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Fall 2002 Course Descriptions

All courses below are approved to be taught in Fall 2002; however, some (or all) may not be offered this term.  The course numbers that are offered this term link to the Schedule of Classes.  The complete list below is a good indicator of what may be offered over the next few years (contact department about offerings).  For explanations of course elements see the Key to Course Descriptions.

Mathematics (MATH)  Department Info

MATH 105 -- Mathematics in Modern Society  (3 units)
Description:  The course will examine topics such as voting schemes, apportionment problems, network problems, critical paths, Fibonacci numbers, population models, symmetry, fractals, data analysis, probability and statistics. Registration in math courses numbered 125 or below, 160, and 263, requires all students, including transfer students with or without college level math credit, to take the UA Math Readiness Test. Formerly MATH 122.
Prerequisite(s):  acceptable score on the UA Math Readiness Test.
Usually offered:  Fall, Spring.

MATH 110 -- College Algebra  (4 units)
Description:  Topics include properties of functions and graphs, linear and quadratic equations, polynomial functions, rational functions, exponential and logarithmic functions with applications, sequences and series. Course includes an integrated review of important concepts in intermediate algebra. Students are expected to have a graphing calculator. MATH 110 may be substituted for MATH 117 in any university requirement or prerequisite. Registration in math courses numbered 125 or below, 160, and 263, requires all students, including transfer students with or without college level math credit, to take the UA Math Readiness Test. Credit will not be given for this course if the student has credit in a higher level math course; these students will be dropped from the course. Students with unusual circumstances can petition the Mathematics Department for exemption from this rule. This policy does not infringe on the student's rights granted by the university policy on repeating a course. Formerly MATH 121.
Prerequisite(s):  acceptable score on Math Readiness Test.
Usually offered:  Fall, Spring.

MATH 111 -- Plane Trigonometry  (2 units)
Description:  Not applicable to the mathematics major or minor. Students with credit in MATH 120R or MATH 120S obtain one unit of graduation credit for MATH 111. Registration in math courses numbered 125 or below, 160, and 263, requires all students, including transfer students with or without college level math credit, to take the UA Math Readiness Test. Credit will not be given for this course if the student has credit in a higher level math course; these students will be dropped from the course. Students with unusual circumstances can petition the Mathematics Department for exemption from this rule. This policy does not infringe on the student's rights granted by the university policy on repeating a course. Formerly MATH 118.
Prerequisite(s):  acceptable score on the UA Math Readiness Test.
Usually offered:  Fall, Spring.

MATH 112 -- College Algebra Accelerated  (3 units)
Temporary course:  offered during Fall 2002 only.
Description:  Topics include properties of functions and graphs, linear and quadratic equations, polynomial functions, rational functions, exponential and logarithmic functions with applications, sequences and series. Students are expected to have a graphing calculator. MATH 112 may be substituted for MATH 121 or 110 in any university requirement or prerequisite. Registration in math courses numbered 125 or below, 160, and 263, requires all students, including transfer students with or without college level math credit, to take the UA Math Readiness Test. Credit will not be given for this course if the student has credit in a higher level math course; these students will be dropped from the course. Students with unusual circumstances can petition the Mathematics Department for exemption from this rule. This policy does not infringe on the student's rights granted by the university policy on repeating a course.
Prerequisite(s):  A satisfactory score on the UA Math Placement Exam.

MATH 113 -- Elements of Calculus  (3 units)
Description:  Introductory topics in differential and integral calculus. Registration in math courses numbered 125 or below, 160, and 263, requires all students, including transfer students with or without college level math credit, to take the UA Math Readiness Test. Formerly MATH 123.
Prerequisite(s):  MATH 110 or acceptable score on UA Math Readiness Test. Credit allowed for only one of the following courses: MATH 113, MATH 124, or MATH 125.
Usually offered:  Fall, Spring.

MATH 114 -- Finite Mathematics  (3 units)
Description:  Elements of set theory and counting techniques, probability theory, linear systems of equations, matrix algebra; linear programming with simplex method, Markov chains. Registration in math courses numbered 125 and below, 160, and 263, requires all students, including transfer students with or without college level math credit, to take the UA Math Readiness Test. Formerly MATH 119.
Prerequisite(s):  MATH 110 or acceptable score on the UA Math Readiness Test.
Usually offered:  Fall, Spring.

MATH 115A -- Business Mathematics I  (3 units)
Description:  Probability, conditional probability, Bayes' Theorem, random variables, random sampling, compound interest, expected value, computer simulation, and spreadsheet functions. The course is based on an electronic text, with extensive use of spreadsheets, downloaded data, and team reports on major business projects.
Prerequisite(s):  MATH 110, MIS 111. Prerequisite courses taken at UA or must have an acceptable score on the MRT. Credit allowed for only one of the following pairs of courses: MATH 113 and MATH 114, or MATH 115A and MATH 115B.
Usually offered:  Fall, Spring.

MATH 115B -- Business Mathematics II  (3 units)
Description:  Variance, normal distributions, distribution of the sample mean, integration, differentiation, advanced spreadsheet functions, and computer simulation. The course is based on an electronic text, with extensive use of spreadsheets, downloaded data, and team reports on major business projects.
Prerequisite(s):  MATH 115A. Course must be taken at UA. Credit allowed for only one of the following pairs of courses: MATH 113 and MATH 114, or MATH 115A and MATH 115B.
Usually offered:  Fall, Spring.

MATH 120R -- Calculus Preparation  (4 units)
Description:  Reviews algebra and trigonometry; study of functions including polynomial, rational, exponential, logarithmic and trigonometric. For students who have high school credit in college algebra and trigonometry but have not attained a sufficient score on the UA Math Readiness Test to enter calculus. Students with credit in both MATH 110 and MATH 111 receive no credit for MATH 120R. Students with credit in MATH 111, but not MATH 110, receive three units of graduation credit for MATH 120R. Students with credit in MATH 110 but not MATH 111, will receive one unit of graduation credit for MATH 120R. Graphing calculators are required in this course. Registration in math courses numbered 125 or below, 160, and 263, requires all students, including transfer students with or without college level math credit, to take the UA Math Readiness Test. Credit will not be given for this course if the student has credit in a higher level math course; these students will be dropped from the course. Students with unusual circumstances can petition the Mathematics Department for exemption from this rule. This policy does not infringe on the student's rights granted by the university policy on repeating a course.
Prerequisite(s):  acceptable score on UA Math Readiness Test.
Usually offered:  Fall, Spring.

MATH 120S -- Calculus Prep, Self-Study  (2 units)
Description:  A self-study course designed for students registered in MATH 124 who need more review of algebra, functions, graphs, trigonometry. Students can drop MATH 124 and add MATH 120S at a time designated by the Mathematics Department.
Prerequisite(s):  consent of current MATH 124 instructor. Credit allowed for only one of MATH 120S; MATH 110 and MATH 111; or MATH 120R.
Usually offered:  Fall.

MATH 124 -- Calculus I with Applications  (5 units)
Description:  Introduction to calculus with an emphasis on understanding and problem solving. Concepts are presented graphically and numerically as well as algebraically. Elementary functions, their properties and uses in modeling; the key concepts of derivative and definite integral; techniques of differentiation, using the derivative to understand the behavior of functions; applications to optimization problems in physics, biology and economics. A graphing calculator is required in this course. Registration in math courses numbered 125 or below, 160, and 263, requires all students, including transfer students with or without college level math credit, to take the UA Math Readiness Test. Credit will not be given for this course if the student has credit in a higher level math course; these students will be dropped from the course. Students with unusual circumstances can petition the Mathematics Department for exemption from this rule. This policy does not infringe on the student's rights granted by the university policy on repeating a course.
Prerequisite(s):  MATH 120R, or MATH 110 and MATH 111, or an acceptable score on the UA Math Readiness Test. Credit allowed for only one of the following courses: MATH 113, MATH 124, or MATH 125.
Usually offered:  Fall, Spring.

MATH 125 -- Calculus I  (3 units)
Description:  An accelerated version of 124. Introduction to calculus with an emphasis on understanding and problem solving. Concepts are presented graphically and numerically as well as algebraically. Elementary functions, their properties and uses in modeling; the key concepts of derivative and definite integral; techniques of differentiation, using the derivative to understand the behavior of functions; applications to optimization problems in physics, biology and economics. A graphing calculator is required for this course. Registration in math courses numbered 125 or below, 160, and 263, requires all students, including transfer students with or without college level math credit, to take the UA Math Readiness Test. Credit will not be given for this course if the student has credit in a higher level math course; these students will be dropped from the course. Students with unusual circumstances can petition the Mathematics Department for exemption from this rule. This policy does not infringe on the student's rights granted by the university policy on repeating a course. Formerly MATH 125A.
Prerequisite(s):  acceptable score on UA Mathematics Readiness Test. Credit allowed for only one of the following courses: MATH 113, MATH 124, or MATH 125.
Usually offered:  Fall, Spring.

