Mathematics
Courses
For course descriptions not found in the 2008-2009 General Catalog, please contact the department for more information.
All Prerequisites listed below may be replaced by an equivalent or higher-level course. The listings of quarters in which courses will be offered are only tentative. Please consult the Department of Mathematics to determine the actual course offerings each year.
Lower-Division
3C. Pre-Calculus (4) Functions and their graphs. Linear and polynomial functions, zeroes, inverse functions, exponential and logarithmic, trigonometric functions and their inverses. Emphasis on understanding algebraic, numerical and graphical approaches making use of graphing calculators. (No credit given if taken after Math. 4C, 1A/10A, or 2A/20A.) Prerequisite: two or more years of high school mathematics or equivalent.
4C. Pre-Calculus for Science and Engineering (4) Review of polynomials. Graphing functions and relations: graphing rational functions, effects of linear changes of coordinates. Circular functions and right triangle trigonometry. Reinforcement of function concept: exponential, logarithmic, and trigonometric functions. Vectors. Conic sections. Polar coordinates. Three lectures, one recitation. (No credit given if taken after Math. 1A/10A or 2A/20A. Two units of credit given if taken after Math. 3C.) Three or more years of high school mathematics or equivalent recommended. Prerequisite: Math Placement Exam qualifying score, or Math. 3C with a grade of C– or better.
10A. Calculus (4) Differentiation and integration of algebraic functions. Fundamental theorem of calculus. Applications. (No credit given if taken after Math. 20A). Prerequisite: Math Placement Exam qualifying score, or AP Calculus AB score of 2, or SAT II Math. Level 2 score of 600 or higher, or Math. 3C with a grade of C or better, or Math. 4C with a grade of C– or better.
10B. Calculus (4) Further applications of the definite integral. Calculus of trigonometric, logarithmic, and exponential functions. Complex numbers. (No credit given if taken after Math. 2B/20B. Formerly numbered Math. 1B.) Prerequisite: AP Calculus AB score of 3, 4, or 5, or Math. 10A with a grade of C– or better, or Math. 20A with a grade of C– or better.
10C. Calculus (4) Vector geometry, velocity, and acceleration vectors. (No credit given if taken after Math. 2C/20C. Formerly numbered Math. 1C.) Prerequisite: AP Calculus BC score of 3, 4, or 5, or Math. 10B with a grade of C– or better, or Math. 20B with a grade of C– or better.
11. Elementary Probability and Statistics (4) Events and probabilities, combinatorics, conditional probability, Bayes formula. Discrete random variables: mean, variance; binomial, multinomial, Poisson distributions. Continuous random variables: densities, mean, variance; normal, uniform, exponential distributions. Sample statistics, confidence intervals, regression. Applications. Intended for biology and social science majors. Prerequisites: AP Calculus BC score of 3, 4, or 5, or Math. 10B with a grade of C– or better, or Math. 20B with a grade of C– or better, and concurrent enrollment in Math. 11L.
11L. Elementary Probability and Statistics Laboratory (1) Introduction to the use of software in probabilistic and statistical analysis. Emphasis on understanding connections between the theory of probability and statistics, numerical results of real data, and learning techniques of data analysis and interpretation useful for solving scientific problems. Prerequisites: AP Calculus BC score of 3, 4, or 5, or Math. 10B with a grade of C– or better, or Math. 20B with a grade of C– or better, and concurrent enrollment in Math. 11.
15A. Discrete Mathematics (4) Basic discrete mathematical structures: sets, relations, functions, sequences, equivalence relations, partial orders, number systems. Methods of reasoning and proofs: propositional logic, predicate logic, induction, recursion, pigeonhole principle. Infinite sets and diagonalization. Basic counting techniques; permutations and combinations. Applications will be given to digital logic design, elementary number theory, design of programs, and proofs of program correctness. Equivalent to CSE 20. Credit not offered for both Math. 15A and CSE 20. Prerequisites: CSE 8A or CSE 8B or CSE 11. CSE 8B or CSE 11 may be taken concurrently with Math. 15A/CSE 20.
15B. Mathematics for Algorithm and Systems (4) This course introduces mathematical tools for the qualitative and quantitative analysis of algorithms and computer systems. Topics to be covered include basic enumeration and counting techniques; recurrence relations; graph theory; asymptotic notation; elementary applied discrete probability. Equivalent to CSE 21. Prerequisite: Math. 15A or CSE 20 or 160A; CSE 12 is strongly recommended for CSE 21.
20A. Calculus for Science and Engineering (4) Foundations of differential and integral calculus of one variable. Functions, graphs, continuity, limits, derivative, tangent line. Applications with algebraic, exponential, logarithmic, and trigonometric functions. Introduction to the integral. (Two credits given if taken after Math. 1A/10A and no credit given if taken after Math. 1B/10B or Math. 1C/10C. Formerly numbered Math. 2A.) Prerequisite: Math Placement Exam qualifying score, or AP Calculus AB score of 2 or 3, or SAT II Math. 2C score of 650 or higher, or Math. 4C with a grade of C– or better, or Math. 10A with a grade of C– or better.
20B. Calculus for Science and Engineering (4) Integral calculus of one variable and its applications, with exponential, logarithmic, hyperbolic, and trig-onometric functions. Methods of integration. Infinite series. Polar coordinates in the plane and complex exponentials. (Two units of credits given if taken after Math. 1B/10B or Math. 1C/10C.)Prerequisite: AP Calculus AB score of 4 or 5, or AP Calculus BC score of 3, or Math. 20A with a grade of C– or better, or Math. 10B with a grade of C– or better, or Math. 10C with a grade of C– or better.
20C. Calculus and Analytic Geometry for Science and Engineering (4) Vector geometry, vector functions and their derivatives. Partial differentiation. Maxima and minima. Double integration, Two units of credit given if taken after Math. 10C. Formerly numbered Math. 21C. Prerequisite: AP Calculus BC score of 4 or 5, or Math. 20B with a grade of C– or better.
20D. Introduction to Differential Equations (4) Ordinary differential equations: exact, separable, and linear; constant coefficients, undetermined coefficients. Variations of parameters. Series solutions. Systems. Laplace transforms. Techniques for engineering sciences. Computing symbolic and graphical solutions using Matlab. Formerly numbered Math. 21D. May be taken as repeat credit for Math. 21D.Prerequisite: Math. 20C (or Math. 21C) with a grade of C– or better.
