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Course Criteria
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3.00 Credits
Bonin Introduction to combinatorial enumeration. Basic counting techniques, inclusion-exclusion principle, recurrence relations, generating functions, pigeonhole principle, bijective correspondences. Prerequisite: Math 71 or permission of instructor.
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3.00 Credits
Bonin Divisibility of integers, prime numbers, greatest common divisor, the Euclidean algorithm, congruence, the Chinese remainder theorem, number theoretic functions, M?bius inversion, Euler's phi function, and applications to cryptography and primality testing. Prerequisite: Math 71 or permission of instructor.
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3.00 Credits
Abrams, Schmitt Study of groups and associated concepts, including Lagrange's theorem, Cayley's theorem, the fundamental theorem of homomorphisms, and applications to counting. Prerequisite: Math 71 and 84 or permission of instructor.
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3.00 Credits
Abrams Study of rings, through maximal and prime ideals, and the study of fields, through Galois theory. Prerequisite: Math 121 or permission of instructor.
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3.00 Credits
Yi Theory of vector spaces, linear transformations, and matrices. Quadratic and bilinear forms. Characteristic polynomials and the Cayley-Hamilton theorem. Similarity and Jordan canonical form. Prerequisite: Math 71 and 84 or permission of instructor.
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3.00 Credits
Ullman Fundamental concepts, techniques, and results of graph theory. Topics include trees, connectivity, traversability, matchings, coverings, colorability, planarity, networks, and Polya enumeration. Prerequisite: Math 71 or permission of instructor.
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3.00 Credits
Bonin Projective spaces, projectivities, conics, pairs and pencils of conics, finite planes, coordinates, collineation, Desarguesian planes. Prerequisite: Math 120 or 121 or permission of the instructor.
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3.00 Credits
Junghenn A rigorous study of differentiation, integration, and convergence. Topics include sequences and series, continuity and differentiability of real-valued functions of a real variable, the Riemann integral, sequences of functions, and power series. Prerequisite: Math 32?and either 71 or 84 or permission of instructor.
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3.00 Credits
Ullman Continuation of Math 139. Topics include: topology of Rn, derivatives of functions of several variables, inverse and implicit function theorems, multiple integrals, generalized Stokes's theorem. Prerequisite: Math 33 and 139 or permission of instructor.
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3.00 Credits
Musielak, Ren A first course in ordinary differential equations with an emphasis on mathematical modeling: solution curves, direction fields, existence and uniqueness, approximate solutions, first and second order linear equations, linear systems, phase portraits, and Laplace transforms. Prerequisite: Math 32 and 84 or permission of instructor.
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