2.  Either one course in the physical sciences if (a) above is completed or one course in the biological sciences if (b) or (c) above is completed

The major requirements for the B.A. and B.S. degrees in Mathematics are as follows:

For the Bachelor of Science

Lower-division requirements for all programs are MATH 009A-MATH 009B-MATH 009C, MATH 010A-MATH 010B, MATH 046, CS 010 (CS 012 is recommended).

1.  Pure Mathematics program (56 units)

a)  Thirty-six (36) units of upper-division mathematics to include at least 24 units from MATH 131, MATH 132, MATH 145A-MATH 145B, MATH 151A-MATH 151B-MATH 151C, MATH 171, MATH 172
b)  At least three from (a) above must be from MATH 145A-MATH 145B, MATH 151A-MATH 151B-MATH 151C
c)  Courses in the MATH 190-199 series are excluded
d)  Twenty (20) additional units of upper-division mathematics, upper-division computer science, or other related courses approved by the Undergraduate Advisor (For students who wish to pursue graduate work, courses in complex variables, differential equations, and probability may be particularly useful.)

2.  Applied Mathematics programs

  MATH 113 or MATH 131, MATH 132, MATH 146A-MATH 146B-MATH 146C and the courses in one of the following options:

a)  Biology option
(1)  BIOL 005A, BIOL 005B, BIOL 005C
(2)  MATH 149A
(3)  Three courses from MATH 120, MATH 121, MATH 135A-MATH 135B, MATH 149B-MATH 149C
(4)  BIOL 102, BIOL 105, BIOL 108, BIOL 117
(5)  Four (4) additional units of upper-division biology

b)  Chemistry option
(1)  CHEM 001A-CHEM 001B-CHEM 001C
(2) Either PHYS 040A, PHYS 040B, PHYS 040C (preferred); or PHYS 002A, PHYS 002B, PHYS 002C
(3)  Four courses from MATH 120, MATH 135A-MATH 135B, MATH 149A-MATH 149B-MATH 149C, MATH 165A-MATH 165B
(4)  CHEM 110A-CHEM 110B, CHEM 111, CHEM 113
(5)  Four (4) additional units of upper-division chemistry

c)  Economics option
(1)  MATH 120, MATH 121, MATH 149A-MATH 149B-MATH 149C
(2)  Twenty (20) units of upper-division economics, including ECON 102A, ECON 107, ECON 108, ECON 110

d)  Environmental Sciences option
(1)  CHEM 001A-CHEM 001B-CHEM 001C
(2)  ECON 006/ENSC 006
(3)  GEO 001 is recommended
(4)  MATH 149A
(5)  Three courses from MATH 120, MATH 121, MATH 135A-MATH 135B, MATH 149B-MATH 149C; CS 177; STAT 155
(6)  ENSC 100, ENSC 100L, ENSC 101, ENSC 102
(7)  Eight (8) additional units of upper-division environmental sciences

e)  Physics option
(1)  MATH 135A, MATH 165A-MATH 165B
(2)  Either MATH 120 or MATH 171
(3)  PHYS 130A-PHYS 130B
(4)  Either PHYS 135A-PHYS 135B, PHYS 136 or PHYS 156A-PHYS 156B

f)  Statistics option
(1)  MATH 120, MATH 149A-MATH 149B-MATH 149C
(2)  Either STAT 130 or STAT 146
(3)  STAT 161, STAT 170A, STAT 170B, STAT 171

3.  Computational Mathematics program

a)  MATH 112, MATH 113 or MATH 131, MATH 120, MATH 132, MATH 135A-MATH 135B
b)  CS 012, CS 014, CS 141, CS 150. One course to be chosen from the list of approved technical elective courses.
c)  Twenty-four (24) units of technical electives to be chosen from
(1)  MATH 121, MATH 125A-MATH 125B, MATH 146A-MATH 146B-MATH 146C, MATH 149A-MATH 149B-MATH 149C, MATH 171
(2)  CS 130, CS 166, CS 170, CS 177

It is the responsibility of the honors candidates to notify the department of their eligibility.