20E. Vector Calculus (4) Change of variable in multiple integrals, Jacobian Line integrals, Green’s theorem. Vector fields, gradient fields, divergence, curl. Spherical and cylindrical coordinates. Taylor series in several variables. Surface integrals, Stoke’s theorem. Gauss’ theorem and its applications. Conservative fields. (Zero units given if Math. 2F previously. Formerly numbered Math. 2F) Prerequisite: Math. 20C (or Math. 21C) with a grade of C– or better.
20F. Linear Algebra (4) Matrix algebra, solution of systems of linear equations by Gaussian elimination, determinants. Linear and affine subspaces, bases of Euclidean spaces. Eigenval-ues and eigenvectors, quadratic forms, orthogonal matrices, diagonalization of symmetric matrices. Applications. Computing symbolic and graphical solutions using Matlab. (Zero units given if Math. 2EA previously. Formerly numbered 2EA.) Prerequisite: Math. 20C (or Math. 21C) with a grade of C– or better.
87. Freshman Seminar (1) The Freshman Seminar Program is designed to provide new students with the opportunity to explore an intellectual topic with a faculty member in a small seminar setting. Freshman seminars are offered in all campus departments and undergraduate colleges, and topics vary from quarter to quarter. Enrollment is limited to 15 to 20 students, with preference given to entering freshman. Prerequisite: none.
95. Introduction to Teaching Math (2) (Cross-listed with EDS 30) Revisit students' learning difficulties in mathematics in more depth to prepare students to make meaningful observations of how K-12 teachers deal with these difficulties. Explore how instruction can use students' knowledge to pose problems that stimulate students' intellectual curiosity. Prerequisites: none.
Upper-Division
100A-B-C. Modern Algebra (4-4-4) An introduction to the methods and basic structures of higher algebra: sets and mappings, the integers, rational, real and complex numbers, groups, rings (especially polynomial rings) and ideals, fields, real and complex vector spaces, linear transformations, inner product spaces, matrices, triangular form, diagonalization. Both 100 and 103 cannot be taken for credit. Three lectures, one recitation. Prerequisites: Math. 20F, and Math. 109 or consent of instructor. (F,W,S)
102. Applied Linear Algebra (4) A second course in linear algebra from a computational yet geometric point of view. Elementary Hermitian matrices, Schur’s theorem, normal matrices, and quadratic forms. Moore-Penrose generalized inverse and least square problems. Vector and matrix norms. Characteristic and singular values. Canonical forms. Determinants and multilinear algebra. Three lectures, one recitation. Prerequisite: Math. 20F. (W)
103A-B. Modern Applied Algebra (4-4) Abstract algebra with applications to computation. Set algebra and graph theory. Finite state machines. Boolean algebras and switching theory. Lattices. Groups, rings and fields: applications to coding theory. Recurrent sequences. Three lectures, one recitation. Both 100 and 103 cannot be taken for credit. Prerequisites: Math. 20F and Math. 109 (may be taken concurrently). (F,W)
104A-B-C. Number Theory (4-4-4) Topics from number theory with applications and computing. Possible topics are: congruences, reciprocity laws, quadratic forms, prime number theorem, Riemann zeta function, Fermat’s conjecture, diophantine equations, Gaussian sums, algebraic integers, unique factorization into prime ideals in algebraic number fields, class number, units, splitting of prime ideals in extensions, quadratic and cyclotomic fields, partitions. Possible applications are Fast Fourier Transform, signal processing, coding, cryptography. Three lectures. Prerequisite: consent of instructor.
107A-B. Computer Algebra (4-4) An introduction to algebraic computation. Compu-tational aspects of groups, rings, fields, etc. Data representation and algorithms for symbolic computation. Polynomials and their arithmetic. The use of a computer algebra system as an experimental tool in mathematics. Programming using algebra systems. Prerequisite: prior or concurrent enrollment in the Math. 100 or 103 sequence.
109. Mathematical Reasoning (4) This course uses a variety of topics in mathematics to introduce the students to rigorous mathematical proof, emphasizing quantifiers, induction, negation, proof by contradiction, naive set theory, equivalence relations and epsilon-delta proofs. Required of all departmental majors. Prerequisite: Math. 20F.
110. Introduction to Partial Differential Equations (4) Fourier series, orthogonal expansions, and eigenvalue problems. Sturm-Liouville theory. Separation of variables for partial differential equations of mathematical physics, including topics on Bessel functions and Legendre polynomials. Prerequisites: Math. 20D (or 21D) and 20F, or consent of instructor. (F,S)
111A-B. Mathematical Modeling (4-4) An introduction to mathematical modeling in the physical and social sciences, concentrating on one or more topics that vary from year to year. Students work on independent or group projects. May be repeated for credit when topics change. Prerequisites: Math. 20D and Math. 20F, or consent of instructor.
120A. Elements of Complex Analysis (4) Complex numbers and functions. Analytic functions, harmonic functions, elementary conformal mappings. Complex integration. Power series. Cauchy’s theorem. Cauchy’s formula. Residue theorem. Three lectures, one recitation. Prerequisite or co-registration: Math. 20E, or consent of instructor. (F,W)
120B. Applied Complex Analysis (4) Applications of the Residue theorem. Conformal mapping and applications to potential theory, flows, and temperature distributions. Fourier transformations. Laplace transformations, and applications to integral and differential equations. Selected topics such as Poisson’s formula. Dirichlet problem. Neumann’s problem, or special functions. Three lectures, one recitation. Prerequisite: Math. 120A. (W,S)
121A. Foundations of Teaching and Learning Mathematics I (4) Develop teachers' knowledge base (knowledge of mathematics content, pedagogy, and student learning) in the context of advanced mathematics. This course builds on the previous courses where these components of knowledge were addressed exclusively in the context of high-school mathematics. Prerequisites: Introduction to Teaching Math (Math. 95), Calculus 10C or 20C.
121B. Foundations of Teaching and Learning Math II (4) Examine how learning theories can consolidate observations about conceptual development with the individual student as well as the development of knowledge in the history of mathematics. Examine how teaching theories explain the effect of teaching approaches addressed in the previous courses. Prerequisites: Foundations of Teaching and Learning Mathematics I (Math. 121A), Calculus 10C or 20C.