MATH 129 -- Calculus II  (3 units)
Description:  Continuation of 124 or 125. Techniques of symbolic and numerical integration, applications of the definite integral to geometry, physics, economics, and probability; differential equations from a numerical, graphical, and algebraic point of view; modeling using differential equations, approximations by Taylor series. A graphing calculator is required for this course. Formerly MATH 125B.
Prerequisite(s):  MATH 124 or MATH 125. Credit allowed for only one of the following: MATH 129 or MATH 250A.
Usually offered:  Fall, Spring.

MATH 160 -- Basic Statistics  (3 units)
Description:  Organizing data: displaying distributions, measures of center, measures of spread, scatterplots, correlation, regression, and their interpretation. Design of experiments: simple random samples and their sampling distribution, models from probability, normal distributions, and normal approximations. Statistical inference: confidence intervals and hypothesis testing, t procedures and chi-square tests. Not intended for those who plan further studies in statistics. Registration in math courses numbered 125 or below, 160, and 263, requires all students, including transfer students with or without college level math credit, to take the UA Mathematics Readiness Test.
Prerequisite(s):  MATH 110 or an acceptable score on the UA Mathematics Readiness Test. Credit allowed for only one of the following: MATH 160 or MATH 263.
Usually offered:  Fall, Spring.

MATH 195B -- From the Pendulum to the Lynx and the Hare  (1 unit)
Description:  Introduction to non-linear dynamics and chaos. Mathematical content; historical significance; implications for the biological and physical sciences. This course is intended for entry-level students with a passion for mathematics and science. Emphasis on concepts as opposed to algebraic manipulation. Opportunity to study non-linear systems on the computer will be provided.  This is a First-Year Colloquium Course.
Prerequisite(s):  simultaneous enrollment in calculus recommended.
Identical to:  ECOL 195B; ECOL is home department.
Usually offered:  Fall.

MATH 197A -- Basic Statistical Computation  (1 unit)
Description:  Statistical computation using computer software. Projects accompany material in MATH 160 and MATH 263.
Prerequisite(s):  Concurrent registration, MATH 160 or MATH 263.
Usually offered:  Fall, Spring.

MATH 199 -- Independent Study  (1-4 units)
Description:  Qualified students working on an individual basis with professors who have agreed to supervise such work.
May be repeated:  an unlimited number of times, consult your department for details and possible restrictions.
Usually offered:  Fall, Spring, Summer.

MATH 199H -- Honors Independent Study  (1-6 units)
Description:  Qualified students working on an individual basis with professors who have agreed to supervise such work.
May be repeated:  an unlimited number of times, consult your department for details and possible restrictions.
Usually offered:  Fall, Spring.

MATH 202 -- Introduction to Symbolic Logic  (3 units)
Description:  Truth-functional logic and quantification theory; deductive techniques and translation into symbolic notation.
Identical to:  PHIL 202; PHIL is home department.
Usually offered:  Fall, Spring.

MATH 215 -- Introduction to Linear Algebra  (3 units)
Description:  Vector spaces, linear transformations and matrices. There is some emphasis on the writing of proofs.
Prerequisite(s):  MATH 129 or MATH 250A.
Usually offered:  Fall, Spring.

MATH 223 -- Vector Calculus  (4 units)
Description:  Vectors, differential and integral calculus of several variables.
Prerequisite(s):  MATH 129 or MATH 250A.
Usually offered:  Fall, Spring.

MATH 243 -- Discrete Mathematics in Computer Science  (3 units)
Description:  Set theory, logic, algebraic structures; induction and recursion; graphs and networks.
Prerequisite(s):  MATH 129 or MATH 250A.
Usually offered:  Fall, Spring.

MATH 250A -- Calculus and Differential Equations I  (3 units)
Description:  Integral calculus with applications, techniques of integration, solving first order differential equations using separation of variables, introduction to autonomous first order differential equations. The sequence MATH 250A-250B substitutes for the pair of courses MATH 129-254 or the pair MATH 129-355; however, MATH 250A alone does not substitute for MATH 129.
Prerequisite(s):  score of 4 or 5 on the "AB" Advanced Placement Calculus Exam, consent of instructor. Credit allowed for only one of the following: MATH 250A or MATH129.
Usually offered:  Fall.

MATH 250B -- Calculus and Differential Equations II  (3 units)
Description:  First order differential equations and modeling, approximations and series, second order differential equations, linear and nonlinear autonomous systems. The sequence MATH 250A-250B substitutes for the pair of courses MATH 129-254 or the pair MATH 129-355; however, MATH 250B alone does not substitute for MATH 254 or MATH 355.
Prerequisite(s):  MATH 250A. Credit allowed for only one of the following: MATH 250B, MATH 254, or MATH 355.
Usually offered:  Spring.

MATH 254 -- Introduction to Ordinary Differential Equations  (3 units)
Description:  Solution methods for ordinary differential equations, qualitative techniques; includes matrix methods approach to systems of linear equations and series solutions.
Prerequisite(s):  MATH 223. Credit allowed for only one of these courses: MATH 254, MATH 355 or MATH 250B.
Usually offered:  Fall, Spring.

MATH 263 -- Introduction to Statistics and Biostatistics  (3 units)
Description:  Organizing data; distributions, measures of center and spread, scatterplots, nonlinear models and transformations, correlation, regression. Design of experiments: models from probability, discrete and continuous random variables, normal distributions, sampling distributions, the central limit theorem. Statistical inference; confidence intervals and test of significance, t procedures, inference for count data, two-way tables and chi-square procedures, inference for regression, analysis of variance. Registration in math courses numbered 125 or below, 160, and 263, requires all students, including transfer students with or without college level math credit, to take the UA Mathematics Readiness Test.
Prerequisite(s):  MATH 110 or an acceptable score on the UA Math Readiness Test. Credit allowed for only one of MATH 160 or MATH 263.
Usually offered:  Fall, Spring.

MATH 294A -- Problem-Solving Laboratory  (1 unit)
Description:  The practical application, on an individual basis, of previously studied theory and the collection of data for future theoretical interpretation.
May be repeated:  an unlimited number of times, consult your department for details and possible restrictions.
Usually offered:  Fall, Spring.

MATH 299 -- Independent Study  (2-4 units)
Description:  Qualified students working on an individual basis with professors who have agreed to supervise such work.
May be repeated:  an unlimited number of times, consult your department for details and possible restrictions.
Usually offered:  Fall, Spring, Summer.

MATH 299H -- Honors Independent Study  (1-3 units)
Description:  Qualified students working on an individual basis with professors who have agreed to supervise such work.
May be repeated:  an unlimited number of times, consult your department for details and possible restrictions.
Usually offered:  Fall.

MATH 301 -- Understanding Elementary Mathematics  (4 units)
Description:  Development of a basis for understanding the common processes in elementary mathematics related to the concepts of number, measurement, geometry and probability.
Prerequisite(s):  MATH 110 or MATH 105. Open to elementary education majors only.
Usually offered:  Fall, Spring.

MATH 302A -- Understanding Elementary Mathematics (A)  (3 units)
Description:  Development of a basis for understanding the common processes in elementary mathematics related to whole numbers, fractions, integers, and probability.
Prerequisite(s):  MATH 105 or MATH 110 or acceptable score on the Math Readiness Test.
Usually offered:  Fall, Spring.

MATH 302B -- Understanding Elementary Mathematics (B)  (3 units)
Description:  Development of a basis for understanding the common processes in elementary mathematics related to estimation, graphing of functions, measurement, geometry, and data analysis.
Usually offered:  Fall, Spring.

MATH 310 -- Harmonic Analysis  (3 units)
Description:  The course treats the interplay between algebra and analysis in a way that enhances both subjects. Specific examples of functions and the groups related to them will be discussed.
Prerequisite(s):  MATH 129 or MATH 250A; MATH 215.
Usually offered:  Spring.

MATH 315 -- Introduction to Number Theory and Modern Algebra  (3 units)
Description:  Elementary number theory, complex numbers, field axioms, polynomial rings; techniques for solving polynomial equations with integer and real coefficients.
Prerequisite(s):  MATH 323.
Usually offered:  Spring.

MATH 322 -- Mathematical Analysis for Engineers  (3 units)
Description:  Complex functions and integration, line and surface integrals, Fourier series, partial differential equations.
Prerequisite(s):  MATH 250B or MATH 355. Credit allowed for only one of the following: MATH 322 or MATH 422.
Usually offered:  Fall, Spring.

MATH 323 -- Formal Mathematical Reasoning and Writing  (3 units)
Description:  Elementary real analysis as an introduction to abstract mathematics and the use of mathematical language. Elementary logic and quantifiers; manipulations with sets, relations and functions, including images and pre-images; properties of the real numbers; supremum and infimum; other topics selected from cardinality, the topology of the real line, sequence and limits of sequences and functions; the emphasis throughout is on proving theorems.  This is a Writing Emphasis Course.
Prerequisite(s):  satisfaction of the upper-division writing proficiency requirement; MATH 215.
Usually offered:  Fall, Spring.