Minor

The following are the requirements for a minor in Mathematics.

1. Lower-division requirements (20 units): MATH 009A-MATH 009B-MATH 009C, MATH 010A-MATH 010B
2. Upper-division requirements: Twenty-four (24) units of upper-division mathematics courses

Students with a minor in Mathematics should consult with a faculty advisor in Mathematics to construct a specific program consistent with their goals.

See Minors under the College of Natural and Agricultural Sciences in the Undergraduate Studies section of this catalog for additional information on minors.

Education Abroad Program

To qualify for MATH 009A, MATH 022, and MATH 023, a student must score at least 36 (60%) on the Pre-calculus Examination. To qualify for MATH 005, MATH 014, and MATH 015, a student must score at least 18 (30%) on the Pre-Calculus Examination or at least 27 (60%) on the Mathematical Analysis Examination.

MATH 003. Basic Algebra. (0)

Lecture, two hours; laboratory, four hours. Prerequisite(s): none. Basic algebra, linear functions and equations, quadratic functions and equations, operations with functions. This course is not intended to meet any mathematics or physical science requirement and is intended for students who plan to take MATH 005 but are not prepared to take that course. Carries workload credit equivalent to four units but does not count towards graduation units.

MATH 005. Introduction to College Mathematics. (5)

Lecture, four hours; discussion, one hour. Prerequisite(s): MATH 003 with a grade of "C-" or better or equivalent, or a sufficiently high test score on the Mathematical Analysis Examination, as determined by the Mathematics Department. A study of inequalities, absolute value, functions, graphing, logarithms, trigonometry, roots of polynomials, and other elementary concepts of mathematics.

MATH 009A-MATH 009B-MATH 009C. First-Year Calculus. (4-4-4)

Lecture, three hours; discussion, one hour. Prerequisite(s): for MATH 009A: MATH 005 with a grade of "C-" or better or equivalent; for MATH 009B: MATH 009A or MATH 09HA with a grade of "C-" or better; for MATH 009C: MATH 009B or MATH 09HB with a grade of "C-" or better. 009A. Introduction to the differential calculus of functions of one variable; 009B. Introduction to the integral calculus of functions of one variable; 009C. Further topics from integral calculus, improper integrals, infinite series, Taylor's series, and Taylor's theorem. Credit is awarded for only one of MATH 009A or MATH 09HA, only one of MATH 009B or MATH 09HB, and only one of MATH 009C or MATH 09HC.

MATH 09HA-MATH 09HB-MATH 09HC. First Year Honors Calculus. (4-4-4)

Lecture, three hours; discussion, one hour. Prerequisite(s): for MATH 09HA: a score of 47 or higher on the Mathematics Placement Precalculus Examination; for MATH 09HB: either a score of 4 or higher on the AB Advanced Placement Test in Mathematics or a grade of "A-" or above in MATH 009A or MATH 09HA; for MATH 09HC: a grade of "A-" or above in MATH 009B or MATH 09HB. Honors course corresponding to MATH 009A-MATH 009B-MATH 009C for students with strong mathematical backgrounds. Emphasis is on theory and rigor. Credit is awarded for only one of MATH 009A or MATH 09HA, only one of MATH 009B or MATH 09HB, and only one of MATH 009C or MATH 09HC.

MATH 010A-MATH 010B. Calculus of Several Variables. (4-4)

Lecture, three hours; discussion, one hour. Prerequisite(s): for 010A: MATH 009B; for 010B: MATH 009C and MATH 010A. 010A: Euclidean geometry, matrices and linear functions, determinants, partial derivatives, directional derivatives, Jacobians, gradients, chain rule, Taylor's theorem for several variables. 010B: Vector, differential calculus continued, implicit differentiation, extreme values, multiple integration, line integrals, vector field theory, theorems of Gauss, Green and Stokes.