130A. Ordinary Differential Equations (4) Linear and nonlinear systems of differential equations. Stability theory, perturbation theory. Applications and introduction to numerical solutions. Three lectures. Prerequisites: Math. 20D/21D and 20F. (F)
130B. Ordinary Differential Equations (4) Existence and uniqueness of solutions to differential equations. Local and global theorems of continuity and differentiabillity. Three lectures. Prerequisites: Math. 20D/21D and 20F, and Math. 130A. (W)
131. Variational Methods in Optimization (4) Maximum-minimum problems. Normed vector spaces, functionals, Gateaux variations. Euler-Lagrange multiplier theorem for an extremum with constraints. Calculus of variations via the multiplier theorem. Applications may be taken from a variety of areas such as the following: applied mechanics, elasticity, economics, production planning and resource allocation, astronautics, rocket control, physics, Fermat’s principle and Hamilton’s principle, geometry, geodesic curves, control theory, elementary bang-bang problems. Three lectures, one recitation. Prerequisites: Math. 20D/21D and 20F or consent of instructor. (S)
132A. Elements of Partial Differential Equations and Integral Equations (4) Basic concepts and classification of partial differential equations. First order equations, characteristics. Hamilton-Jacobi theory, Laplace’s equation, wave equation, heat equation. Separation of variables, eigenfunction expansions, existence and uniqueness of solutions. Three lectures. Prerequisite: Math. 110 or consent of instructor. (W)
132B. Elements of Partial Differential Equations and Integral Equations (4) Relation between differential and integral equations, some classical integral equations, Volterra integral equations, integral equations of the second kind, degenerate kernels, Fredholm alternative, Neumann-Liouville series, the resolvent kernel. Three lectures. Prerequisite: Math. 132A. (S)
140A-B-C. Foundations of Analysis (4-4-4) Axioms, the real number system, topology of the real line, metric spaces, continuous functions, sequences of functions, differentiation, Riemann-Stieltjes integration, partial differentiation, multiple integration, Jacobians. Additional topics at the discretion of the instructor: power series, Fourier series, successive approximations of other infinite processes. Three lectures, one recitation. Prerequisites: Math. 20F and Math. 109 or consent of instructor. Credit cannot be obtained for both Math. 140A-B and 142A-B. (F,W,S)
142A-B. Advanced Calculus (4-4) The number system. Functions, sequences, and limits. Continuity and differentiability. The Riemann integral. Transcendental functions. Limits and continuity. Infinite series. Sequences and series of functions. Uniform convergence. Taylor series. Improper integrals. Gamma and Beta functions. Fourier series. Three lectures. Prerequisites: Math. 20F and Math. 109 (concurrent enrollment in Math. 109 allowed.) Credit cannot be obtained for both Math. 140A-B and 142A-B.
150A. Differential Geometry (4) Differential geometry of curves and surfaces. Gauss and mean curvatures, geodesics, parallel displacement, Gauss-Bonnet theorem. Three lectures. Prerequisites: Math. 20E with a grade of C– or better and Math. 20F with a grade of C- or better, or consent of instructor. (F)
150B. Calculus on Manifolds (4) Calculus of functions of several variables, inverse function theorem. Further topics, selected by instructor, such as exterior differential forms, Stokes’ theorem, manifolds, Sard’s theorem, elements of differential topology, singularities of maps, catastrophes, further topics in differential geometry, topics in geometry of physics. Three lectures. Prerequisite: Math. 150A. (W)
152. Applicable Mathematics and Computing (4) This course will give students experience in applying theory to real world applications such as Internet and wireless communication problems. The course will incorporate talks by experts from industry and students will be helped to carry out independent projects. Topics include graph visualization, labelling, and embeddings, random graphs and randomized algorithms. May be taken 3 times for credit. Prerequisites: Math. 20D or 21D, and 20F or consent of instructor.
153. Geometry for Secondary Teachers (4) Two- and three-dimensional Euclidean geometry is developed from one set of axioms. Pedagogical issues will emerge from the mathematics and be addressed using current research in teaching and learning geometry. This course is designed for prospective secondary school mathematics teachers. Prerequisite: Math. 109.
154. Discrete Mathematics and Graph Theory (4) Basic concepts in graph theory. Combinatorial tools, structures in graphs (Hamiltonian cycles, perfect matching). Properties of graphics and applications in basic algorithmic problems (planarity, k-colorability, traveling salesman problem). Prerequisites: Math. 20F and Math. 109, or consent of instructor.
155A. Computer Graphics (4) Bezier curves and control lines, de Casteljau construction for subdivision, elevation of degree, control points of Hermite curves, barycentric coordinates, rational curves. Three lectures, one recitation, and approximately eight laboratory hours per week. Prerequisites: Math. 20F and programming experience. [Warning: There are duplicate credit restrictions on this course. See section on Duplication of Credit.] (F)
155B. Topics in Computer Graphics (4) Spline curves, spline interpolation, affine and affine cross ratios, polar forms (blossoming), the Oslo algorithm for knot insertion, NURBS and geometric continuity. Three lectures, one recitation, and approximately eight laboratory hours per week. Prerequisite: Math. 155A or consent of instructor. (W)
163. History of Mathematics (4) Topics will vary from year to year in areas of mathematics and their development. Topics may include the evolution of mathematics from the Babylonian period to the eighteenth century using original sources, a history of the foundations of mathematics and the development of modern mathematics. Prerequisite: Math. 20B or consent of instructor. (S)
166. Intro to the Theory of Computation (4) Introduction to formal languages; regular languages; regular expressions, finite automata, minimization, closure properties, decision algorithms, and non-regular languages; context-free languages, context-free grammars, push-down automata, parsing theory, closure properties, and noncontext-free languages; computable languages; turing machines, recursive functions, Church’s thesis, undecidability and the halting problem. Equivalent to CSE 105. Prerequisites: CSE 8B or 9B or 10 or 65 or 62B AND CSE 20 or 160A or Math. 15A or 109 or 100A or 103A.
168A. Topics in Applied Mathematics-Computer Science (4) Topics to be chosen in areas of applied mathematics and mathematical aspects of computer science. May be repeated once for credit with different topics. Three lectures, one recitation. Prerequisite: consent of instructor. (W,S)
170A. Numerical Linear Algebra (4) Analysis of numerical methods for linear algebraic systems and least squares problems. Orthogonalization methods. Ill conditioned problems. Eigenvalue and singular value computations. Three lectures, one recitation. Prerequisites: Math. 20F and knowledge of programming. (F,S)
170B. Numerical Analysis (4) Rounding and discretization errors. Calculation of roots of polynomials and nonlinear equations. Interpolation. Approximation of functions. Three lectures, one recitation. Prerequisites: Math. 20F and knowledge of programming. (W)
170C. Numerical Ordinary Differential Equations (4) Numerical differentiation and integration. Ordinary differential equations and their numerical solution. Basic existence and stability theory. Difference equations. Boundary value problems. Three lectures, one recitation. Prerequisite: Math. 170B or consent of instructor. (S)
171A-B. Mathematical Programming–Numerical Optimization (4-4) Mathematical optimization and applications. Linear programming, the simplex method, duality. Nonlinear programming, Kuhn-Tucker theorem. Selected topics from integer programming, network flows, transportation problems, inventory problems, and other applications. Three lectures, one recitation. Prerequisites: Math. 20F and knowledge of programming.
