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Course Criteria
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4.00 Credits
Development of mathematics over four millennia. Recommended for students preparing to teach mathematics. 4 lecture. Prerequisite: C or better in MAT 215 or consent of instructor.
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4.00 Credits
Basic set theory and logic, relations, functions, mathematical induction, countable and uncountable sets. Emphasis on how to present and understand mathematical proof. 4 lecture/problemsolving. Prerequisite: C or better in MAT 116 or consent of instructor.
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4.00 Credits
Metric spaces and continuity. Analysis of functions of a single variable. Sequences, limits, continuity, differentiation, integration, introduction to function spaces. 4 lecture/problemsolving. Prerequisite for MAT 314: C or better in MAT 215 and MAT 310 or consent of instructor. Prerequisite for MAT 315: C or better in MAT 314 or consent of instructor.
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3.00 Credits
Introduction to Fourier Series and Integrals with applications. Elementary theory of Laplace transformation with applications including the solution of differential equations. 3 lecture/problemsolving. Prerequisite: C or better in MAT 216 or consent of instructor.
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3.00 Credits
Introduction to the algebra and calculus of vectors including the divergence and Stokes' theorem. Introduction to analytic functions of a complex variable. Not open to mathematics majors for math elective credit. 3 lecture/problemsolving. Prerequisite: C or better in MAT 215 or consent of instructor.
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4.00 Credits
Topology of the line and plane, topological spaces, continuity and topological equivalence and topics selected from the following: bases and subbases, metric and normed spaces, countability axioms, separation axioms, compactness, connectedness, product spaces, completeness and function spaces. 4 lecture/problemsolving. Prerequisite: C or better in MAT 310 or consent of instructor.
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4.00 Credits
Fundamentals of the system of integers, divisibility, congruences, theorems of Fermat and Wilson, power residues and indices, quadratic reciprocity, factorization techniques, diophantine equations, theorems of Euler, Gauss and Lagrange. Elementary results concerning the distribution of primes. 4 lecture/problemsolving. Prerequisite: junior standing or consent of instructor.
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4.00 Credits
Euclidean geometry using modern techniques of transformations, inversions. Extension of elementary geometry to elegant results on triangles, circles, polygons, famous theorems of geometry, unsolved problems. Introduction to deductive reasoning and techniques of proof. 4 lecture/problemsolving. Prerequisite: consent of instructor.
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4.00 Credits
The study of graphs, trees, Eulerian, Hamiltonian, planar graphs, connectivity, coloring, independence and covering numbers, directed graphs, theorems of Menger, Ramsey with applications. 4 lecture/problemsolving. Prerequisite: consent of instructor.
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4.00 Credits
Introduction to mathematics of linear programming (LP): algebra and geometry of simplex method, solution of LP problems by GaussJordan elimination method. Duality theory and sensitivity analysis. Development of revised and dual simplex algorithms. Introduction to parametric and separable convex programming. Applications of LP: computational considerations, case studies. 4 lecture/problemsolving. Prerequisites: C or better in MAT 208 and 215 or consent of instructor.
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