MATH 014. Mathematics, A Humanistic Approach. (4)

Lecture, three hours; discussion, one hour. Prerequisite(s): MATH 003 or equivalent. Intended to fulfill the breadth requirement for students outside the natural and agricultural sciences. A survey of numerical and logical methods illustrating the role of mathematics in the development of civilization. Topics will include integral, rational, and irrational numbers; number systems; infinity; the concept of proof; as well as a glimpse of calculus. Only one of MATH 014 or MATH 015 may be taken for credit.

MATH 015. Liberal Arts Mathematics. (4)

Lecture, three hours; discussion, one hour. Prerequisite(s): MATH 003 or equivalent. Designed to fulfill the breadth requirement for students outside the natural and agricultural sciences. Illustrates the interaction of mathematics with other subject areas through the study of selected topics of contemporary mathematics. Topics are chosen from discrete mathematics, counting and probability, and the interaction between algebra and geometry.

MATH 022. Calculus for Business. (5)

Lecture, three hours; discussion, two hours. Prerequisite(s): MATH 005 or equivalent. Relations and functions (linear, polynomial, logarithmic, and exponential), differential calculus of functions of one and two variables, and integration (indefinite and definite) with applications to business and economic problems. Credit will not be given for MATH 022 if it has already been given for MATH 009A or MATH 09HA.

MATH 023. Applied Matrix Algebra. (4)

Lecture, three hours; discussion, one hour. Prerequisite(s): MATH 005 or equivalent. Matrix operations, linear dependence and independence, ranks and inverses, systems of linear equations, determinants, eigenvalues, and eigenvectors with business and economic applications. This course is designed for students who are not mathematics majors and does not count toward fulfillment of the mathematics major requirement.

MATH 046. Introduction to Ordinary Differential Equations. (4)

Lecture, three hours; discussion, one hour. Prerequisite(s): MATH 009C. First order equations, linear second order equations, series solutions. Laplace transforms, applications to the physical and biological sciences.

Lecture, three hours; discussion, one hour. Prerequisite(s): MATH 009A, CS 010. Introduction to the basic concepts of finite and structural mathematics with emphasis on applications to computer science. Topics include axiomatic systems, combinatorics, propositional and predicate calculi, graph theory, trees, state diagrams, networks, induction, elementary enumeration, and recurrence relations.

MATH 113. Applied Linear Algebra. (5)

Lecture, three hours; discussion, two hours. Prerequisite(s): MATH 010A. Matrices and systems of linear equations, determinants, Gaussian elimination and pivoting, vector spaces, linear independence and linear transformation, orthogonality, eigenvalues and eigenvectors. Selected topics and applications. Numerical linear algebra and extensive computer use are integrated with these topics. Credit is awarded for only one of MATH 113 or MATH 131.

MATH 120. Optimization. (4)

Lecture, three hours; discussion, one hour. Prerequisite(s): MATH 010A; MATH 113 or MATH 131 (may be taken concurrently). Introduction to classical optimization, including unconstrained and constrained problems in several variables, Jacobian and Lagrangian methods, and the Kuhn-Tucker conditions. Covers the basic concepts of linear programming, including the simplex method and duality, with applications to other subjects.

MATH 121. Game Theory. (4)

Lecture, three hours; discussion, one hour. Prerequisite(s): MATH 010A. Games in extensive, normal, and characteristic form as models of conflict and/or cooperation. Two-person zero-sum games, minimax theorem, relation to linear programming. Non-zero-sum games, Nash equilibrium theorem, bargaining, the core, Shapley value. Economic market games.

MATH 125A-MATH 125B. Introduction to Combinatorics. (4-4)

Lecture, three hours; discussion, one hour. Prerequisite(s): MATH 009C, MATH 112. Elements of graph theory, Polya's theory of counting, principle of inclusion-exclusion, Hall matching theorem, combinatorial designs.

