Two-hour presentation required.
Partial differentiation, implicit functions, exponential and logarithmic functions, extrema, optimization, constrained optimization. Magnetostatic equilibria and stability.Lecture, three hours. May be repeated for credit. Universal enveloping algebra.
Cohomology of Lie algebras. Variable content may include Abelian varieties, invariant theory, Hodge theory, geometry over finite fields, K-theory, homotopical algebra, and derived algebraic geometry. Two-hour presentation required. Click the button below to take our survey. Requisite: course 31A with grade of C- or better. Theorems of Weyl, Levi-Mal'cev. Professor, Mathematics/Computer Science/Electrical Engineering/Chemical & Biomolecular … Analytic continuation.
Requisites: courses 210A, 210B, 210C. S/U or letter grading.Seminar, three hours. Enforced requisites: courses 33A, and 170A or 170E or Statistics 100A. Normal families. Students can enroll in individual courses or apply to a certificate program while completing their coursework. Kernel theorem. Proper and finite morphisms. May not be repeated. P/NP or letter grading.Discussion, one hour. Basic characterizing postulates; development of a logical structure of theorems. Introduction to K-12 mathematics activity in U.S. Cultivation of interest in teaching through exploration of sequences of mathematical content and habits of mind taught in K-12. P/NP or letter grading.Lecture, three hours; discussion, one hour. Introduction to mathematical logic, aiming primarily at completeness and incompleteness theorems of Gödel. P/NP grading.
Students practice and evaluate communication skills.
P/NP grading.Lecture, three hours. May be repeated for credit with consent of instructor. Baroclinic instability, Eady model. We partner with these entities to provide rich and transformative Mathematical experiences in urban schools. Numerical solution for systems of ordinary differential equations; initial and boundary value problems. Not open for credit to students with credit for course 110A. Requisite: course 275C. Cohomology of Lie algebras. Cauchy integral formula and residue calculus. and continuous (exponential, gamma, chi-square, normal) distributions, bivariate distributions, distributions of functions of random variables (including moment generating functions and central limit theorem). Basic measure theory. P/NP or letter grading.Lecture, three hours; discussion, one hour. Introduction to numerical methods with emphasis on algorithms, analysis of algorithms, and computer implementation issues.
Requisites: courses 33A, 33B, 131A. Infinite products. S/U grading.Seminar, two hours. Requisite: course 225A. May not be applied toward MA degree requirements.Prerequisite: bachelor's degree in mathematics or equivalent. Discussion of classical numerical algorithms and novel parallel algorithms.
Topics include representation theory, transfer theory, infinite Abelian groups, free products and presentations of groups, solvable and nilpotent groups, classical groups, algebraic groups.Lecture, three hours. Numerical solution for elliptic, parabolic, and hyperbolic partial differential equations. Emphasis on practice of programming rather than problem solving or fundamental algorithms.
Limited to students in College Honors Program. Requisites: courses 110A (or 117), 120A (or 123), and 131A, with grades of C- or better. Fourier inversion formula, Plancherel theorem, convergence of Fourier series, convolution.
Primality testing and factorization methods. Topics include qualitative theory of differential equations, bifurcation theory, and Hamiltonian systems; differential dynamics, including hyperbolic theory and quasiperiodic dynamics; ergodic theory; low-dimensional dynamics. Derivatives, Riemann integral, sequences and series of functions, power series, Fourier series. Direct methods for solving linear systems. Math 195 -- Community Internships in Mathematics Education
S/U or letter grading.Lecture, three hours; discussion, one hour. Topics include model formulation, data visualization, nondimensionalization and order-of-magnitude physics, introduction to discrete and continuous dynamical systems, and introduction to discrete and continuous stochastic models. The UCLA Math Project is seeking your input on Professional Development for the 2020-2021 academic year. Harmonic functions. May be repeated for credit. Introduction to basic formulas and calculation procedures of complex analysis of one variable relevant to applications.