Pre-requisite: MATH 115A.
Ring of integers, integral domains, fields, polynomial domains, unique factorization.
Pre-requisite: MATH 32B, 33B.
Rigorous introduction to foundations of real analysis; real numbers, point set topology in Euclidean space, functions, continuity.
Pre-requisite: MATH 31A.
Introduction to differential calculus of several variables, vector field theory.
Pre-requisite: MATH 32B, 33B.
Introduction to basic formulas and calculation procedures of complex analysis of one variable relevant to applications. Topics include Cauchy/Riemann equations, Cauchy integral formula, power series expansion, contour integrals, residue calculus.
Pre-requisite: Successful completion of Mathematics Diagnostic Test.
Differential calculus and applications; introduction to integration.
Pre-requisite: MATH 31A, 31B.
Discrete structures commonly used in computer science and mathematics, including sets and relations, permutations and combinations, graphs and trees, induction.
Pre-requisite: MATH 33A.
Techniques of proof, abstract vector spaces, linear transformations, and matrices; determinants; inner product spaces; eigenvector theory.
Pre-requisite: MATH 3B or 31B or 32A.
Introduction to linear algebra: systems of linear equations, matrix algebra, linear independence, subspaces, bases and dimension, orthogonality, least-squares methods, determinants, eigenvalues and eigenvectors, matrix diagonalization, and symmetric matrices.
Pre-requisite: MATH 33B.
Dynamical systems analysis of nonlinear systems of differential equations. One- and two- dimensional flows. Fixed points, limit cycles, and stability analysis. Bifurcations and normal forms. Elementary geometrical and topological results. Applications to problems in biology, chemistry, physics, and other fields.
Pre-requisite: MATH 115A.
Quantitative modeling of strategic interaction. Topics include extensive and normal form games, background probability, lotteries, mixed strategies, pure and mixed Nash equilibria and refinements, bargaining; emphasis on economic examples. Optional topics include repeated games and evolutionary game theory.
Pre-requisite: MATH 33A, 33B.
Introduction to fundamental principles and spirit of applied mathematics. Emphasis on manner in which mathematical models are constructed for physical problems. Illustrations from many fields of endeavor, such as physical sciences, biology, economics, and traffic dynamics.
Pre-requisite: MATH 33A, 33B.
Selected topics in differential equations. Laplace transforms, existence and uniqueness theorems, Fourier series, separation of variable solutions to partial differential equations, Sturm/Liouville theory, calculus of variations, two-point boundary value problems, Green’s functions.
Pre-requisite: MATH 3B.
Multivariable modeling, matrices and vectors, eigenvalues and eigenvectors, linear and nonlinear systems of differential equations, probabilistic applications of integration.
Pre-requisite: Successful completion of Mathematics Diagnostic Test.
Linear and polynomial functions and their graphs, applications to optimization. Inverse, exponential, and logarithmic functions. Trigonometric functions.
Basic statistical procedures and their application to research and practice in various areas of psychology.
Lecture, four hours. Requisites: course 10 with a grade of C or better, and one course from Mathematics 2, Program in Computing 10A, Statistics 10, or one term of calculus. Designed for pre-majors.
Pre-requisites: Mathematics 31A, 31B.
Introduction to probability and statistics for economists, with emphasis on rigorous arguments. Not open to students with credit for former Statistics 11.