MATH 131. Linear Algebra I. (4)

Lecture, three hours; discussion, one hour. Prerequisite(s): MATH 010A. An introduction to vector spaces, matrices, and linear transformations. Only one of the MATH 113 or MATH 131 may be taken for credit.

MATH 132. Linear Algebra II. (4)

Lecture, three hours; discussion, one hour. Prerequisite(s): MATH 113 or MATH 131. Further topics in linear algebra including eigenvalues, Hermitian and unitary matrices, positive definite matrices, and canonical forms.

MATH 133. Geometry. (4)

Lecture, three hours; discussion, one hour. Prerequisite(s): MATH 113 or MATH 131 or consent of instructor. Elementary theory of affine and projective planes, the line at infinity, finite geometries, Euclidean and non-Euclidean geometries, groups of transformations, and other algebraic structures related to geometry.

MATH 135A-MATH 135B. Numerical Analysis. (4-4)

Lecture, three hours; discussion, one hour. Prerequisite(s): CS 010 or equivalent; MATH 113 or MATH 131 (may be taken concurrently). Numerical methods for the determination of solutions to nonlinear equations and simultaneous linear equations. Interpolation, numerical integration, and the numerical solution of ordinary differential equations. Techniques of error analysis. Computer applications.

MATH 136. Introduction to the Theory of Numbers. (4)

Lecture, three hours; discussion, one hour. Prerequisite(s): MATH 113 or MATH 131. Prime and composite integers, number theoretic functions, diophantine equations, congruences, quadratic reciprocity, additive arithmetic.

MATH 137A-MATH 137B. Plane Curves. (4)

Lecture, three hours; discussion, one hour. Prerequisite(s): MATH 010B; MATH 132; for MATH 137B: MATH 137A. The complex projective plane, homogeneous polynomials, plane curves; intersection multiplicities and Bezout's theorem; simple and singular points, tangents, duality; structure of cubic curves; birational transformations and resolution of singularities.

MATH 138A. Introduction to Differential Geometry. (4)

Lecture, three hours; discussion, one hour. Prerequisite(s): MATH 113 or MATH 131. Elementary theory of curves and surfaces. First and second fundamental forms.

MATH 138B. Introduction to Differential Geometry. (4) S

Lecture, three hours; discussion, one hour. Prerequisite(s): MATH 010B, MATH 138A. Gaussian curvature; geodesics; Gauss-Bonnet Theorem.

MATH 144. Introduction to Set Theory. (4)

Lecture, three hours; discussion, one hour. Prerequisite(s): MATH 010A. Algebra of subsets of a set. Algebra of relations and functions. Cardinal and ordinal numbers and their arithmetic operations. The well-ordering theorem, transfinite induction, and Zorn's lemma.

MATH 145A. Introduction to Topology. (4)

Lecture, three hours; discussion, one hour. Prerequisite(s): MATH 144. Elementary topology in metric spaces.

MATH 145B. Introduction to Topology. (4)

Lecture, three hours; discussion, one hour. Prerequisite(s): MATH 145A. Geometric topology, algebra associated with finite complexes and applications.

MATH 146A-MATH 146B-MATH 146C. Ordinary and Partial Differential Equations. (4-4-4)

Lecture, three hours; discussion, one hour. Prerequisite(s): MATH 010A-MATH 010B, MATH 046. Theory of linear differential equations, orthogonal expansions, boundary value problems for ordinary and partial differential equations, separation of variables, transform methods.

MATH 149A-MATH 149B-MATH 149C. Probability and Mathematical Statistics. (4-4-4)

Lecture, three hours; laboratory, one hour. Prerequisite(s): MATH 010A-MATH 010B, MATH 046 (may be taken concurrently). An introduction to the mathematical theory of probability and statistics. Discrete and continuous distributions, sampling distributions, tests of hypotheses, estimation, maximum likelihood techniques, regression and correlation. Students may not receive credit for more than one of the sequences MATH 149A-MATH 149B-MATH 149C and STAT 160A-STAT 160B-STAT 160C.

