Taken Course History
MATH 431 Complex Analysis I
by pinarongan on Jun.14, 2010, under Taken Course History
Complex differentiation, Cauchy-Riemann equations, holomorphic functions, conformal mappings, contour integration, Cauchy’s theorem, Taylor and Laurent series, open mapping theorem, maximum modulus principle, applications of the residue theorem.
MATH 411 Mathematical Logic
by pinarongan on Jun.14, 2010, under Taken Course History
Prepositional and quantificational logic, formal grammar, semantical interpretation, formal deduction, completeness theorems, selected topics from model theory and proof theory.
MATH 343 Probability
by pinarongan on Jun.14, 2010, under Taken Course History
Sets and counting, probability and relative frequency, conditional probability, Bayes’ theorem, independence, discrete and continuous random variables, binomial, Poisson and normal distributions, functions of random variables, law of large numbers, generating functions, characteristic functions, moments, compound distributions, central limit theorems, Markov chains and their limiting probabilities.
MATH 336 Numerical Analysis
by pinarongan on Jun.14, 2010, under Taken Course History
Solutions of nonlinear equations, Newton’s method, fixed points and functional iterations, LU factorization, pivoting, norms, analysis of errors, orthogonal factorization and least square problems, polynomial interpolation, spline interpolation, numerical differentiation, Richardson extrapolation, numerical integration, Gaussian quadratures, error analysis.
MATH 333 Fourier Series
by pinarongan on Jun.14, 2010, under Taken Course History
Topics from the theory of integration, Fourier series, Dirichlet kernel and convergence tests, orthogonal families, convergence in the mean, Parseval’s equation, Fejér and Poisson kernels, applications.
MATH 332 Real Analysis II
by pinarongan on Jun.14, 2010, under Taken Course History
Sequences and series of functions, Arzelà-Ascoli theorem, Stone-Weierstrass theorem, Fourier series, inverse and implicit function theorems, integration.
MATH 331 Real Analysis I
by pinarongan on Jun.14, 2010, under Taken Course History
Metric spaces, convergence, completeness, continuity, compactness, connectedness, contraction mapping principle.
MATH 327 Number Theory
by pinarongan on Jun.14, 2010, under Taken Course History
Divisibility theory, Euclidean algorithm, congruences, solutions of polynomial congruences, primitive roots, power residues, quadratic reciprocity law, arithmetical functions, distribution of prime numbers, Pell’s equation, quadratic forms, some Diophantine equations.
MATH 322 Algebra II
by pinarongan on Jun.14, 2010, under Taken Course History
Vector spaces over an arbitrary field, linear independence and bases, linear transformations and matrices, fields, field extensions, algebraic extensions, Kronecker’s theorem, finite fields.
MATH 321 Algebra I
by pinarongan on Jun.14, 2010, under Taken Course History
Introduction to group theory, subgroups, Lagrange’s theorem, factor groups, permutation groups, group homomorphisms, isomorphism theorems, introduction to ring theory, ideals, ring homomorphisms, divisibility, polynomial rings, field of rational functions.