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Course Criteria
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3.00 Credits
GER 3/B Metric and topological spaces, continuity, homeomorphisms, compactness, connectedness, homotopy, fundamental group. prereq: MATH 351 3 hrs, 3 cr.
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3.00 Credits
GER 3/B Rigorous treatment of foundations of calculus, including topology of real line and higher dimensional spaces. Basic results on continuous functions. prereqs: MATH 156, 250, 260 3 hrs, 3 cr.
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3.00 Credits
GER 3/B Integration, sequences and series, uniform convergence, differentiation of functions of several variables, inverse and implicit function theorems, formula for change of variables. prereq: MATH 351 3 hrs, 3 cr.
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3.00 Credits
GER 3/B Complex numbers, analytic functions, elementary functions, contour integrals, Cauchy integral theory, series. prereqs: MATH 156, 255 3 hrs, 3 cr.
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3.00 Credits
GER 3/B Linear flows, qualitative theory of low-dimensional nonlinear systems, introduction to chaos in discrete one-dimensional dynamical systems. prereqs: MATH 250, 260 3 hrs, 3 cr.
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3.00 Credits
GER 3/B A survey of the central results and techniques of metalogic, principally mathematical induction, the soundness and completeness of theorems for first-order logic, the Skolem Theorem and Church's Theorem on undecidability. Cross-listed as PHIL 375. prereq: MATH 260 or perm instr. 3 hrs, 3 cr.
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3.00 Credits
GER 3/B Axiomatic approach to set theory: axiom of choice, Zorn's Lemma, transfinite arithmetic. prereqs: two of the following: MATH 260, 311, 351, 352 3 hrs, 3 cr.
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3.00 Credits
GER 3/B Study of such issues as the nature of demonstration or proof and the nature of mathematical knowledge and mathematical objects such as numbers and sets. Cross-listed as PHIL 376. prereqs: ENGL 120; one PHIL course; second course in PHIL or MATH ( precalculus or beyond) 3 hrs, 3 cr.
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3.00 Credits
GER 3/B Accuracy and precision, convergence, iterative and direct methods. Topics selected from: solution of polynomial equations and linear systems of equations, curve fitting and function approximation, interpolation, differentiation and integration, differential equations. prereq: MATH 250 and MATH 260 or permission of the instructor. 3 hrs, 3 cr.
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3.00 Credits
GER 3/B Open to Jr/Sr only. Independent study and reading under direction of faculty member. prereq: perm dept. 1-3 hrs, 1-3 cr.
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