MATH 151A-MATH 151B-MATH 151C. Advanced Calculus. (4-4-4)

Lecture, three hours; discussion, one hour. Prerequisite(s): MATH 010A-MATH 010B, MATH 046, MATH 145A, or consent of instructor. A rigorous development of mathematical analysis. Real and complex numbers. Sequences and series. Continuity. Differentiation. The Riemann-Stieltjes integral. Sequences and series of functions. Functions of several variables.

MATH 153. History of Mathematics. (4) S

Lecture, three hours; discussion, one hour or term paper, three hours. Prerequisite(s): MATH 009C or consent of instructor. A survey from a historical point of view of various developments in mathematics with particular emphasis on the nineteenth and early twentieth centuries.

MATH 165A-MATH 165B. Introduction to Complex Variables. (4-4)

Lecture, three hours; discussion, one hour. Prerequisite(s): MATH 010B. An introduction to the theory of analytic functions of a complex variable. Mappings by elementary functions, complex integrals, and Cauchy's theorem. Power series and Laurent series, the theory of residues, and conformal mapping. Applications to physical problems.

MATH 171. Introduction to Modern Algebra. (4)

Lecture, three hours; discussion, one hour. Prerequisite(s): MATH 131, MATH 144. An introduction to the fundamental concepts of modern algebra: groups, subgroups, quotient groups, homomorphisms, symmetry groups, fundamental properties of rings, integral domains, ideals, and quotient rings.

MATH 172. Modern Algebra. (4) S

Lecture, three hours; discussion, one hour. Prerequisite(s): MATH 171. Fundamental concepts of modern algebra: groups, fields, polynomials, geometric constructions, algebraic coding, boolean algebras.

MATH 190. Special Studies. (1-5)

To be taken with the consent of the chair of the department as a means of meeting special curricular problems.

MATH 191 (E-Z). Seminar in Mathematics. (1-4)

Seminar, one to four hours. Prerequisite(s): upper-division standing or consent of instructor. Additional prerequisites may be required for segments of this course; see Department. Consideration of selected current problems in mathematics.

MATH 194. Independent Reading. (1-2)

Independent reading in materials not covered in course work. Normally taken in the senior year. Total credit for MATH 194 may not exceed four units.

MATH 198-I. Internship in Mathematics. (1-4)

Variable hours. Prerequisite(s): upper-division standing, with at least 12 units of upper-division credits toward the major. An academic internship to provide the student with career experience as a mathematician in a governmental, industrial, or research unit under the joint supervision of an off-campus sponsor and a faculty member in Mathematics. Each individual program must have the prior approval of both supervisors and the department chair. A final written report is required. Graded Satisfactory (S) or No Credit (NC). May be repeated for a total of eight units.

Lecture, three hours; discussion, one hour. Prerequisite(s): MATH 171, MATH 172, or equivalents. Basic theory of groups, rings, modules and fields. The Sylow theorems, modules over a principal ideal domain, the functors hom and tensor, the tensor and exterior algebras, applications to matrices, algebraic and transcendental extensions of fields and Galois theory.

MATH 205A-MATH 205B-MATH 205C. Topology. (4-4-4)

Lecture, three hours; research, three hours. Prerequisite(s): MATH 145B or equivalent. Introduction to point-set topology, homotopy theory and homology theory.

MATH 209A-MATH 209B-MATH 209C. Real Analysis. (4-4-4)

Lecture, three hours. Prerequisite(s): MATH 151C. Measure theory, integration, representation theorems. Complex measures, integration on product spaces, differentiation. Lebesgue spaces, Hilbert space, Banach space.