173. Mathematical Software–Scientific Programming (4) Development of high quality mathematical software for the computer solution of mathematical problems. Three lectures, one recitation. Prerequisites: Math. 170A or Math. 174 and knowledge of FORTRAN. (W)
174. Numerical Methods for Physical Modeling (4) (Conjoined with Math. 274) Floating point arithmetic, direct and iterative solution of linear equations, iterative solution of nonlinear equations, optimization, approximation theory, interpolation, quadrature, numerical methods for initial and boundary value problems in ordinary differential equations. Students may not receive credit for both Math. 174 and PHYS 105, AMES 153 or 154. Students may not receive credit for Math. 174 if Math. 170A, B, or C has already been taken. Graduate students will do an extra assignment/exam. Prerequisites: Math. 20D with a grade of C– or better and Math. 20F with a grade of C– or better, or consent of instructor.
175. Numerical Methods for Partial Differential Equations (4) (Conjoined with Math. 275) Mathematical background for working with partial differential equations. Survey of finite difference, finite element, and other numerical methods for the solution of elliptic, parabolic, and hyperbolic partial differential equations. Formerly Math. 172; students may not receive credit for Math. 175/275 and Math. 172. Graduate students will complete additional coursework/exam. Prerequisite: Math. 174 or Math. 274 or consent of instructor.
176. Advanced Data Structures (4) Descriptive and analytical presentation of data structures and algorithms. Lists, tables, priority queues, disjoint subsets, and dictionaries data types. Data structuring techniques include linked lists, arrays, hashing, and trees. Performance evaluation involving worst case, average and expected case, and amortized analysis. Crecit not offered for both Math. 176 and CSE 100. Equivalent to CSE 100. Prerequisites: CSE 12, CSE 21, or Math. 15B, and CSE 30, or consent of instructor.
180A. Introduction to Probability (4) Probability spaces, random variables, independence, conditional probability, distribution, expectation, joint distributions, central-limit theorem. Three lectures. (2 units of credit offered for Math. 180A if Econ. 120A previously, no credit offered if Econ. 120A concurrently.) Prerequisites: Math. 20C (or 21C). (F)
180B. Introduction to Stochastic Processes I (4) Random vectors, multivariate densities, covariance matrix, multivariate normal distribution. Random walk, Poisson process. Other topics if time permits. Three lectures. Prerequisites: Math. 20D (or 21D), Math. 20F, and Math. 180A. (W)
180C. Introduction to Stochastic Processes II (4) Markov chains in discrete and continuous time, random walk, recurrent events. If time permits, topics chosen from stationary normal processes, branching processes, queuing theory. Three lectures. Prerequisite: Math. 180B. (S)
181A. Introduction to Mathematical Statistics (4) Random samples, linear regression, least squares, testing hypotheses, and estimation. Neyman-Pearson lemma, likelihood ratios. Three lectures, one recitation. Prerequisites: Math. 180A and 20F. [Warning: There are duplicate credit restrictions on this course. See section on Duplication of Credit.] (W)
181B. Introduction to Mathematical Statistics (4) Goodness of fit, special small sample distribution and use, nonparametric methods. Kolmogorov-Smirnov statistics, sequential analysis. Three lectures. Prerequisite: Math. 181A. (S)
181C. Mathematical Statistics (4) Nonparametric Statistics. Topics covered may include the following: Classical rank test, rank correlations, permutation tests, distribution free testing, efficiency, confidence intervals, nonparametric regression and density estimation, resampling techniques (bootstrap, jackknife, etc.) and cross validations. Prerequisites: Math. 181A, 181B previously or concurrently.
181E. Mathematical Statistics (4) Time Series. Analysis of trends and seasonal effects, autoregressive and moving averages models, forecasting, informal introduction to spectral analysis. Prerequisites: Math. 181A, 181B previously or concurrently.
183. Statistical Methods (4) Introduction to probability. Discrete and continuous random variables–binomial, Poisson and Gaussian distributions. Central limit theorem. Data analysis and inferential statistics: graphical techniques, confidence intervals, hypothesis tests, curve fitting. (Credit not offered for Math. 183 if Econ. 120A, ECE 109, Math. 180A, Math. 181A, or Math. 186 previously or concurrently taken.) Prerequisite: Math. 20C (21C) with a grade of C– or better, or consent of instructor. (F,S)
184A. Mathematical Foundations of Computer Science (4) Enumeration of combinatorial structures. Ranking and unranking. Graph theory with applications and algorithms. Recursive algorithms. Circuit design. Inclusion-exclusion. Generating functions. Polya theory. Three lectures, one recitation. Prerequisite: Math. 15B or CSE 21 or Math. 109 or consent of instructor. (W,S)
185. Introduction to Computational Statistics (4) Statistical analysis of data by means of package programs. Regression, analysis of variance, discriminant analysis, principal components, Monte Carlo simulation, and graphical methods. Emphasis will be on understanding the connections between statistical theory, numerical results, and analysis of real data. Prerequisites: Math. 181B with a grade of C– or better, or concurrent enrollment.
186. Probability Statistics for Bioinformatics (4) This course will cover discrete and random variables, data analysis and inferential statistics, likelihood estimators and scoring matrices with applications to biological problems. Introduction to Binomial, Poisson, and Gaussian distributions, central limit theorem, applications to sequence and functional analysis of genomes and genetic epidemiology. (Credit not offered for Math. 186 if Econ. 120A, ECE 109, Math. 180A, Math. 181A, or Math. 183 previously or concurrently.) Prerequisites: Math. 20C (21C) with a grade of C– or better, or consent of instructor.
187. Introduction to Cryptography (4) An introduction to the basic concepts and techniques of modern cryptography. Classical cryptanalysis. Probabilistic models of plaintext. Monalphabetic and polyalphabetic substitution. The one-time system. Caesar-Vigenere-Playfair-Hill substitutions. The Enigma. Modern-day developments. The Data Encryption Standard. Public key systems. Security aspects of computer networks. Data protection. Electronic mail. Three lectures, one recitation. Prerequisite: programming experience. (S)
188. Design and Analysis of Algorithms (4) Introduction to the design and analysis of efficient algorithms. Basic techniques for analyzing the time requirements of algorithms. Algorithms for sorting, searching, and pattern matching, algorithms for graphs and networks. NP-complete problems. Equivalent to CSE 101. Prerequisites: CSE 100 or Math. 176A for Math. 188; CSE 12, CSE 21, and CSE 100 for CSE 101.