MATH 330 -- Topics in Geometry  (3 units)
Description:  Topics to be selected from 2- and 3-dimensional combinatorial geometry, postulational Euclidean geometry, Euclidean transformational geometry, symmetry, and 2-dimensional crystallography.
Prerequisite(s):  MATH 215.
Usually offered:  Fall.

MATH 344 -- Foundations of Computing  (3 units)
Description:  Fundamental methods for understanding, developing, verifying and analyzing algorithms: predicate logic, induction, program verification, recurrences, discrete probability, regular expressions.
Prerequisite(s):  MATH 243.
Identical to:  C SC 344; C SC is home department.
Usually offered:  Fall, Spring, Summer.

MATH 355 -- Analysis of Ordinary Differential Equations  (3 units)
Description:  Linear and nonlinear equations; basic solution techniques; qualitative and numerical methods; systems of equations; computer studies; applications drawn from physical, biological and social sciences.
Prerequisite(s):  MATH 215. Credit allowed for only one of these courses: MATH 355, MATH 254, or MATH 250B.
Usually offered:  Fall, Spring.

MATH 362 -- Introduction to Probability Theory  (3 units)
Description:  Sample spaces, random variables and their properties, with considerable emphasis on applications.
Prerequisite(s):  MATH 113, MATH 129, or MATH 250A.
Usually offered:  Fall, Spring.

MATH 380 -- Math Models In Biology  (3 units)
Description:  Introduction to mathematical techniques in the biological sciences. Applications include biochemistry, physiology, and ecology.
Prerequisite(s):  MATH 129 or consent of instructor.
Identical to:  ECOL 380; ECOL is home department.
Usually offered:  Fall.

MATH 380L -- Math Models in Biology Lab  (1 unit)
Description:  Lab will be designed to allow students to wed theory and experimentation in the development and exploration of mathematical models in biology.
Prerequisite(s):  MATH 129 or consent of instructor; Concurrent registration, ECOL 380.
Identical to:  ECOL 380L; ECOL is home department.
Usually offered:  Fall.

MATH 397A -- Mathematics Education  (1 unit)
Description:  The practical application of theoretical learning within a group setting and involving an exchange of ideas and practical methods, skills, and principles.
Prerequisite(s):  MATH 315 or MATH 330. Open to teaching majors in mathematics only.
Usually offered:  Fall, Spring.

MATH 399 -- Independent Study  (1-5 units)
Description:  Qualified students working on an individual basis with professors who have agreed to supervise such work.
May be repeated:  an unlimited number of times, consult your department for details and possible restrictions.
Usually offered:  Fall, Spring, Summer.

MATH 399H -- Honors Independent Study  (3 units)
Description:  Qualified students working on an individual basis with professors who have agreed to supervise such work.
May be repeated:  an unlimited number of times, consult your department for details and possible restrictions.
Usually offered:  Fall, Spring.

MATH 401A -- Symbolic Logic  (3 units)
Description:  Intermediate propositional logic and quantificational theory, natural deduction, axiom systems, elementary metatheorems, introduction to notions of modal logic, selected topics in philosophy of logic. Credit allowed for only one of these course: PHIL 401A, PHIL 402.
Identical to:  PHIL 401A; PHIL is home department.
May be convened with:  MATH 501A.
Usually offered:  Fall.

MATH 401B -- Symbolic Logic  (3 units)
Description:  Advanced propositional logic and quantification theory; metatheorems on consistency, independence, and completeness; set theory, number theory, and modal theory; recursive function theory and Goedel's incompleteness theorem.
Identical to:  PHIL 401B; PHIL is home department.
May be convened with:  MATH 501B.
Usually offered:  Spring.

MATH 402 -- Mathematical Logic  (3 units)
Description:  [Taught alternate years 2001 - 2002] Sentential calculus, predicate calculus; consistency, independence, completeness, and the decision problem. Designed to be of interest to majors in mathematics or philosophy.
Prerequisite(s):  MATH 124 or MATH 125; experience with theoretical mathematical reasoning. Credit allowed for only one of these courses: MATH 402 or MATH 401A.
Identical to:  C SC 402, PHIL 402.
May be convened with:  MATH 502.
Usually offered:  Fall.

MATH 403 -- Foundations of Mathematics  (3 units)
Description:  [Taught alternate years 2001 - 2002] Topics in set theory such as functions, relations, direct products, transfinite induction and recursion, cardinal and ordinal arithmetic; related topics such as axiomatic systems, the development of the real number system, recursive functions.
Prerequisite(s):  MATH 215.
Identical to:  PHIL 403.
May be convened with:  MATH 503.
Usually offered:  Spring.

MATH 404 -- History of Mathematics  (3 units)
Description:  The development of mathematics from ancient times through the 17th century, with emphasis on problem solving. The study of selected topics from each field is extended to the 20th century.
Prerequisite(s):  MATH 215 or MATH 223.
May be convened with:  MATH 504.
Usually offered:  Fall.

MATH 405 -- Mathematics in the Secondary School  (3 units)
Description:  Study and analysis of curriculum changes in school mathematics, with emphasis on the design and content of experimental programs.
Prerequisite(s):  or Concurrent registration, MATH 315, MATH 330, MATH 362.
Identical to:  TTE 405; TTE is home department.
Usually offered:  Spring.

MATH 406 -- Methods of Teaching Mathematics in Secondary Schools  (4 units)
Temporary course:  offered during Fall 2002 only.
Description:  Provides students with knowledge and experience to enable them to become effective secondary Mathematics teachers. Emphasis on modes of instruction, problem-solving, use of technology, assessment, and national standards w/ special attention to teaching of geometry, algebra, statistics, and discrete mathematics.

MATH 408 -- Topics in Harmonic Analysis  (3 units)
Description:  Fast fourier transforms, classical fourier analysis, related group theory done concretely.
Prerequisite(s):  MATH 215; MATH 322 or MATH 323.
May be convened with:  MATH 508.
Usually offered:  Fall, Spring.

MATH 410 -- Matrix Analysis  (3 units)
Description:  General introductory course in the theory of matrices.
Prerequisite(s):  MATH 254 or MATH 355 or MATH 250B; knowledge of matrix operations (as contained in, for example, MATH 215 or SIE 270). Credit allowed for only one of the following: MATH 410, MATH 413.
Usually offered:  Fall, Spring.

MATH 413 -- Linear Algebra  (3 units)
Description:  Vector spaces, linear transformations and matrices, eigenvalues, bilinear forms, orthogonal and unitary transformations.
Prerequisite(s):  MATH 323. Credit allowed for only one of the following: MATH 413, MATH 410.
May be convened with:  MATH 513.
Usually offered:  Fall, Spring.

MATH 415A -- Introduction to Abstract Algebra  (3 units)
Description:  Introduction to groups, rings, and fields.
Prerequisite(s):  MATH 323.
May be convened with:  MATH 515A.
Usually offered:  Fall.

MATH 415B -- Second Course in Abstract Algebra  (3 units)
Description:  A continuation of 415A. Topics may include Galois theory, linear and multilinear algebra, finite fields and coding theory. Polya enumeration.
Prerequisite(s):  MATH 415A.
May be convened with:  MATH 515B.
Usually offered:  Spring.

MATH 421 -- Complex Variables with Applications  (3 units)
Description:  Complex numbers, analytic functions, harmonic functions, elementary functions, complex integration, Cauchy's integral theorem, series representations for analytic functions, residue theory, conformal mapping, applications to steady-state temperature and oscillating systems.
Prerequisite(s):  MATH 254 or MATH 355 or MATH 250B. Credit allowed for only one of the following: MATH 421 or MATH 424.
May be convened with:  MATH 521.
Usually offered:  Spring.

MATH 422 -- Advanced Applied Analysis  (3 units)
Description:  Review of multivariable calculus, series solutions of differential equations, Laplace transforms, Fourier series, introduction to partial differential equations.
Prerequisite(s):  MATH 254 or MATH 355 or MATH 250B. Credit allowed for only one of the following: MATH 422 or MATH 322.
May be convened with:  MATH 522.
Usually offered:  Fall.

MATH 424 -- Theory of Complex Variables  (3 units)
Description:  Complex numbers, complex-valued functions, analytic functions, elementary functions, series, residues and poles, mapping by elementary functions, conformal mapping, the Schwarz-Christoffel transformation, integral formulas of Poisson type.
Prerequisite(s):  MATH 323 or consent of instructor. Credit allowed for only one of the following:MATH 424 or MATH421.
May be convened with:  MATH 524.
Usually offered:  Fall, Spring.

MATH 425A -- Real Analysis of One Variable  (3 units)
Description:  Continuity and differentiation of functions of one variable. Riemann integration, sequences of functions and uniform convergence.
Prerequisite(s):  MATH 323.
May be convened with:  MATH 525A.
Usually offered:  Fall.

