408
USC Dornsife College of Letters, Arts and Sciences
MATH 126 Calculus II (4, FaSpSm) A continu-
MATH 245 Mathematics of Physics and Engineering I (4, FaSp) First-order differen-
MATH 407 Probability Theory (4, FaSp)
MATH 265 Mathematical and Computational Methods for Neuroscience (4, FaSp)
MATH 408 Mathematical Statistics (4, Sp)
ation of MATH 125: trigonometric functions; applications of integration; techniques of integration; indeterminate forms; infinite series; Taylor series; polar coordinates. Prerequisite: MATH 125. MATH 127 Enhanced Calculus I (4, Fa)
Applications of integration, review of techniques of integration, infinite sequences and series, some beginning linear algebra, ordinary differential equations. Designed for students who earn a score of 4 or 5 on the Advanced Placement Calculus AB Examination, or a score of 3 or 4 on the BC Examination. Admission to course by departmental approval. (Duplicates credit in MATH 126.) MATH 200 Elementary Mathematics from an Advanced Standpoint (4, FaSp) An expli-
cation of arithmetic and geometry, including the algebraic operations, number bases, plane and solid figures; and coordinate geometry. Prerequisite: MATH 040x or math placement exam. MATH 208x Elementary Probability and Statistics (4, FaSp) Descriptive statistics,
probability concepts, discrete and continuous random variables, mathematical expectation and variance, probability sampling, Central Limit Theorem, estimation and hypothesis testing, correlation and regression. Not available for major credit to mathematics majors. Prerequisite: MATH 118x or MATH 125. MATH 218 Probability for Business (4, FaSpSm) Basic probability, discrete and
continuous distributions, expectation and variance, independence. Sampling, estimation, confidence intervals, hypothesis testing. Prerequisite: MATH 118x or MATH 125. MATH 225 Linear Algebra and Linear Differential Equations (4, FaSp) Matrices,
systems of linear equations, vector spaces, linear transformations, eigenvalues, systems of linear differential equations. Prerequisite: MATH 126. MATH 226 Calculus III (4, FaSp) A continu-
ation of MATH 126; vectors, vector valued functions; differential and integral calculus of functions of several variables; Green’s theorem. Prerequisite: MATH 126. MATH 227 Enhanced Calculus II (4, Sp)
A continuation of MATH 127; vectors and vector spaces, functions of several variables, partial differential equations, optimization theory, multiple integration; Green’s Stokes’, divergence theorems. Prerequisite: MATH 127 or MATH 225.
tial equations; second-order linear differential equations; determinants and matrices; systems of linear differential equations; Laplace transforms. Prerequisite: MATH 226.
Differential calculus of multivariable functions, optimization, elementary linear algebra and matrix theory, principal component analysis, elementary differential equations, systems, qualitative theory, numerical methods, scientific computation. Prerequisite: MATH 125; recommended preparation: MATH 126 or equivalent or AP credit for Calculus BC. MATH 307 Statistical Inference and Data Analysis I (4, Fa) Probability, counting,
independence, distributions, random variables, simulation, expectation, variance, covariance, transformations, law of large numbers, Central limit theorem, estimation, efficiency, maximum likelihood, Cramer-Rao bound, bootstrap. Prerequisite: MATH 118 or MATH 125. MATH 308 Statistical Inference and Data Analysis II (4, Sp) Confidence intervals,
hypothesis testing, p-values, likelihood ratio, nonparametrics, descriptive statistics, regression, multiple linear regression, experimental design, analysis of variance, categorical data, chi-squared tests, Bayesian statistics. Prerequisite: MATH 307.
Probability spaces, discrete and continuous distributions, moments, characteristic functions, sequences of random variables, laws of large numbers, central limit theorem, special probability laws. Prerequisite: MATH 226. Principles for testing hypotheses and estimation, small sample distributions, correlation and regression, nonparametric methods, elements of statistical decision theory. Prerequisite: MATH 407. MATH 410 Fundamental Concepts of Modern Algebra (4, FaSp) Sets; relations; groups;
homomorphisms; symmetric groups; Abelian groups; Sylow’s theorems; introduction to rings and fields. Prerequisite: MATH 225. MATH 425ab Fundamental Concepts of Analysis (a: 4, FaSp; b: 4, Sp) a: The real
number system, metric spaces, limits, continuity, derivatives and integrals, infinite series. b: Implicit function theorems, Jacobians, transformations, multiple integrals, line integrals. Prerequisite: MATH 226; MATH 425a before MATH 425b.
MATH 430 Theory of Numbers (4, Fa) Introduction to the theory of numbers, including prime factorization, congruences, primitive roots, N-th power residues, number theoretic functions, and certain diophantine equations. Prerequisite: MATH 126. MATH 432 Applied Combinatorics (4, Sp)
MATH 370 Applied Algebra (4, Sp) Induc-
tion, Euclidean algorithm, factorization, congruence classes, Rings, RSA algorithm, Chinese remainder theorem, codes, polynomials, fundamental theorem of algebra, polynomial multiplication, Fourier transform, and other topics. Prerequisite: MATH 226; MATH 225 or MATH 245. MATH 390 Special Problems (1-4) Super-
vised, individual studies. No more than one registration permitted. Enrollment by petition only. MATH 395 Seminar in Problem Solving (2, max 8) Systematic approach to solving
non-standard and competition level math problems on inequalities, infinite sums and products, combinatorics, number theory, and games. Recommended preparation: MATH 126. MATH 400 Foundations of Discrete Mathematics (4, Fa) Methods of proof, predicate
calculus, set theory, order and equivalence relations, partitions, lattices, functions, cardinality, elementary number theory and combinatorics. Prerequisite: MATH 225 or MATH 226.
Mathematical induction, counting principles, arrangements, selections, binomial coefficients, generating functions, recurrence relations, inclusion-exclusion, symmetric groups, graphs, Euler and Hamiltonian circuits, trees, graph algorithms; applications. Prerequisite: MATH 225 or MATH 226. MATH 434 Geometry and Transformations (4, Fa) Incidence and separation properties
of planes and spaces. Geometric inequalities, models of Riemannian and hyperbolic geometry. Isometrics, Jordan measure, constructions, and affine geometry. MATH 435 Vector Analysis and Introduction to Differential Geometry (4, Sp) Vectors,
elements of vector analysis, applications to curves and surfaces, standard material of differential geometry. Prerequisite: MATH 226. MATH 440 Topology (4, Fa) Cardinals,
topologies, separation axioms. Compactness, metrizability, function spaces; completeness; Jordan curve theorem. Recommended preparation: upper division MATH course.