190. Introduction to Topology (4) Topological spaces, subspaces, products, sums and quotient spaces. Compactness, connectedness, separation axioms. Selected further topics such as fundamental group, classification of surfaces, Morse theory, topological groups. May be repeated for credit once when topics vary, with consent of instructor. Three lectures. Prerequisite: Math. 109 or consent of instructor. (W)
191. Topics in Topology (4) Topics to be chosen by the instructor from the fields of differential algebraic, geometric, and general topology. Three lectures. Prerequisite: Math. 190 or consent of instructor. (S)
192. Senior Seminar in Mathematics (1) The Senior Seminar Program is designed to allow senior undergraduates to meet with faculty members in a small group setting to explore an intellectual topic in mathematics at the upper-division level. Topics will vary from quarter to quarter. Senior seminars may be taken for credit up to four times, with a change in topic, and permission of the department. Enrollment is limited to twenty students, with preference given to seniors. Prerequisites: department stamp and/or consent of instructor.
193A. Actuarial Mathematics (4) Probabilistic Foundations of Insurance. Short-term risk models. Survival distributions and life tables. Introduc-tion to life insurance. Prerequisite: Math. 180A or 183, or consent of instructor.
193B. Actuarial Mathematics (4) Life Insurance and Annuities. Analysis of premiums and premium reserves. Introduction to multiple life functions and decrement models as time permits. Prerequisite: Math. 193A.
194. The Mathematics of Finance (4) Introduction to the mathematics of financial models. Basic probabilistic models and associated mathematical machinery will be discussed, with emphasis on discrete time models. Concepts covered will include conditional expectation, martingales, optimal stopping, arbitrage pricing, hedging, European and American options. Prerequisites: Math. 20D (21D), Math. 20F, and Math. 180A or 183.
195. Introduction to Teaching in Mathematics (4) Students will be responsible for and teach a class section of a lower-division mathematics course. They will also attend a weekly meeting on teaching methods. (Does not count towards a minor or major.) Five lectures, one recitation. Prerequisite: consent of instructor. (F,W,S)
196. Student Colloquium (1) A variety of topics and current research results in mathematics will be presented by guest lecturers and students under faculty direction. May be taken for P/NP grade only. Prerequisite: upper-division status.
197. Mathematics Internship (2 or 4) An enrichment program which provides work experience with public/private sector employers. Subject to the availablility of positions, students will work in a local company under the supervision of a faculty member and site supervisor. Units may not be applied towards major graduation requirements. Prerequisites: completion of 90 units, 2 upper-division mathematics courses, an overall 2.5 UCSD G.P.A., consent of mathematics faculty coordinator, and submission of written contract. Department stamp required.
199. Independent Study for Undergraduates (2 or 4) Independent reading in advanced mathematics by individual students. Three periods. (P/NP grades only.) Prerequisite: permission of department. (F,W,S)
199H. Honors Thesis Research for Undergraduates (2-4) Honors thesis research for seniors participating in the Honors Program. Research is conducted under the supervision of a mathematics faculty member. Prerequisites: admission to the Honors Program in mathematics, department stamp.
Graduate
200A-B-C. Algebra (4-4-4) Group actions, factor groups, polynomial rings, linear algebra, rational and Jordan canonical forms, unitary and Hermitian matrices, Sylow theorems, finitely generated abelian groups, unique factorization, Galois theory, solvability by radicals, Hilbert Basis Theorem, Hilbert Nullstellensatz, Jacobson radical, semisimple Artinian rings. Prerequisite: consent of instructor.
201A-B. Basic Topics in Algebra (4-4) Recommended for all students specializing in algebra. Basic topics include categorical algebra, commutative algebra, group representations, homological algebra, nonassociative algebra, ring theory. Prerequisites: Math. 200A-B-C or consent of instructor. (F,W,S)
202B-C. Applied Algebra (4-4) Algebra from a computational perspective using Maple, Mathematica and Matlab. Groups, rings, linear algebra, rational and Jordan forms, unitary and Hermitian matrices, matrix decompositions, perturbation of eigenvalues, group representations, symmetric functions, fast Fourier transform, commutative algebra, Grobner basis, finite fields. Prerequisite: consent of instructor.
203A-B-C. Algebraic Geometry (4-4-4) Places, Hilbert Nullstellensatz, varieties, product of varieties: correspondences, normal varieties. Divisors and linear systems; Riemann-Roch theorem; resolution of singularities of curves. Grothendieck schemes; cohomology, Hilbert schemes; Picard schemes. Prerequisites: Math. 200A-B-C. (F,W,S)
204. Topics in Number Theory (4) Topics in analytic number theory, such as zeta functions and L-functions and the distribution of prime numbers, zeros of zeta functions and Siegel’s theorem, transcendence theory, modular forms, finite and infinite symmetric spaces. Prerequisite: consent of instructor.
205. Topics in Algebraic Number Theory (4) Topics in algebraic number theory, such as cyclotomic and Kummer extensions, class number, units, splitting of primes in extensions, zeta functions of number fields and the Brauer-Siegel Theorem, class field theory, elliptic curves and curves of higher genus, complex multiplication. Prerequisite: consent of instructor.
207A-B-C. Topics in Algebra (4-4-4) In recent years, topics have included number theory, commutative algebra, noncommutative rings, homological algebra, and Lie groups. May be repeated for credit with consent of advisor. Prerequisite: consent of instructor.
208. Seminar in Algebra (1-4) Prerequisite: consent of instructor. (S/U grades permitted.)
209. Seminar in Number Theory (1 to 4) Prerequisite: consent of instructor. (S/U grades permitted.)
210A. Mathematical Methods in Physics and Engineering (4) Complex variables with applications. Analytic functions, Cauchy’s theorem, Taylor and Laurent series, residue theorem and contour integration techniques, analytic continuation, argument principle, conformal mapping, potential theory, asymptotic expansions, method of steepest descent. Prerequisites: Math. 20DEF, 140A/142A or consent of instructor.