MATH 425B -- Real Analysis of Several Variables  (3 units)
Description:  Continuity and differentiation in higher dimensions, curves and surfaces; change of coordinates; theorems of Green, Gauss and Stokes; exact differentials.
Prerequisite(s):  MATH 425A.
May be convened with:  MATH 525B.
Usually offered:  Spring.

MATH 430 -- Second Course in Geometry  (3 units)
Description:  [Taught alternate years 2000 - 2001] Topics may include low-dimensional topology; map coloring in the plane, networks (graphs) polyhedra, two-dimensional surfaces and their classification, map coloring on surfaces (Heawood's estimate, Ringel-Young theory), knots and links or projective geometry.
Prerequisite(s):  MATH 215.
May be convened with:  MATH 530.
Usually offered:  Spring.

MATH 434 -- Introduction to Topology  (3 units)
Description:  [Taught alternate years 2000-2001] Properties of metric and topological spaces and their maps; topics selected from geometric and algebraic topology, including the fundamental group.
Prerequisite(s):  MATH 323.
Usually offered:  Spring.

MATH 443 -- Theory of Graphs and Networks  (3 units)
Description:  Undirected and directed graphs, connectivity, circuits, trees, partitions, planarity, coloring problems, matrix methods, applications in diverse disciplines.
Prerequisite(s):  MATH 323 or MATH 243 or graduate standing.
Identical to:  C SC 443.
May be convened with:  MATH 543.
Usually offered:  Fall.

MATH 446 -- Theory of Numbers  (3 units)
Description:  [Taught alternate years 2000 - 2001] Divisibility properties of integers, primes, congruencies, quadratic residues, number-theoretic functions.
Prerequisite(s):  MATH 215.
May be convened with:  MATH 546.
Usually offered:  Spring.

MATH 447 -- Combinatorial Mathematics  (3 units)
Description:  [Taught alternate years 2000 - 2001] Enumeration and construction of arrangements and designs; generating functions; principle of inclusion-exclusion; recurrence relations; a variety of applications.
Prerequisite(s):  MATH 215 or MATH 243.
May be convened with:  MATH 547.
Usually offered:  Spring.

MATH 454 -- Ordinary Differential Equations and Stability Theory  (3 units)
Description:  General theory of initial value problems, linear systems and phase portraits, linearization of nonlinear systems, stability and bifurcation theory, limit cycles and Poincare-Bendixson theory, an introduction to chaotic dynamics.
Prerequisite(s):  MATH 254 or MATH 355 or MATH 250B.
Usually offered:  Fall.

MATH 456 -- Applied Partial Differential Equations  (3 units)
Description:  Properties of partial differential equations and techniques for their solution: Fourier methods, Green's functions, numerical methods.
Prerequisite(s):  MATH 322 or MATH 422.
May be convened with:  MATH 556.
Usually offered:  Spring.

MATH 461 -- Elements of Statistics  (3 units)
Description:  Probability spaces, random variables, standard distributions, point and interval estimation, tests of hypotheses; includes use of standard Statistical software package.
Prerequisite(s):  MATH 223.
Usually offered:  Fall, Spring.

MATH 464 -- Theory of Probability  (3 units)
Description:  Probability spaces, random variables, weak law of large numbers, central limit theorem, various discrete and continuous probability distributions.
Prerequisite(s):  MATH 322 or MATH 323.
May be convened with:  MATH 564.
Usually offered:  Fall.

MATH 466 -- Theory of Statistics  (3 units)
Description:  Sampling theory. Point estimation. Limiting distributions. Testing Hypotheses. Confidence intervals. Large sample methods.
Prerequisite(s):  MATH 464.
May be convened with:  MATH 566.
Usually offered:  Spring.

MATH 468 -- Applied Stochastic Processes  (3 units)
Description:  Applications of Gaussian and Markov processes and renewal theory; Wiener and Poisson processes, queues.
Prerequisite(s):  MATH 464.
May be convened with:  MATH 568.
Usually offered:  Spring.

MATH 473 -- Automata, Grammars and Languages  (3 units)
Description:  Finite automata, regular expressions, and their applications; context-free grammars, pushdown automata, and their applications; Turing machines and undecidability; the Chomsky hierarchy. This is a Writing Emphasis Course.
Prerequisite(s):  C SC 344.
Identical to:  C SC 473; C SC is home department.
Usually offered:  Fall.

MATH 475A -- Mathematical Principles of Numerical Analysis  (3 units)
Description:  Analysis of errors in numerical computations, solution of linear algebraic systems of equations, matrix inversion, eigenvalues, roots of nonlinear equations, interpolation and approximation.
Prerequisite(s):  MATH 254 or MATH 355 or MATH 250B, MATH 215; knowledge of a scientific programming language.
Identical to:  C SC 475A.
Usually offered:  Fall.

MATH 475B -- Mathematical Principles of Numerical Analysis  (3 units)
Description:  Numerical integration, solution of systems of ordinary differential equations, initial value and boundary value problems.
Prerequisite(s):  MATH 475A.
Identical to:  C SC 475B.
Usually offered:  Spring.

MATH 479 -- Game Theory and Mathematical Programming  (3 units)
Description:  [Taught alternate years 2001-2002] Linear inequalities, games of strategy, minimax theorem, optimal strategies, duality theorems, simplex method.
Prerequisite(s):  MATH 410 or MATH 413 or MATH 415A.
Identical to:  C SC 479.
May be convened with:  MATH 579.
Usually offered:  Spring.

MATH 481 -- Basic Scientific Computing  (2 units)
Description:  Covers essentials of modern computing environment and tools, for both Windows and Unix-based environments. Course includes classroom and hands-on instruction. No computing experience necessary.
May be convened with:  MATH 581.
Usually offered:  Fall, Spring.

MATH 485 -- Mathematical Modeling  (3 units)
Description:  Development, analysis, and evaluation of mathematical models for physical, biological, social, and technical problems; both analytical and numerical solution techniques are required.  This is a Writing Emphasis Course.
Prerequisite(s):  satisfaction of the upper-division writing proficiency requirement; MATH 422.
May be convened with:  MATH 585.
Usually offered:  Spring.

MATH 496N -- Non-Linear Dynamics of Biological Systems  (2-4 units)
Description:  Non-linear dynamics of biological systems with applications in biochemistry, ecology, epidemiology, and molecular biology. Student/faculty presentations, opportunity for independent projects.
Prerequisite(s):  two semester of calculus, consent of instructor.
May be repeated:  for credit 4 times (maximum 5 enrollments).
Identical to:  ECOL 496N; ECOL is home department.
Usually offered:  Spring.

MATH 498 -- Senior Capstone  (1-3 units)
Description:  A culminating experience for majors involving a substantive project that demonstrates a synthesis of learning accumulated in the major, including broadly comprehensive knowledge of the discipline and its methodologies. Senior standing required.
Usually offered:  Fall, Spring.

MATH 498H -- Honors Thesis  (3 units)
Description:  An honors thesis is required of all the students graduating with honors. Students ordinarily sign up for this course as a two-semester sequence. The first semester the student performs research under the supervision of a faculty member; the second semester the student writes an honors thesis.
May be repeated:  for a total of 9 units of credit.
Usually offered:  Fall, Spring.

MATH 499 -- Independent Study  (1-5 units)
Description:  Qualified students working on an individual basis with professors who have agreed to supervise such work.
May be repeated:  an unlimited number of times, consult your department for details and possible restrictions.
Usually offered:  Fall, Spring, Summer.

MATH 499H -- Honors Independent Study  (3 units)
Description:  Qualified students working on an individual basis with professors who have agreed to supervise such work.
May be repeated:  an unlimited number of times, consult your department for details and possible restrictions.
Usually offered:  Fall, Spring.

MATH 500 -- History of Mathematics for Elementary School  (3 units)
Description:  Topics will include the history of numbers, numerals, and computation, and the history of elementary geometry, algebra, statistics, probability, computing devices, and other topics appropriate to the elementary school mathematics curriculum. This course is applicable to the MA in TTE (with Specialization in Elementary Mathematics). It is not applicable to graduate degree programs in mathematics.
Usually offered:  Spring.

MATH 501A -- Symbolic Logic  (3 units)
Description:  Intermediate propositional logic and quantificational theory, natural deduction, axiom systems, elementary metatheorems, introduction to notions of modal logic, selected topics in philosophy of logic. Credit allowed for only one of these course: PHIL 401A, PHIL 402. Graduate-level requirements include an in-depth research project on a central theme or topic of the course.
Identical to:  PHIL 501A; PHIL is home department.
May be convened with:  MATH 401A.
Usually offered:  Fall.

MATH 501B -- Symbolic Logic  (3 units)
Description:  Advanced propositional logic and quantification theory; metatheorems on consistency, independence, and completeness; set theory, number theory, and modal theory; recursive function theory and Goedel's incompleteness theorem. Graduate-level requirements include an in-depth research project on a central theme or topic of the course.
Identical to:  PHIL 501B; PHIL is home department.
May be convened with:  MATH 401B.
Usually offered:  Spring.

