040x Basic Mathematical Skills (4, FaSp) Intensive review of arithmetic and algebra. Not available for degree credit. Graded CR/NC.
100x Mathematics: The Third Culture (4) Current applications of mathematical concepts; selections from algebra, geometry, combinatorics, logic, set theory, probability, statistics, calculus, and mathematical programming. Not available for major credit to science majors. Prerequisite: MATH 040x or placement exam.
108 Introductory College Mathematics (4, FaSpSm) Equations and inequalities; systems of linear equations; functions; graphs; exponential, logarithmic, and trigonometric functions; polynomial and rational functions; analytic geometry. Prerequisite: MATH 040x or placement exam.
116 Mathematics for the Social Sciences I (4, FaSp) Finite mathematics with application to the social sciences; elementary set theory and logic; counting techniques; probability; statistics; matrices and systems of linear equations. Selected topics. Prerequisite: MATH 040x or placement exam.
117 Introduction to Mathematics for Business and Economics (4, FaSpSm) Functions, graphs, polynomial and rational functions, exponential and logarithmic functions, matrices, systems of linear equations, elementary probability. Prerequisite: MATH 040x or skill level exam in Math.
118x Fundamental Principles of the Calculus (4, FaSpSm) Derivatives; extrema. Definite integral; fundamental theorem of the calculus. Functions of several variables; partial derivatives; multiple integrals; Lagrange multipliers. Not available for credit toward a degree in mathematics. Prerequisite: MATH 117 or placement exam.
125 Calculus I (4, FaSpSm) Limits; continuity, derivatives and applications; antiderivatives; the fundamental theorem of calculus; exponential and logarithmic functions. Prerequisite: MATH 108 or placement exam.
126 Calculus II (4, FaSpSm) A continuation of 125: trigonometric functions; applications of integration; techniques of integration; indeterminate forms; infinite series; Taylor series; polar coordinates. Prerequisite: MATH 125.
190 Accelerated Math Tutorial (2, FaSp) Supervised individual studies in advanced topics from real analysis, modern algebra, and multi-variable calculus. Intended for students in the Accelerated Math Program only.
200 Elementary Mathematics from an Advanced Standpoint (4, FaSp) An explication of arithmetic and geometry, including the algebraic operations, number bases, plane and solid figures; and coordinate geometry. Prerequisite: MATH 040x or placement exam.
208x Elementary Probability and Statistics (4, Fa) 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.
216 Mathematics for the Social Sciences II (4) Continuation of MATH 116. Further topics in probability, elementary functions, graphing, and analytic geometry; elementary calculus; derivatives, integrals of simple functions.
218 Probability for Business (4, FaSpSm) Combinatorial probability, discrete and continuous distributions, expectation and variance, joint distributions, independence. Models for random phenomena, foundations of simulation and stochastic modeling. Prerequisite: MATH 118x.
225 Linear Algebra and Linear Differential Equations (4, FaSpSm) Matrices, systems of linear equations, vector spaces, linear transformations, eigenvalues, systems of linear differential equations. Prerequisite: MATH 126.
226 Calculus III (4, FaSpSm) A continuation of MATH 126; vectors, vector valued functions; differential and integral calculus of functions of several variables; Green's theorem. Prerequisite: MATH 126.
245 Mathematics of Physics and Engineering I (4, FaSpSm) First-order differential equations; second-order linear differential equations; determinants and matrices; systems of linear differential equations; Laplace transforms. Prerequisite: MATH 226.
270 Proof Techniques and Mathematical Structures (4, FaSp) Proof types and techniques, statement calculus and axioms, number systems, basic set theory, order and equivalence relations, functions, cardinality, algebraic structures.
390 Special Problems (1-4) Supervised, individual studies. No more than one registration permitted. Enrollment by petition only.
406 Probability and Statistics for Secondary Teachers (4) Descriptive statistics, analysis of sample data, statistical inference, probability, distributions and applications in the physical, biological, and social sciences. Credit applicable only to the M.A. (teacher's option).
407 Probability Theory (4, Fa) 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.
408 Mathematical Statistics (4, Sp) Principles for testing hypotheses and estimation, small sample distributions, correlation and regression, nonparametric methods, elements of statistical decision theory. Prerequisite: MATH 407.
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.
425ab Fundamental Concepts of Analysis (a: 4, FaSpSm; b: 4, Sp) a: The real number system, 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.
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.
432 Applied Combinatorics (4, Sp) 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 or departmental approval.
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.
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.
440 Topology (4, Fa) Cardinals, topologies, separation axioms. Compactness, metrizability, function spaces; completeness; Jordan curve theorem. Recommended preparation: upper division MATH course.
445 Mathematics of Physics and Engineering II (4, FaSpSm) Vector field theory; theorems of Gauss, Green, and Stokes; Fourier series and integrals; complex variables; linear partial differential equations; series solutions of ordinary differential equations. Prerequisite: MATH 245.
447 Variational Methods (4) Euler-Lagrange equations, Hamilton's principle, eigenvalue problems in linear algebra and differential equations, Rayleigh-Ritz and finite-element methods; examples from geometry, physics, and numerical analysis. Prerequisite: MATH 225 or MATH 245 or departmental approval.
450 History of Mathematics (4, Sp) Evolution of mathematical ideas and techniques as seen through a study of the contributions of eminent mathematicians to the formulation and solution of celebrated problems. Prerequisite: MATH 225 or MATH 245; recommended preparation: upper division MATH course.
458 Numerical Methods (4, FaSp) Rounding errors in digital computation; solution of linear algebraic systems; Newton's method for nonlinear systems; matrix eigenvalues; polynomial approximation; numerical integration; numerical solution of ordinary differential equations. Prerequisite: MATH 225 or MATH 245.
460 Introduction to Mathematical Logic (4) Development of the first order predicate calculus. Fundamental metamathematical notions.
461 Linear Inequalities and Linear Programming (4) Linear equations and inequalities; the simplex method and variations; linear and integer programming problems; flows in networks. Prerequisite: MATH 225 or MATH 245.
462 Axiomatic Set Theory (4) Detailed development of general set theory via the Zermelo-Fraenkel axiom system. Special attention to the role of the axiom of choice. Prerequisite: MATH 460.
465 Ordinary Differential Equations (3, Sp) Linear systems, phase plane analysis, existence and uniqueness, stability of linear and almost linear systems, Lyapunov's method, nonlinear oscillations, flows, invariant surfaces, and bifurcation. Prerequisite: MATH 225 or MATH 245.
466 Dynamic Modeling (4, Fa) Formulation and study of models arising in population dynamics, growth of plankton, pollution in rivers, highway traffic, morphogenesis and tidal dynamics: stability, oscillations, bifurcations, chaos. The lab will consist of computer simulation of models using commercially available software. Prerequisite: MATH 225 or MATH 245 or departmental approval.
471 Topics in Linear Algebra (4) Polynomial rings, vector spaces, linear transformations, canonical forms, inner product spaces. Prerequisite: MATH 225; recommended preparation: MATH 410.
475 Introduction to Theory of Complex Variables (4, Sp) Limits and infinite series; line integrals; conformal mapping; single-valued functions of a complex variable; applications. Primarily for advanced students in engineering. Prerequisite: MATH 226.
490x Directed Research (2-8, max 8, FaSpSm) Individual research and readings. Not available for graduate credit. Prerequisite: departmental approval.
499 Special Topics (2-4, max 8) Lectures on advanced material not covered in regularly scheduled courses. No more than two registrations allowed. Prerequisite: departmental approval.
Produced by the USC Division of Student Affairs, Office of University Publications, May 1, 1995