210B. Mathematical Methods in Physics and Engineering (4) Linear algebra and functional analysis. Vector spaces, orthonormal bases, linear operators and matrices, eigenvalues and diagonalization, least squares approximation, infinite-dimensional spaces, completeness, integral equations, spectral theory, Green’s functions, distributions, Fourier transform. Prerequisite: Math. 210A or consent of instructor. (W)
210C. Mathematical Methods in Physics and Engineering (4) Calculus of variations: Euler-Lagrange equations, Noether’s theorem. Fourier analysis of functions and distributions in several variables. Partial differential equations: Laplace, wave, and heat equations; fundamental solutions (Green’s functions); well-posed problems. Prerequisite: Math. 210B or consent of instructor. (S)
212A. Introduction to the Mathematics of Systems and Control (4) Linear and nonlinear systems, and their input-output behavior, linear continuous time and discrete-time systems, reachability and controllability for linear systems, feedback and stabilization, eigenvalue placement, nonlinear controllability, feedback linearization, disturbance rejection, nonlinear stabilization, Lyapunov and control-Lyapunov functions, linearization principle for stability. Prerequisites: Math. 102 or equivalent, Math. 120A or equivalent, Math. 142A or equivalent.
212B. Introduction to the Mathematics of Systems and Control (4) Observability notions, linearization principle for observability. Realization theory for linear systems, observers and dynamic feedback, detectability, external stability for linear systems, frequency-domain considerations, dynamic programming, quadratic cost, state estimation and Kalman filtering, nonlinear stabilizing optimal controls, calculus of variations, and the Maximum Principle. Prerequisite: Math. 212A.
212C. Introduction to the Mathematics of Systems and Control (4) Topics of current interest on systems theory, control, and estimation to be chosen by instructor. Prerequisite: Math. 212B.
216. Topics in Pure Mathematics (4) This course brings together graduate students, postdocs, and faculty to examine a current research topic of broad interest. Previously covered topics include: noncommutative geometry, Loop groups, geometric quantization. Prerequisite: consent of instructor.
217A. Topics in Applied Mathematics (4) In recent years, topics have included applied complex analysis, special functions, and asymptotic methods. May be repeated for credit with consent of advisor. Prerequisite: consent of instructor.
220A-B-C. Complex Analysis (4-4-4) Complex numbers and functions. Cauchy theorem and its applications, calculus of residues, expansions of analytic functions, analytic continuation, conformal mapping and Riemann mapping theorem, harmonic functions. Dirichlet principle, Riemann surfaces. Prerequisites: Math. 140A-B or consent of instructor. (F,W,S)
221A. Topics in Several Complex Variables (4) Formal and convergent power series, Weierstrass preparation theorem; Cartan-Ruckert theorem, analytic sets; mapping theorems; domains of holomorphy; proper holomorphic mappings; complex manifolds; modifications. Prerequisites: Math. 200A and 220A-B-C or consent of instructor.
229. Computing Technology for Mathematics (2) Preparation for making effective use of computer technology in research and teaching of mathematics. UNIX basics, document preparation using TEX, Internet resources, HTML, computer technology in teaching. Prerequisite: graduate status in mathematics. Course not offered in 2008–09.
231A-B-C. Partial Differential Equations (4-4-4) Existence and uniqueness theorems. Cauchy-Kowalewski theorem, first order systems. Hamilton-Jacobi theory, initial value problems for hyperbolic and parabolic systems, boundary value problems for elliptic systems. Green’s function, eigenvalue problems, perturbation theory. Prerequisites: Math. 210A-B or 240A-B-C or consent of instructor.
237A-B. Topics in Differential Equations (4-4) May be repeated for credit with consent of advisor. Prerequisite: consent of instructor.
240A-B-C. Real Analysis (4-4-4) Lebesgue integral and Lebesgue measure, Fubini theorems, functions of bounded variations, Stieltjes integral, derivatives and indefinite integrals, the spaces L and C, equi-continuous families, continuous linear functionals general measures and integrations. Prerequisites: Math. 140A-B-C. (F,W,S)
241A-B. Functional Analysis (4-4) Metric spaces and contraction mapping theorem; closed graph theorem; uniform boundedness principle; Hahn-Banach theorem; representation of continuous linear functionals; conjugate space, weak topologies; extreme points; Krein-Milman theorem; fixed-point theorems; Riesz convexity theorem; Banach algebras. Prerequisites: Math.240A-B-C or consent of instructor.
242. Topics in Fourier Analysis (4) A course on Fourier analysis in Euclidean spaces, groups, symmetric spaces. Prerequisite: Math. 240A-B-C or consent of instructor.
247A-B-C. Topics in Real Analysis (4-4-4) In recent years, topics have included Fourier analysis, distribution theory, martingale theory, operator theory. May be repeated for credit with consent of advisor. Prerequisite: consent of instructor.
248. Seminar in Real Analysis (1 to 4) Prerequisite: consent of instructor. (S/U grades permitted.)
250A-B-C. Differential Geometry (4-4-4) Differential manifolds, Sard theorem, tensor bundles, Lie derivatives, DeRham theorem, connections, geodesics, Riemannian metrics, curvature tensor and sectional curvature, completeness, characteristic classes. Differential manifolds immersed in Euclidean space. Prerequisite: consent of instructor. (F,W,S)
251A-B-C. Lie Groups (4-4-4) Lie groups, Lie algebras, exponential map, subgroup subalgebra correspondence, adjoint group, universal enveloping algebra. Structure theory of semi-simple Lie groups, global decompositions, Weyl group. Geometry and analysis on symmetric spaces. Prerequisites: Math. 200 and 250 or consent of instructor. (F,W,S)
256. Seminar in Lie Groups and Lie Algebras (2 to 4) Various topics in Lie groups and Lie algebras, including structure theory, representation theory, and applications. Prerequisite: consent of instructor. (F,W,S)
257A. Topics in Differential Geometry (4) In recent years, topics have included Morse theory and general relativity. May be repeated for credit with consent of advisor. Prerequisite: consent of instructor.
257B. Topics in Differential Geometry (4) In recent years, topics have included Morse theory and general relativity. May be repeated for credit with consent of advisor. Math. 257A must be taken before Math. 257B. Prerequisite: consent of instructor.
257C. Topics in Differential Geometry (4) In recent years, topics have included Morse theory and general relativity. May be repeated for credit with consent of advisor. Math. 257B must be taken before Math. 257C. Prerequisite: consent of instructor.
258. Seminar in Differential Geometry (1-4) Various topics in differential geometry. Prerequisite: consent of instructor.
259A-B-C. Geometrical Physics (4-4-4) Manifolds, differential forms, homology, deRham’s theorem. Riemannian geometry, harmonic forms. Lie groups and algebras, connections in bundles, homotopy sequence of a bundle, Chern classes. Applications selected from Hamiltonian and continuum mechanics, electromagnetism, thermodynamics, special and general relativity, Yang-Mills fields. Prerequisite: graduate standing in mathematics, physics, or engineering, or consent of instructor.