MATH 502 -- Mathematical Logic  (3 units)
Description:  [Taught alternate years 2001 - 2002] Sentential calculus, predicate calculus; consistency, independence, completeness, and the decision problem. Designed to be of interest to majors in mathematics or philosophy. [Taught alternate years 2001 - 2002] Graduate-level requirements include more extensive problem sets or advanced projects.
Identical to:  C SC 502, PHIL 502.
May be convened with:  MATH 402.
Usually offered:  Fall.

MATH 503 -- Foundations of Mathematics  (3 units)
Description:  [Taught alternate years 2001 - 2002] Topics in set theory such as functions, relations, direct products, transfinite induction and recursion, cardinal and ordinal arithmetic; related topics such as axiomatic systems, the development of the real number system, recursive functions. [Taught alternate years 2001-2002] Graduate-level requirements include more extensive problem sets or advanced projects.
Identical to:  PHIL 503.
May be convened with:  MATH 403.
Usually offered:  Spring.

MATH 504 -- History of Mathematics  (3 units)
Description:  The development of mathematics from ancient times through the 17th century, with emphasis on problem solving. The study of selected topics from each field is extended to the 20th century. Graduate-level requirements include more extensive problem sets or advanced projects.
Prerequisite(s):  not applicable to M.A., M.S., or Ph.D. degrees for math majors except for the M.A. teaching option.
May be convened with:  MATH 404.
Usually offered:  Fall.

MATH 505 -- Arithmetic and Number Theory for Elementary Teachers  (3 units)
Description:  Elementary school teachers will be introduced to creative mathematics through a series of exploratory problems. The problems are designed to give the teachers an insight into problem solving as well as ideas to use in their own classrooms. Solving problems using elementary arithmetic will be used to examine the two main facets of mathematics: abstract thinking and concrete modeling. This course is applicable to the MA in TTE (with Specialization in Elementary Mathematics). It is not applicable to graduate degree programs in mathematics.
Usually offered:  Fall, Spring, Summer.

MATH 507 -- Problem Solving in High School  (3 units)
Description:  Exploratory problems in algebra, geometry, and number theory will be worked on, written up, and presented to the class. Students will be encouraged to work in groups. Basic principles of problem solving will be discussed throughout.
Prerequisite(s):  open only to M.A. in Math (Teaching Option) and M.A. in TTE.
Usually offered:  Fall.

MATH 508 -- Topics in Harmonic Analysis  (3 units)
Description:  Fast fourier transforms, classical fourier analysis, related group theory done concretely. Graduate-level requirements include writing a paper dealing with almost periodic functions and their fourier series and solve a set of problems dealing with this topic.
May be convened with:  MATH 408.
Usually offered:  Fall, Spring.

MATH 509C -- Statistics for Research  (3 units)
Description:  Statistical concepts and methods applied to research in other scientific disciplines. Principles of estimation and hypothesis testing for standard one-and two-sample procedures. Correlation, linear regression. Contingency tables and analysis of variance.
Prerequisite(s):  MATH 110.
Identical to:  GENE 509C, PCOL 509C.
Usually offered:  Fall, Spring.

MATH 510 -- Algebra for Elementary School  (3 units)
Description:  The course aims at strengthening teachers' understanding of algebra (focusing on a study of patterns and functions), to explore algebra and pre-algebra activities appropriate for K-8 and to discuss research issues related to the learning and teaching of algebra in these grades.
Usually offered:  Fall, Spring, Summer.

MATH 511A -- Algebra  (3 units)
Description:  Structure of groups, rings, modules, algebras; Galois theory.
Prerequisite(s):  MATH 415A and MATH 415B, or MATH 413 and MATH 415A.
Usually offered:  Fall.

MATH 511B -- Algebra  (3 units)
Description:  Structure of groups, rings, modules, algebras; Galois theory.
Prerequisite(s):  MATH 511A.
Usually offered:  Spring.

MATH 512 -- Modern Algebra for Secondary Teachers  (3 units)
Description:  The course studies fields, specifically the rationals, the reals and the complex numbers. Specific topics include The Fundamental Theorem of Algebra, factoring, Rolle's Theorem, Descartes' Rule of Signs and Sturm's Algorithm for root separation.
Prerequisite(s):  open only to M.A. in Math (Teaching Option) and M.A. in TTE.
Usually offered:  Spring.

MATH 513 -- Linear Algebra  (3 units)
Description:  Vector spaces, linear transformations and matrices, eigenvalues, bilinear forms, orthogonal and unitary transformations. Graduate-level requirements include more extensive problem sets or advanced projects.
May be convened with:  MATH 413.
Usually offered:  Fall, Spring.

MATH 514A -- Algebraic Number Theory  (3 units)
Description:  [Taught alternate years 2001-2002] Dedekind domains, complete fields, class groups and class numbers, Dirichlet unit theorem, algebraic function fields.
Prerequisite(s):  MATH 511B.
Usually offered:  Fall.

MATH 515A -- Introduction to Abstract Algebra  (3 units)
Description:  Introduction to groups, rings, and fields. Graduate-level requirements include more extensive problem sets or advanced projects.
May be convened with:  MATH 415A.
Usually offered:  Fall.

MATH 515B -- Second Course in Abstract Algebra  (3 units)
Description:  A continuation of 415A. Topics may include Galois theory, linear and multilinear algebra, finite fields and coding theory. Polya enumeration. Graduate-level requirements include more extensive problem sets or advanced projects.
May be convened with:  MATH 415B.
Usually offered:  Spring.

MATH 517A -- Group Theory  (3 units)
Description:  [Taught alternate years 2000-2001] Selections from such topics as finite groups, abelian groups, characters and representations.
Prerequisite(s):  MATH 511B.
May be repeated:  for credit 4 times (maximum 5 enrollments).
Usually offered:  Fall.

MATH 517B -- Group Theory  (3 units)
Description:  [Taught alternate years 2000-2001] Selections from such topics as finite groups, abelian groups, characters and representations.
Prerequisite(s):  MATH 517A.
May be repeated:  for credit 4 times (maximum 5 enrollments).
Usually offered:  Spring.

MATH 518 -- Topics in Algebra  (3 units)
Description:  Advanced topics in groups, rings, fields, algebras; content varies.
May be repeated:  for credit 4 times (maximum 5 enrollments).
Usually offered:  Fall, Spring.

MATH 519 -- Topics in Number Theory and Combinatorics  (3 units)
Description:  Advanced topics in algebraic number theory, analytic number theory, class fields, combinatorics; content varies.
May be repeated:  for credit 4 times (maximum 5 enrollments).
Usually offered:  Fall, Spring.

MATH 520A -- Complex Analysis  (3 units)
Description:  Analyticity, Cauchy's integral formula, residues, infinite products, conformal mapping, Dirichlet problem, Riemann mapping theorem.
Prerequisite(s):  MATH 424.
Usually offered:  Fall.

MATH 520B -- Complex Analysis  (3 units)
Description:  Rudiments of Riemann surfaces.
Prerequisite(s):  MATH 520A or MATH 582.
Usually offered:  Spring.

MATH 521 -- Complex Variables with Applications  (3 units)
Description:  Complex numbers, analytic functions, harmonic functions, elementary functions, complex integration, Cauchy's integral theorem, series representations for analytic functions, residue theory, conformal mapping, applications to steady-state temperature and oscillating systems. Graduate-level requirements include more extensive problem sets or advanced projects.
May be convened with:  MATH 421.
Usually offered:  Spring.

MATH 522 -- Advanced Applied Analysis  (3 units)
Description:  Review of multivariable calculus, series solutions of differential equations, Laplace transforms, Fourier series, introduction to partial differential equations. Graduate-level requirements include more extensive problem sets or advanced projects.
May be convened with:  MATH 422.
Usually offered:  Fall.

MATH 523A -- Real Analysis  (3 units)
Description:  Lebesgue measure and integration, differentiation, Radon-Nikodym theorem, Lp spaces, applications.
Prerequisite(s):  MATH 425A.
Usually offered:  Fall.

MATH 523B -- Real Analysis  (3 units)
Description:  Lebesgue measure and integration, differentiation, Radon-Nikodym theorem, Lp spaces, applications.
Prerequisite(s):  MATH 523A.
Usually offered:  Spring.

MATH 524 -- Theory of Complex Variables  (3 units)
Description:  Complex numbers, complex-valued functions, analytic functions, elementary functions, series, residues and poles, mapping by elementary functions, conformal mapping, the Schwarz-Christoffel transformation, integral formulas of Poisson type. Graduate-level requirements include more extensive problem sets or advanced project.
May be convened with:  MATH 424.
Usually offered:  Fall, Spring.