MATH 210A-MATH 210B. Complex Analysis. (4-4)

Lecture, three hours. Prerequisite(s): MATH 151C and MATH 165A. Complex functions, Cauchy's theorem and consequences, Taylor and Laurent series, representation theorems for meromorphic and entire functions, residues, harmonic functions, analytic continuation, conformal mapping, and Riemann surfaces.

MATH 211A-MATH 211B. Ordinary Differential Equations. (4-4)

Lecture, three hours; discussion, one hour. Prerequisite(s): MATH 151C. Existence and uniqueness of solutions, linear differential equations, singularities of the first and second kinds, self-adjoint eigenvalue problems on a finite interval, singular self-adjoint boundary-value problems for second-order equations; method of averaging and numerical integration; autonomous systems. Method of Liapounov; stability for linear systems.

MATH 212. Partial Differential Equations. (4)

Lecture, three hours; discussion, one hour. Prerequisite(s): MATH 151C and MATH 165A. Classical theory of initial and boundary value problems for hyperbolic, parabolic and elliptic partial differential equations.

MATH 216A-MATH 216B. |Combinatorial Theory. (4-4)

Lecture, three hours; discussion, one hour. Introduction to Combinatorial Optimization and Combinatorial Geometry including flows on networks, matroids, linear programming, lattices, exchange properties, Mobius function, Galois connection, coordinization.

MATH 217A-MATH 217B. Theory of Probability. (4-4)

Lecture, three hours; discussion, one hour. Prerequisite(s): MATH 209A-MATH 209B-MATH 209C. Weak and strong limit theorems including the laws of large numbers, the central limit problem, and infinitely divisible distributions. Martingales and other topics in stochastic processes.

MATH 220. Approximation Theory. (4)

Lecture, three hours; research, three hours. Prerequisite(s): MATH 209C. The study of the best approximation operator including the classical Chebyshev theory concerning approximations of continuous functions from a fixed finite-dimensional subspace (e.g. nth degree polynomials). Also a study of the minimal projection operator.

MATH 221. Several Complex Variables. (4)

Lecture, three hours; research, three hours. Prerequisite(s): MATH 151A-MATH 151B, MATH 165A-MATH 165B. Hartog's theorems, domains of holomorphy, pseudoconvexity, Levi's problem, coherent analytic sheaves, Cartan's theorems A and B.

MATH 223. Algebraic Number Theory. (4)

Lecture, three hours; discussion, one hour. Prerequisite(s): MATH 201A. Algebraic number theory, including principal ideal domains, integral independence, algebraic number fields, classical ideal theory in Dedekind domains, classes of ideals, valuations, p-adic number.

MATH 224. Introduction to Homological Algebra. (4)

Lecture, three hours; outside research, three hours. Prerequisite(s): MATH 201C or consent of instructor. Theory of derived functors and its application to rings and associative algebras.

MATH 225A-MATH 225B. Commutative Algebra. (4-4)

Lecture, three hours; outside research, three hours. Prerequisite(s): MATH 201A-MATH 201B-MATH 201C. Basic theory of commutative rings, primary decomposition, integral dependence and valuation rings, intersection theorem of Krull, structure theorems for complete local rings, geometric local rings.

MATH 227A-MATH 227B. Lie Algebras. (4-4)

Lecture, three hours; outside research,three hours. Prerequisite(s): MATH 201A-MATH 201B. Basic definitions; solvable and nilpotent Lie algebras; structure and classification of semisimple Lie algebras; enveloping algebras and representation theory; representations of semisimple Lie algebras; generalization to Kac-Moody Lie algebras; and modular Lie algebras.

MATH 228. Functional Analysis. (4)

Lecture, three hours; discussion, one hour. Prerequisite(s): MATH 209A-MATH 209B-MATH 209C. Topological linear spaces; function spaces; linear operators; spectral theory; operational calculus; and further selected topics.

