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Course Criteria
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3.00 Credits
Lec. 3. Credit 3. Prerequisite: C or better in MATH 2110 . Complex numbers, calculus of complex variables, analytic functions, Cauchy’s Theorem, series, the Residue Theorem, and applications.
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1.00 - 3.00 Credits
Credit 1-3. Prerequisite: Consent of instructor. Readings and study under the supervision of a qualified staff member.
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3.00 Credits
Lec. 3-3. Credit 3-3. Prerequisite: C or better in MATH 2010 or equivalent and C or better in MATH 3400 . Groups and subgroups including cyclic abelian, finite; permutation groups, group homomorphisms, cosets and Lagrange’s Theorem, normal subgroups and factor groups. Rings including integral domains, unique factorization domains and Euclidean domains, ideals and factor rings, ring homomorphisms, fields and their extensions, geometric constructions.
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3.00 Credits
Lec. 3-3. Credit 3-3. Prerequisite: C or better in MATH 4010 . Groups and subgroups including cyclic abelian, finite; permutation groups, group homomorphisms, cosets and Lagrange’s Theorem, normal subgroups and factor groups. Rings including integral domains, unique factorization domains and Euclidean domains, ideals and factor rings, ring homomorphisms, fields and their extensions, geometric constructions.
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3.00 Credits
Lec. 3. Credit 3. Prerequisite: C or better in MATH 3400 or consent of instructor. Properties of integers, division algorithms, prime numbers, diophantine equations, and congruences.
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3.00 Credits
Lec. 2. Rec. 2. Credit 3. Prerequisite: C or better in MATH 3400 or consent of instructor. Rigorous treatment of functions of one and several variables, improper integrals, sequences, infinite series, uniform convergence, and applications. Students are expected to improve their ability to work in an abstract setting using precise definitions and formal proofs and to present their work in class.
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3.00 Credits
Lec. 2. Rec. 2. Credit 3. Prerequisite: C or better in MATH 4110 (5110) . Rigorous treatment of functions of one and several variables, improper integrals, sequences, infinite series, uniform convergence, and applications. Students are expected to improve their ability to work in an abstract setting using precise definitions and formal proofs and to present their work in class.
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3.00 Credits
Lec. 3. Credit 3. Prerequisite: C or better in MATH 1920 . Iterative methods for nonlinear equations, computational error analysis, convergence of iterative techniques, interpolation, numerical differentiation and integration, approximate solutions of initial-value problems, boundary-value problems, and nonlinear systems, and direct and iterative methods for linear systems.
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3.00 Credits
Lec. 3. Credit 3. Prerequisite: C or better in MATH 2120 or consent of instructor. Iterative methods for nonlinear equations, computational error analysis, convergence of iterative techniques, interpolation, numerical differentiation and integration, approximate solutions of initial-value problems, boundary-value problems, and nonlinear systems, and direct and iterative methods for linear systems.
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3.00 Credits
Lec. 3. Credit 3. Prerequisite: C or better in MATH 2110 and MATH 2120 . Systems of ordinary differential equations, matrix methods, approximate solutions, stability theory, basic theory of nonlinear equations and differential systems, trajectories, phase space stability, and construction of liapunov functions.
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