MATH 525A -- Real Analysis of One Variable  (3 units)
Description:  Continuity and differentiation of functions of one variable. Riemann integration, sequences of functions and uniform convergence. Graduate-level requirements include more extensive problem sets or advanced projects.
May be convened with:  MATH 425A.
Usually offered:  Fall.

MATH 525B -- Real Analysis of Several Variables  (3 units)
Description:  Continuity and differentiation in higher dimensions, curves and surfaces; change of coordinates; theorems of Green, Gauss and Stokes; exact differentials. Graduate-level requirements include more extensive problem sets or advanced projects.
May be convened with:  MATH 425B.
Usually offered:  Spring.

MATH 527A -- Principles of Analysis  (3 units)
Description:  Advanced-level review of linear algebra and multivariable calculus; survey of real, complex and functional analysis, and differential geometry with emphasis on the needs of applied mathematics.
Prerequisite(s):  MATH 410, MATH 424, and a differential equations course.
Usually offered:  Fall.

MATH 527B -- Principles of Analysis  (3 units)
Description:  Advanced-level review of linear algebra and multivariable calculus; survey of real, complex and functional analysis, and differential geometry with emphasis on the needs of applied mathematics.
Prerequisite(s):  MATH 527A.
Usually offered:  Spring.

MATH 528A -- Banach and Hilbert Spaces  (3 units)
Description:  [Taught alternate years 2000-2001] Introduction to the theory of normed spaces, Banach spaces and Hilbert spaces, operators on Banach spaces, spectral theory of operators on Hilbert spaces, applications.
Prerequisite(s):  MATH 527B, MATH 523A.
Usually offered:  Fall.

MATH 528B -- Banach and Hilbert Spaces  (3 units)
Description:  [Taught alternate years 2000-2001] Introduction to the theory of normed spaces, Banach spaces and Hilbert spaces, operators on Banach spaces, spectral theory of operators on Hilbert spaces, applications.
Prerequisite(s):  MATH 528A.
Usually offered:  Spring.

MATH 529 -- Topics in Modern Analysis  (3 units)
Description:  Advanced topics in measure and integration, complex analysis in one and several complex variables, probability, functional analysis, operator theory; content varies.
Usually offered:  Fall, Spring.

MATH 530 -- Second Course in Geometry  (3 units)
Description:  [Taught alternate years 2000 - 2001] Topics may include low-dimensional topology; map coloring in the plane, networks (graphs) polyhedra, two-dimensional surfaces and their classification, map coloring on surfaces (Heawood's estimate, Ringel-Young theory), knots and links or projective geometry. [Taught alternate years 2000-2001] Graduate-level requirements include more extensive problem sets or advanced projects.
May be convened with:  MATH 430.
Usually offered:  Spring.

MATH 531 -- Algebraic Topology  (3 units)
Description:  [Taught alternate years 2001-2002] Poincare duality, fixed point theorems, characteristic classes, classification of principal bundles, homology of fiber bundles, higher homotopy groups, low dimensional manifolds.
Prerequisite(s):  MATH 534B.
Usually offered:  Fall.

MATH 534A -- Topology-Geometry  (3 units)
Description:  Point set topology, the fundamental group, calculus on manifolds. Homology, de Rham cohomology, other topics. Examples will be emphasized.
Prerequisite(s):  MATH 415A, MATH 425A.
Usually offered:  Fall.

MATH 534B -- Topology-Geometry  (3 units)
Description:  Point set topology, the fundamental group, calculus on manifolds. Homology, de Rham cohomology, other topics. Examples will be emphasized.
Prerequisite(s):  MATH 534A.
Usually offered:  Spring.

MATH 535A -- The Mathematics of Computer Graphics  (3 units)
Description:  The Mathematical aspects of computer graphics, including scan conversion methods, projective geometry and geometric transformations, the construction and rendering of curves and surfaces, and color models.
Prerequisite(s):  C SC 352; MATH 215, MATH 322, or MATH 410.
Identical to:  C SC 535A.
Usually offered:  Fall.

MATH 536A -- Algebraic Geometry  (3 units)
Description:  [Taught alternate years 2000-2001] Affine and projective varieties, morphisms and rational maps. Dimension, degree and smoothness. Basic coherent sheaf theory and Cech cohomology. Line bundles, Riemann-Roch theorem.
Prerequisite(s):  MATH 520A, MATH 534A.
Usually offered:  Fall.

MATH 536B -- Algebraic Geometry  (3 units)
Description:  [Taught alternate years 2000-2001] Affine and projective varieties, morphisms and rational maps. Dimension, degree and smoothness. Basic coherent sheaf theory and Cech cohomology. Line bundles, Riemann-Roch theorem.
Prerequisite(s):  MATH 536A.
Usually offered:  Spring.

MATH 537A -- Global Differential Geometry  (3 units)
Description:  [Taught alternate years 2001-2002] Surfaces in R3, structure equations, curvature. Gauss-Bonnet theorem, parallel transport, geodesics, calculus of variations, Jacobi fields and conjugate points, topology and curvature; Riemannian geometry, connections, curvature tensor, Riemannian submanifolds and submersions, symmetric spaces, vector bundles. Morse theory, symplectic geometry.
Prerequisite(s):  MATH 534A, MATH 534B.
Usually offered:  Fall.

MATH 537B -- Global Differential Geometry  (3 units)
Description:  [Taught alternate years 2001-2002] Surfaces in R3, structure equations, curvature. Gauss-Bonnet theorem, parallel transport, geodesics, calculus of variations, Jacobi fields and conjugate points, topology and curvature; Riemannian geometry, connections, curvature tensor, Riemannian submanifolds and submersions, symmetric spaces, vector bundles. Morse theory, symplectic geometry.
Prerequisite(s):  MATH 537A.
Usually offered:  Spring.

MATH 538 -- Topics in Geometry and Topology  (3 units)
Description:  Advanced topics in point set and algebraic topology, algebraic geometry, differential geometry; content varies.
May be repeated:  for credit 4 times (maximum 5 enrollments).
Usually offered:  Fall, Spring.

MATH 539 -- Algebraic Coding Theory  (3 units)
Description:  [Taught alternate years 2001-2002] Construction and properties of error correcting codes; encoding and decoding procedures and information rate for various codes.
Prerequisite(s):  MATH 415A.
Identical to:  ECE 539.
Usually offered:  Spring.

MATH 543 -- Theory of Graphs and Networks  (3 units)
Description:  Undirected and directed graphs, connectivity, circuits, trees, partitions, planarity, coloring problems, matrix methods, applications in diverse disciplines. Graduate-level requirements include more extensive problem sets or advanced projects.
Identical to:  C SC 543.
May be convened with:  MATH 443.
Usually offered:  Fall.

MATH 546 -- Theory of Numbers  (3 units)
Description:  [Taught alternate years 2000 - 2001] Divisibility properties of integers, primes, congruencies, quadratic residues, number-theoretic functions. [Taught alternate years 2000-2001] Graduate-level requirements include more extensive problem sets or advanced projects.
May be convened with:  MATH 446.
Usually offered:  Spring.

MATH 547 -- Combinatorial Mathematics  (3 units)
Description:  [Taught alternate years 2000 - 2001] Enumeration and construction of arrangements and designs; generating functions; principle of inclusion-exclusion; recurrence relations; a variety of applications. [Taught alternate years 2000-2001] Graduate-level requirements include more extensive problem sets or advanced projects.
May be convened with:  MATH 447.
Usually offered:  Spring.

MATH 550 -- Mathematical Population Dynamics  (4 units)
Description:  Ecological population dynamics, demography and human epidemiology. Emphasis on mathematical models and techniques for data analysis with particular reference to dynamical systems and chaos.
Prerequisite(s):  ordinary differential equations as MATH 254 or MATH 355, full calculus sequence, upper-division ecology course (ECOL 302).
Typical structure:  3 hours lecture, 3 hours laboratory.
Identical to:  ECOL 550; ECOL is home department.
Usually offered:  Spring.

MATH 553A -- Partial Differential Equations  (3 units)
Description:  [Taught alternate years 2000-2001] Theory and examples of linear equations; characteristics, well-posed problems, regularity, variational properties, asymptotics. Topics in nonlinear equations, such as shock waves, diffusion waves, and estimates in Sobolev spaces.
Prerequisite(s):  MATH 523B or MATH 527B or MATH 583B.
Usually offered:  Fall.

MATH 553B -- Partial Differential Equations  (3 units)
Description:  [Taught alternate years 2000-2001] Theory and examples of linear equations; characteristics, well-posed problems, regularity, variational properties, asymptotics. Topics in nonlinear equations, such as shock waves, diffusion waves, and estimates in Sobolev spaces.
Prerequisite(s):  MATH 553A.
Usually offered:  Spring.

MATH 554 -- Ordinary Differential Equations  (3 units)
Description:  [Taught alternate years 2000-2001] General theory of linear systems, Foquet theory. Local theory of nonlinear systems, stable manifold and Hartman-Grobman theorems. Poincare-Bendixson theory, limit cycles, Poincare maps. Bifurcation theory, including the Hopf theorem.
Prerequisite(s):  MATH 413 or consent of instructor.
Usually offered:  Fall.