MATH 229A-MATH 229B. Stochastic Processes. (4-4)

Lecture, three hours; outside research, three hours. Prerequisite(s): MATH 217A-MATH 217B or consent of instructor. Sample path analysis of stochastic processes: separability and regularity properties. Topics from martingale and Markov processes, stochastic integration, semimartingales and stochastic differential equations. Each of these topics has an extensive theory, and so the courses are repeatable.

MATH 232A. Geometry I (Introduction to Manifolds). (4)

Lecture, three hours; outside research, three hours. Prerequisite(s): MATH 131 and MATH 151C. Basic notions and examples; vector fields and flows; tensors and vector bundles; differential forms, integration and deRham's theorem.

MATH 232B. Geometry II (Introduction to Differential). (4)

Lecture, three hours; outside research, three hours. Prerequisite(s): MATH 232A. Local and global theory of curves. Surfaces in R3: the Gauss map, fundamental forms, curvature. Riemannian geometry: the Levi-Civita connection, curvature, geodesics, exponential map, completeness, Gauss-Bonnet theorem for surfaces.

MATH 241. Mathematical Physics: Classical Mechanics. (4)

Lecture, three hours; outside research, three hours. Prerequisite(s): MATH 205A-MATH 205B-MATH 205C or PHYS 205 or consent of instructor. Hamilton's principle of least action. Variational methods and Lagrange's equations. Hamilton's equations. Introduction to symplectic geometry and its applications to classical mechanics. Poisson brackets. Conserved quantities and Noether's theorem. Examples of Hamiltonian and dissipative dynamical systems. Introduction to classical chaos.

MATH 242. Mathematical Physics: Quantum Mechanics. (4)

Lecture, three hours; outside research, three hours. Prerequisite(s): MATH 209A-MATH 209B-MATH 209C, MATH 228; or consent of instructor. Foundations of quantum theory together with the relevant mathematics. Probabilistic interpretation of quantum mechanics, self-adjoint operators and physical observables, noncommutativity and the uncertainty principle. Spectral theory for (unbounded) self-adjoint operators. Stone's theorem and other topics.

MATH 243A-MATH 243B. Algebraic Geometry. (4-4)

Lecture, three hours; outside research, three hours. Prerequisite(s): MATH 201A-MATH 201B-MATH 201C; MATH 205A or concurrent enrollment or equivalent. Algebraic varieties in affine and projective space, mappings and correspondences, sheaves and cohomology, detailed study of curves and special topics.

MATH 246A-MATH 246B. Algebraic Topology. (4-4)

Lecture, three hours; discussion, one hour. Prerequisite(s): MATH 205B. An introduction to simplices, geometric complexes and polytopes, manifolds, dimension theory, the topological index, homotopy, homology and transformation groups.

MATH 260. Seminar. (1-4)

Variable hours. Prerequisite(s): consent of department. Seminar on special topics of mathematics in preparation for individual research. Course is repeatable.

MATH 289. Colloquium in Mathematics. (1)

Prerequisite(s): graduate standing. Specialized discussions by staff, students and visiting scientists on current research topics in Mathematics. Graded Satisfactory (S) or No Credit (NC). Course is repeatable.

MATH 290. Directed Studies. (1-6)

Prerequisite(s): consent of instructor. Research and special studies in mathematics. Graded Satisfactory (S) or No Credit (NC). Course may be repeated.

MATH 299. Research for Thesis or Dissertation. (1-12)

Prerequisite(s): consent of department. Graded Satisfactory (S) or No Credit (NC). Course is repeatable.

Clinic, two hours. Prerequisite(s): Limited to Teaching Assistants and Associates in Mathematics. Supervised teaching in upper- and lower-division Mathematics courses. Required fall and winter quarters of all Mathematics Teaching Assistants and Associates. Intended to aid in the learning of effective teaching methods such as the handling of Mathematics discussion sections, preparation and grading of examinations, and student relations. Graded Satisfactory (S) or No Credit (NC).