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MATH 540A: Abstract Algebra I
3.00 Credits
California State University-Los Angeles
Prerequisite: MATH 444. Group theory including symmetric groups; group actions on sets; Sylow theorems and finitely generated abelian groups; ring theory including polynomial rings, division rings, Euclidean domains, principal ideal domains and unique factorization domains. Letter grade only (A-F). (Lecture 3 hrs.)
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MATH 540A - Abstract Algebra I
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MATH 540B: Abstract Algebra II
3.00 Credits
California State University-Los Angeles
Prerequisite: MATH 540A. Modules; Field extensions; Finite fields; Splitting fields, Galois theory. Commutative ring theory including chain conditions and primary ideals. Topics of current interest. Letter grade only (A-F). (Lecture 3 hrs.)
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MATH 540B - Abstract Algebra II
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MATH 560A: Functional Analysis I
3.00 Credits
California State University-Los Angeles
Prerequisites: MATH 247, 361B. Linear spaces, metric and topological spaces, normed linear spaces; four principles of functional analysis: Hahn-Banach, Open Mapping, Uniform Boundedness, and Closed Graph theorems; adjoint spaces; normed space convergence, conjugate spaces, and operator spaces; Banach Fixed Point theorem; Hilbert spaces. Letter grade only (A-F). (Lecture 3 hrs.)
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MATH 560A - Functional Analysis I
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MATH 560B: Functional Analysis II
3.00 Credits
California State University-Los Angeles
Prerequisite: MATH 560A or consent of instructor. Spectral theory of operators on normed spaces; special operators; elementary theory of Banach algebras; selected topics from applied functional analysis. (Lecture 3 hrs.)
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MATH 560B - Functional Analysis II
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MATH 561A: Real Analysis I
3.00 Credits
California State University-Los Angeles
Prerequisite: MATH 361B. Theory of measure and integration, focusing on the Lebesgue integral on Euclidean space, particularly the real line. Modes of convergence. Fatou's Lemma, the monotone convergence theorem and the dominated convergence theorem. Fubini's theorem.Letter grade only (A-F). (Lecture 3 hrs.)
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MATH 561A - Real Analysis I
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MATH 561B: Real Analysis II
3.00 Credits
California State University-Los Angeles
Prerequisite: MATH 561A or consent of instructor. Lp spaces of functions. Holder's inequality. Minkowski's inequality. Norm convergence, weak convergence and duality in Lp. Further topics from convergence of Fourier series, measure-theoretic probability, the Radon-Nikodym theorem; other topics depending on time and interest.Letter grade only (A-F). (Lecture 3 hrs.)
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MATH 561B - Real Analysis II
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MATH 562A: Complex Analysis I
3.00 Credits
California State University-Los Angeles
Prerequisite: MATH 361B. (MATH 461 is recommended.) Axiomatic development of real and complex numbers; elements of point set theory; differentiation and analytic functions, classical integral theorems; Taylor's series, singularities, Laurent series, calculus of residues. Letter grade only (A-F). (Lecture 3 hrs.)
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MATH 562A - Complex Analysis I
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MATH 562B: Complex Analysis II
3.00 Credits
California State University-Los Angeles
Prerequisite: MATH 562A. Multiple-valued functions, Riemann surfaces; analytic continuation; maximum modulus theorem; conformal mapping with applications, integral functions; gamma function, zeta function, special functions. Letter grade only (A-F). (Lecture 3 hrs.)
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MATH 562B - Complex Analysis II
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MATH 563: Applied Analysis
3.00 Credits
California State University-Los Angeles
Prerequisites: MATH 361B. Hilbert Spaces, Lp spaces, Distributions, Fourier Transforms, and applications to differential and integral equations from physics and engineering. (Lecture 3 hrs.)
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MATH 563 - Applied Analysis
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MATH 564: Applied Nonlinear Ordinary Differential Equations
3.00 Credits
California State University-Los Angeles
Prerequisites: MATH 361B; 364A or 370A. Stability and asymptotic analysis, Perturbation methods, Phase plane analysis, Bifurcation, Chaos, Applications to science and engineering. (Lecture 3 hrs.)
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MATH 564 - Applied Nonlinear Ordinary Differential Equations
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