MATH 556 -- Applied Partial Differential Equations  (3 units)
Description:  Properties of partial differential equations and techniques for their solution: Fourier methods, Green's functions, numerical methods. Graduate-level requirements include more extensive problem sets or advanced projects.
May be convened with:  MATH 456.
Usually offered:  Spring.

MATH 557A -- Dynamical Systems and Chaos  (3 units)
Description:  Qualitative theory of dynamical systems, phase space analysis, bifurcation, period doubling, universal scaling, onset of chaos. Applications drawn from atmospheric physics, biology, ecology, fluid mechanics and optics.
Prerequisite(s):  MATH 454 or (MATH 254 and MATH 422): and MATH 421 or MATH 424.
Usually offered:  Fall.

MATH 557B -- Dynamical Systems and Chaos  (3 units)
Description:  Qualitative theory of dynamical systems, phase space analysis, bifurcation, period doubling, universal scaling, onset of chaos. Applications drawn from atmospheric physics, biology, ecology, fluid mechanics and optics.
Prerequisite(s):  MATH 557A.
Usually offered:  Spring.

MATH 558 -- Probability and Statistics  (3 units)
Description:  The course includes mathematical modeling, measures of central tendency and dispersion, discrete probability, applications, Bayes' theorem, Chebyshev's Inequality, binomial and normal distributions, hypothesis testing, and game theory. This course is only for M.A. in Math (Teaching Option) and M.A. in TTE.
Prerequisite(s):  open only to M.A. in Math (Teaching Option) and M.A. in TTE.
Usually offered:  Fall.

MATH 559A -- Lie Groups and Lie Algebras  (3 units)
Description:  [Taught alternate years 2000-2001] Correspondence between Lie groups and Lie algebras, structure and representation theory, applications to topology and geometry of homogeneous spaces, applications to harmonic analysis.
Prerequisite(s):  MATH 511A, MATH 523A, MATH 534A, MATH 534B or consent of instructor.
Usually offered:  Fall.

MATH 559B -- Lie Groups and Lie Algebras  (3 units)
Description:  [Taught alternate years 2000-2001] Correspondence between Lie groups and Lie algebras, structure and representation theory, applications to topology and geometry of homogeneous spaces, applications to harmonic analysis.
Prerequisite(s):  MATH 559A.
Usually offered:  Spring.

MATH 561 -- Regression and Multivariate Analysis  (3 units)
Description:  Regression analysis including simple linear regression and multiple linear regression. Analysis of variance and covariance. Residual analysis. Variable selection techniques, collinearity, non-linear models and transformations. Cross-validation for model selection. Methods for analysis of multivariate observations. Multivariate expectations and covariance matrices. Multivariate normal distribution. Hotelling's T-square distribution. Principal components. Students will be expected to utilize standard statistical software packages for computational purposes.
Prerequisite(s):  MATH 410 or MATH 413; one of MATH 461, MATH 466, or MATH 509.
Usually offered:  Fall.

MATH 562 -- Time Series Analysis  (3 units)
Description:  Methods for analysis of time series data. Time domain techniques. ARIMA models. Estimation of process mean and autocovariance. Model fitting. Forecasting methods. Missing data. Students will be expected to utilize standard statistical software packages for computational purposes.
Usually offered:  Fall.

MATH 563A -- Probability Theory  (3 units)
Description:  [Taught alternate years 2000-2001] Introduction to measure theory, strong law of large numbers, characteristic functions, the central limit theorem, conditional expectations, and discrete parameter martingales.
Prerequisite(s):  MATH 464.
Usually offered:  Fall.

MATH 563B -- Probability Theory  (3 units)
Description:  [Taught alternate years 2000-2001] A selection of topics in stochastic processes from Markov chains, Brownian motion, the functional central limit theorem, diffusions and stochastic differential equations, martingales.
Prerequisite(s):  MATH 563A; MATH 468 recommended.
Usually offered:  Spring.

MATH 564 -- Theory of Probability  (3 units)
Description:  Probability spaces, random variables, weak law of large numbers, central limit theorem, various discrete and continuous probability distributions. Graduate-level requirements include more extensive problem sets or advanced projects.
May be convened with:  MATH 464.
Usually offered:  Fall.

MATH 565A -- Stochastic Processes  (3 units)
Description:  [Taught alternate years 2001-2002] Stationary processes, jump processes, diffusions, applications to problems in science and engineering.
Prerequisite(s):  strong probability background.
Usually offered:  Fall.

MATH 565B -- Stochastic Processes  (3 units)
Description:  [Taught alternate years 2001-2002] Stationary processes, jump processes, diffusions, applications to problems in science and engineering.
Prerequisite(s):  MATH 565A.
Usually offered:  Spring.

MATH 566 -- Theory of Statistics  (3 units)
Description:  Sampling theory. Point estimation. Limiting distributions. Testing Hypotheses. Confidence intervals. Large sample methods. Graduate-level requirements include more extensive problem sets or advanced projects.
May be convened with:  MATH 466.
Usually offered:  Spring.

MATH 567A -- Theoretical Statistics  (3 units)
Description:  [Taught alternate years 2001-2002] Basic decision theory. Bayes' rules for estimation. Admissibility and completeness. The minimax theorem. Sufficiency. Exponential families of distributions. Complete sufficient statistics. Invariant decision problems. Location and scale parameters. Theory of nonparametric statistics. Hypothesis testing. Neyman-Pearson lemma. UMP and UMPU tests. Two-sided tests. Two-sample tests. Confidence sets. Multiple decision problems.
Prerequisite(s):  MATH 466.
Usually offered:  Fall.

MATH 567B -- Theoretical Statistics  (3 units)
Description:  [Taught alternate years 2001-2002] Basic decision theory. Bayes' rules for estimation. Admissibility and completeness. The minimax theorem. Sufficiency. Exponential families of distributions. Complete sufficient statistics. Invariant decision problems. Location and scale parameters. Theory of nonparametric statistics. Hypothesis testing. Neyman-Pearson lemma. UMP and UMPU tests. Two-sided tests. Two-sample tests. Confidence sets. Multiple decision problems.
Prerequisite(s):  MATH 567A.
Usually offered:  Spring.

MATH 568 -- Applied Stochastic Processes  (3 units)
Description:  Applications of Gaussian and Markov processes and renewal theory; Wiener and Poisson processes, queues. Graduate-level requirements include more extensive problem sets or advanced projects.
May be convened with:  MATH 468.
Usually offered:  Spring.

MATH 569 -- Nonparametric Statistics  (3 units)
Description:  [Taught alternate years 2001-2002] Distribution free statistical methods for nominal and ordinal data. Measures of association. Goodness of fit and runs tests. Analysis of one or more groups. Correlation and regression of ranked data. Rank order statistics. Applications of nonparametric statistical inference. Students will be expected to utilize standard statistical software packages for computational purposes.
Prerequisite(s):  MATH 461, MATH 466 or MATH 509C.
Usually offered:  Spring.

MATH 570 -- Categorical Data Analysis  (3 units)
Description:  [Taught alternate years 2001-2002] Two-way contingency tables. Logistic, probit and log-log regression. Loglinear models. Model selection techniques. Testing goodness of fit models. Numerical methods for finding MLE. Treatment of finding ordinal and nominal variables. Poisson and multinomial sampling. Students will be expected to utilize standard statistical software packages for computational purposes.
Prerequisite(s):  MATH 461, MATH 466, or MATH 509C.
Usually offered:  Spring.

MATH 571 -- Design of Experiments  (3 units)
Description:  Principles of designing experiments. Randomization, block designs, factorial experiments, response surface designs, repeated measures, analysis of contrasts, multiple comparisons, analysis of variance and covariance, variance components analysis.
Prerequisite(s):  MATH 223, and one of MATH 461 or MATH 509C.
Usually offered:  Spring.

MATH 572 -- Statistical Consulting  (3 units)
Description:  Course provides instruction and experience in all aspects of statistical consulting. The class is organized as a small consulting lab with instructor acting as director. Students interact with actual clients from university and local business communities.
Prerequisite(s):  two semesters of statistics and consent of instructor.
Usually offered:  Fall.

MATH 573 -- Theory of Computation  (3 units)
Description:  Chomsky hierarchy, undecidability; general recursive functions; recursion theory; computational complexity theory, NP-complete and provably intractable problems.
Prerequisite(s):  C SC 473.
Identical to:  C SC 573; C SC is home department.
Usually offered:  Spring.

MATH 574 -- Introduction to Geostatistics  (3 units)
Description:  Exploratory spatial data analysis, random function models for spatial data, estimation and modeling of variograms and covariances, ordinary and universal kriging estimators and equations, regularization of variograms, estimation of spatial averages, non-linear estimators, includes use of geostatistical software. Application of hydrology, soil science, ecology, geography and related fields.
Prerequisite(s):  linear algebra, basic course in probability and statistics, familiarity with DOS/Windows, UNIX.
Identical to:  GEOG 574.
Usually offered:  Fall.

