300 and MATH 301
Credits: 3 hours
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MATH 464WI      History Of Mathematics
Topics in the History of Mathematics from Babylonian times through the invention and consolidation of Calculus, with some modern subjects as time permits. The course will emphasize proofs, ideas, and arguments as given in original sources (in translation) from around the world and throughout history. In this writing intensive course, one or two term papers, in addition to several short essays and historical proof explications are required. A field trip will be taken to the Linda Hall Library Rare Book Room. This course is of special interest to secondary mathematics teachers as well as mathematics majors.
Credits: 3 hours
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MATH 490      Special Topics
Selected topics in various fields of mathematics. May be repeated for credit when the topic varies. Prerequisite: consent of instructor. On demand.
Credits: 1-3 hours
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