261A. Probabilistic Combinatorics and Algorithms (4) Introduction to the probabilistic method. Combinatorial applications of the linearity of expectation, second moment method, Markov, Chebyschev, and Azuma inequalities, and the local limit lemma. Introduction to the theory of random graphs. Prerequisite: graduate standing or consent of instructor.
261B. Probabilistic Combinatorics and Algorithms II (4) Introduction to probabilistic algorithms. Game theoretic techniques. Applications of the probabilistic method to algorithm analysis. Markov Chains and Random walks. Applications to approximation algorithms, distributed algorithms, online and parallel algorithms. Math. 261A must be taken before Math. 261B. Prerequisite: Math. 261A.
261C. Probabilistic Combinatorics and Algorithms III (4) Advanced topics in the probabilistic combinatorics and probabilistics algorithms. Random graphs. Spectral Methods. Network algorithms and optimization. Statistical learning. Math. 261B must be taken before Math. 261C. Prerequisite: Math. 261B.
262A-B-C. Topics in Combinatorial Mathematics (4-4-4) Development of a topic in combinatorial mathematics starting from basic principles. Problems of enumeration, existence, construction, and optimization with regard to finite sets. Some familiarity with computer programming desirable but not required. Prerequisites: Math. 100A-B-C.
264A-B-C. Combinatorics (4-4-4) Topics from partially ordered sets, Mobius functions, simplicial complexes and shell ability. Enumeration, formal power series and formal languages, generating functions, partitions. Lagrange inversion, exponential structures, combinatorial species. Finite operator methods, q-analogues, Polya theory, Ramsey theory. Representation theory of the symmetric group, symmetric functions and operations with Schur functions. (F,W,S)
268. Seminar in Logic (1 to 4) Prerequisite: consent of instructor. (S/U grades permitted.)
269. Seminar in Combinatorics (1 to 4) Prerequisite: consent of instructor. (S/U grades permitted.)
270A. Numerical Linear Algebra (4) Error analysis of the numerical solution of linear equations and least squares problems for the full rank and rank deficient cases. Error analysis of numerical methods for eigenvalue problems and singular value problems. Iterative methods for large sparse systems of linear equations. Prerequisites: graduate standing or consent of instructor.
270B. Numerical Approximation and Nonlinear Equations (4) Iterative methods for nonlinear systems of equations, Newton's method. Unconstrained and constrained optimization. The Weierstrass theorem, best uniform approximation, least-squares approximation, orthogonal polynomials. Polynomial interpolation, piecewise polynomial interpolation, piecewise uniform approximation. Numerical differentiation: divided differences, degree of precision. Numerical quadrature: interpolature quadrature, Richardson extrapolation, Romberg Integration, Gaussian quadrature, singular integrals, adaptive quadrature. Prerequisites: Math. 270A or consent of instructor.
270C. Numerical Ordinary Differential Equations (4) Initial value problems (IVP) and boundary value problems (BVP) in ordinary differential equations. Linear methods for IVP: one and multistep methods, local truncation error, stability, convergence, global error accumulation. Runge-Kutta (RK) Methods for IVP: RK methods, predictor-corrector methods, stiff systems, error indicators, adaptive time-stepping. Finite difference, finite volume, collocation, spectral, and finite element methods for BVP; a priori and a posteriori error analysis, stability, convergence, adaptivity. Prerequisites: Math. 270B or consent of instructor.
271A-B-C. Numerical Optimization (4-4-4) Formulation and analysis of algorithms for constrained optimization. Optimality conditions; linear and quadratic programming; interior methods; penalty and barrier function methods; sequential quadratic programming methods. Prerequisite: consent of instructor. (F,W,S)
272A. Numerical Partial Differential Equations I (4) Survey of discretization techniques for elliptic partial differential equations, including finite difference, finite element and finite volume methods. Lax-Milgram Theorem and LBB stability. A priori error estimates. Mixed methods. Convection-diffusion equations. Systems of elliptic PDEs. Prerequisites: graduate standing or consent of instructor.
272B. Numerical Partial Differential Equations II (4) Survey of solution techniques for partial differential equations. Basic iterative methods. Preconditioned conjugate gradients. Multigrid methods. Hierarchical basis methods. Domain decomposition. Nonlinear PDEs. Sparse direct methods. Prerequisites: Math. 272A or consent of instructor.
272C. Numerical Partial Differential Equations III (4) Time dependent (parabolic and hyperbolic) PDEs. Method of lines. Stiff systems of ODEs. Space-time finite element methods. Adaptive meshing algorithms. A posteriori error estimates. Prerequisites: Math. 272B or consent of instructor.
273A. Advanced Techniques in Computational Mathematics I (4) Models of physical systems, calculus of variations, principle of least action. Discretization techniques for variational problems, geometric integrators, advanced techniques in numerical discretization. Project-oriented; projects designed around problems of current interest in science, mathematics, and engineering. Prerequisite: graduate standing or consent of instructor.
273B. Advanced Techniques in Computational Mathematics II (4) Nonlinear functional analysis for numerical treatment of nonlinear PDE. Numerical continuation methods, pseudo-arclength continuation, gradient flow techniques, and other advanced techniques in computational nonlinear PDE. Project-oriented; projects designed around problems of current interest in science, mathematics, and engineering. Prerequisite: Math. 273A or consent of instructor.
273C. Advanced Techniques in Computational Mathematics III (4) Adaptive numerical methods for capturing all scales in one model, multiscale and multiphysics modeling frameworks, and other advanced techniques in computational multiscale/multiphysics modeling. Project-oriented; projects designed around problems of current interest in science, mathematics, and engineering. Prerequisite: Math. 273B or consent of instructor.
274. Numerical Methods for Physical Modeling (4) (Conjoined with Math. 174) Floating point arithmetic, direct and iterative solution of linear equations, iterative solution of nonlinear equations, optimization, approximation theory, interpolation, quadrature, numerical methods for initial and boundary value problems in ordinary differential equations. Students may not receive credit for both Math. 174 and PHYS 105, AMES 153 or 154. Students may not receive credit for Math. 174 if Math. 170A, B, or C has already been taken. Graduate students will complete an additional assignment/exam. Prerequisites: Math. 20D with a grade of C– or better and Math. 20F with a grade of C– or better, or consent of instructor.
275. Numerical Methods for Partial Differential Equations (4) (Conjoined with Math. 175) Mathematical background for working with partial differential equations. Survey of finite difference, finite element, and other numerical methods for the solution of elliptic, parabolic, and hyperbolic partial differential equations. Formerly Math. 172; students may not receive credit for Math. 175/275 and Math. 172. Graduate students will complete an additional assignment/exam. Prerequisite: Math. 174 or Math. 274 or consent of instructor.
276. Numerical Analysis in Multi-Scale Biology (4) (Cross-listed with BENG 276/CHEM 276) Introduces mathematical tools to simulate biological processes at multiple scales. Numerical methods for ordinary and partial differential equations (deterministic and stochastic), and methods for parallel computing and visualization. Hands-on use of computers emphasized, students will apply numerical methods in individual projects. Prerequisite: consent of instructor.
277A. Topics in Computational and Applied Mathematics (4) Topics vary from year to year. May be repeated for credit with consent of advisor. Prerequisite: graduate standing or consent of instructor.
277B. Topics in Numerical Mathematics (4) Topics vary from year to year. May be repeated for credit with consent of advisor. Prerequisite: consent of instructor.
278. Seminar in Numerical Mathematics (1 to 4) Prerequisite: consent of instructor. (S/U grades permitted.)
280A-B-C. Probability Theory (4-4-4) Probability measures; Borel fields; conditional probabilities, sums of independent random variables; limit theorems; zero-one laws; stochastic processes. Prerequisites: advanced calculus and consent of instructor. (F,W,S)
281A. Mathematical Statistics (4) Statistical models, sufficiency, efficiency, optimal estimation, least squares and maximum likelihood, large sample theory. Prerequisites: advanced calculus and basic probablilty theory or consent of instructor.
281B. Mathematical Statistics (4) Hypothesis testing and confidence intervals, one- sample and two-sample problems. Bayes theory, statistical decision theory, linear models and regression. Prerequisites: advanced calculus and basic probablilty theory or consent of instructor.
281C. Mathematical Statistics (4) Nonparametrics: tests, regression, density estimation, bootstrap and jackknife. Introduction to statistical computing using S plus. Prerequisites: advanced calculus and basic probablilty theory or consent of instructor.
282A-B. Applied Statistics (4-4) Sequence in applied statistics. First quarter: general theory of linear models with applications to regression analysis. Second quarter: analysis of variance and covariance and experimental design. Third quarter: further topics to be selected by instructor. Emphasis throughout is on the analysis of actual data. Prerequisite: Math. 181B or equivalent or consent of instructor. (S/U grades permitted.)
283. Statistical Methods in Bioinformatics (4) This course will cover material related to the analysis of modern genomic data; sequence analysis, gene expression/functional genomics analysis, and gene mapping/applied population genetics. The course will focus on statistical modeling and inference issues and not on database mining techniques. Prerequisites: one year of calculus, one statistics course or consent of instructor.
285. Stochastic Processes (4) Elements of stochastic processes, Markov chains, hidden Markov models, martingales, Brownian motion, Gaussian processes. Prerequisite: Math. 180A (or equivalent) or consent of instructor.
286. Stochastic Differential Equations (4) Review of continuous martingale theory. Stochastic integration for continuous semimartingales. Existence and uniqueness theory for stochastic differential equations. Strong Markov property. Selected applications. Prerequisite: Math. 280A-B or consent of instructor.
287A. Time Series Analysis (4) Discussion of finite parameter schemes in the Gaussian and non-Gaussian context. Estimation for finite parameter schemes. Stationary processes and their spectral representation. Spectral estimation. Prerequisite: Math. 181B or equivalent or consent of instructor.
287B. Multivariate Analysis (4) Bivariate and more general multivariate normal distribution. Study of tests based on Hotelling’s T2. Principal components, canonical correlations, and factor analysis will be discussed as well as some competing nonparametric methods, such as cluster analysis. Prerequisite: Math. 181B (or equivalent) or consent of instructor.
287C. Advanced Time Series Analysis (4) Nonparametric function (spectrum, density, regression) estimation from time series data. Nonlinear time series models (threshold AR, ARCH, GARCH, etc.) Nonparametric forms of ARMA and GARCH. Multivariate time series. Prerequisite: Math. 287B or consent of instructor.
288. Seminar in Probability and Statistics (1 to 4) Prerequisite: consent of instructor. (S/U grades permitted.)
289A-B. Topics in Probability and Statistics (4-4) In recent years, topics have included Markov processes, martingale theory, stochastic processes, stationary and Gaussian processes, ergodic theory. May be repeated for credit with consent of advisor.
290A-B-C. Topology (4-4-4) Point set topology, including separation axioms, compactness, connectedness. Algebraic topology, including the fundamental group, covering spaces, homology and cohomology. Homotopy or applications to manifolds as time permits. Prerequisites: Math. 100A-B-C and Math. 140A-B-C. (F,W,S)
291A-B-C. Topics in Topology (4-4-4) In recent years, topics have included generalized cohomology theory, spectral sequences, K-theory, homotophy theory. Prerequisites: consent of instructor.
292. Seminar in Topology (1-4) Various topics in topology. Prerequisites: consent of instructor.
294. The Mathematics of Finance (4) Introduction to the mathematics of financial models. Hedging, pricing by arbitrage. Discrete and continuous stochastic models. Martingales. Brownian motion, stochastic calculus. Black-Scholes model, adaptations to dividend paying equities, currencies and coupon-paying bonds, interest rate market, foreign exchange models. Prerequisite: Math. 180A (or equivalent probability course) or consent of instructor.
295. Special Topics in Mathematics (1 to 4) A variety of topics and current research results in mathematics will be presented by staff members and students under faculty direction.
296. Student Colloquium (1 to 2) A variety of topics and current research in mathematics will be presented by guest lecturers and students under faculty direction. Prerequisites: for one unit—upper-division status or consent of instructor (may only be taken P/NP), or graduate status (may only be taken S/U); for two units—consent of instructor, standard grading option allowed.
297. Mathematics Graduate Research Internship (2-4) An enrichment program which provides work experience with public/private sector employers and researchers. Under supervision of a faculty advisor, students provide mathematical consultation services. Prerequisites: consent of instructor.
299. Reading and Research (1 to 12) Independent study and research for the doctoral dissertation. One to three credits will be given for independent study (reading) and one to nine for research. Prerequisite: consent of instructor. (S/U grades permitted.)
Teaching of Mathematics
500. Apprentice Teaching (1 to 4) Supervised teaching as part of the mathematics instructional program on campus (or, in special cases such as the CTF program, off campus). Prerequisite: consent of advisor. (S/U grades only.)