MATH 575A -- Numerical Analysis  (3 units)
Description:  Error analysis, solution of linear systems and nonlinear equations, eigenvalue interpolation and approximation, numerical integration, initial and boundary value problems for ordinary differential equations, optimization.
Prerequisite(s):  MATH 475B or MATH 456.
Identical to:  C SC 575A.
Usually offered:  Fall.

MATH 575B -- Numerical Analysis  (3 units)
Description:  Error analysis, solution of linear systems and nonlinear equations, eigenvalue interpolation and approximation, numerical integration, initial and boundary value problems for ordinary differential equations, optimization.
Prerequisite(s):  MATH 575A.
Identical to:  C SC 575B.
Usually offered:  Spring.

MATH 576A -- Numerical Analysis PDE  (3 units)
Description:  [Taught alternate years 2000-2001] Finite difference, finite element, and spectral discretization methods; semidiscrete, matrix, and Fourier analysis.
Prerequisite(s):  MATH 413, MATH 456, MATH 575B.
Usually offered:  Fall.

MATH 576B -- Numerical Analysis PDE  (3 units)
Description:  [Taught alternate years 2000-2001] Well-posedness, numerical boundary conditions, nonlinear instability, time-split algorithms, special methods for stiff and singular problems.
Prerequisite(s):  MATH 576A.
Usually offered:  Spring.

MATH 577 -- Topics in Applied Mathematics  (3 units)
Description:  Advanced topics in asymptotics, numerical analysis, approximation theory, mathematical theory of mechanics, dynamical systems, differential equations and inequalities, mathematical theory of statistics; content varies.
Usually offered:  Fall, Spring.

MATH 578 -- Computational Methods of Algebra  (3 units)
Description:  Applications of machine computation to various aspects of algebra, such as matrix algorithms, character tables and conjugacy classes for finite groups, coset enumeration, integral matrices, crystallographic groups.
Prerequisite(s):  MATH 415A, knowledge of scientific computer programming language.
Identical to:  C SC 578.
Usually offered:  Spring.

MATH 579 -- Game Theory and Mathematical Programming  (3 units)
Description:  [Taught alternate years 2001-2002] Linear inequalities, games of strategy, minimax theorem, optimal strategies, duality theorems, simplex method. [Taught alternate years 2001-2002] Graduate-level requirements include more extensive problem sets or advanced projects.
Identical to:  C SC 579.
May be convened with:  MATH 479.
Usually offered:  Spring.

MATH 580 -- Calculators and Computers for Elementary Teachers  (3 units)
Description:  Students will use calculators and computers to explore various mathematical topics such as elementary number theory, probability, statistics, geometry, and so on. Emphasis will be placed on how and when to use technology, on becoming comfortable with both calculators and computers, on what are good and poor activities with technology, and on the importance of estimation and good judgment when using technology. Students will be introduced to computer activities using BASIC, LOGO, and appropriate pre-packaged software. This course is applicable to the M.A. in TTE (with Specialization in Elementary Mathematics). It is not applicable to graduate degree programs in mathematics.
Usually offered:  Fall, Summer, Spring.

MATH 581 -- Basic Scientific Computing  (2 units)
Description:  Covers essentials of modern computing environment and tools, for both Windows and Unix-based environments. Course includes classroom and hands-on instruction. No computing experience necessary. Graduate-level requirements include 5 projects.
May be convened with:  MATH 481.
Usually offered:  Fall, Spring.

MATH 582 -- Applied Complex Analysis  (3 units)
Description:  [Taught alternate years 2001-2002] Representations of special functions, asymptotic methods for integrals and linear differential equations in the complex domain, applications of conformal mapping, Wiener-Hopf techniques.
Prerequisite(s):  MATH 424.
Usually offered:  Spring.

MATH 583A -- Principles and Methods of Applied Mathematics  (3 units)
Description:  Boundary value problems; Green's functions, distributions, Fourier transforms, the classical partial differential equations (Laplace, heat, wave) of mathematical physics. Linear operators, spectral theory, integral equations, Fredholm theory.
Prerequisite(s):  MATH 421 or MATH 424 or MATH 520A.
Usually offered:  Fall.

MATH 583B -- Principles and Methods of Applied Mathematics  (3 units)
Description:  Boundary value problems; Green's functions, distributions, Fourier transforms, the classical partial differential equations (Laplace, heat, wave) of mathematical physics. Linear operators, spectral theory, integral equations, Fredholm theory.
Prerequisite(s):  MATH 583A.
Usually offered:  Spring.

MATH 584 -- Technology in Secondary School  (3 units)
Description:  Students will use computers and/or graphing calculators to explore various mathematical topics including number theory, geometry, precalculus, and calculus. Programming capabilities of the calculator or computer will be covered as appropriate.
Prerequisite(s):  open only to M.A. in Math (Teaching Option) and M.A. in TTE.
Usually offered:  Spring.

MATH 585 -- Mathematical Modeling  (3 units)
Description:  Development, analysis, and evaluation of mathematical models for physical, biological, social, and technical problems; both analytical and numerical solution techniques are required. Graduate-level requirements include more advanced projects.
May be convened with:  MATH 485.
Usually offered:  Spring.

MATH 586 -- Case Studies in Applied Mathematics  (1-3 units)
Description:  In-depth treatment of several contemporary problems or problem areas from a variety of fields, but all involving mathematical modeling and analysis; content varies.
May be repeated:  for a total of 6 units of credit.
Usually offered:  Fall, Spring.

MATH 587 -- Perturbation Methods in Applied Mathematics  (3 units)
Description:  [Taught alternate years 2000-2001] Regular and singular perturbations, boundary layer theory, multiscale and averaging methods for nonlinear waves and oscillators.
Prerequisite(s):  MATH 422; MATH 421 or MATH 454.
Usually offered:  Fall.

MATH 588 -- Topics in Mathematical Physics  (3 units)
Description:  Advanced topics in field theories, mathematical theory of quantum mechanics, mathematical theory of statistical mechanics; content varies.
May be repeated:  for credit 4 times (maximum 5 enrollments).
Usually offered:  Fall, Spring.

MATH 589 -- Software Tools for Computational Science and Engineering  (3 units)
Description:  Techniques and tools useful at the interface between mathematical and technical computing on the one hand, and the Internet on the other. Topics include scripting languages such as Perl and Tcl/Tk, graphics file formats, the mathematics of raster and vector graphics, and standard libraries and applications for numerical and symbolic computing. Also, the fundamentals of computer networking from a user's point of view.
Prerequisite(s):  C SC 352 and ability to program in at least one modern high-level language.
Identical to:  C SC 589.
Usually offered:  Spring.

MATH 593 -- Internship  (1-3 units)
Description:  Specialized work on an individual basis, consisting of training and practice in actual service in a technical, business, or governmental establishment.
May be repeated:  an unlimited number of times, consult your department for details and possible restrictions.
Usually offered:  Fall, Spring.

MATH 595A -- Math Instruction  (1 unit)
Description:  The exchange of scholarly information and/or secondary research, usually in a small group setting. Instruction often includes lectures by several different persons. Research projects may or may not be required of course registrants.
May be repeated:  for credit 11 times (maximum 12 enrollments).
Usually offered:  Fall, Spring.

MATH 595B -- Research in Mathematics  (1 unit)
Description:  The exchange of scholarly information and/or secondary research, usually in a small group setting. Instruction often includes lectures by several different persons. Research projects may or may not be required of course registrants.
May be repeated:  for credit 4 times (maximum 5 enrollments).
Usually offered:  Fall, Spring.

MATH 595C -- Research in Applied Mathematics  (1 unit)
Description:  The exchange of scholarly information and/or secondary research, usually in a small group setting. Instruction often includes lectures by several different persons. Research projects may or may not be required of course registrants.
May be repeated:  for credit 4 times (maximum 5 enrollments).
Usually offered:  Fall, Spring.

MATH 596A -- Topics in Mathematics  (1-3 units)
Description:  The development and exchange of scholarly information, usually in a small group setting. The scope of work shall consist of research by course registrants, with the exchange of the results of such research through discussion, reports, and/or papers.
May be repeated:  for a total of 12 units of credit.
Usually offered:  Fall, Spring.

MATH 596E -- Topics in Mathematics for Secondary Teachers  (1-4 units)
Description:  Mathematics appropriate for secondary mathematics teachers. Topics will vary.
May be repeated:  for credit 4 times (maximum 5 enrollments).
Usually offered:  Spring.

MATH 596F -- Topics in Math for Elementary and Middle School Teachers  (3 units)
Description:  This course will focus on connections across key areas in K-8 mathematics (e.g., algebra, geometry, numbers and operations, data analysis and probability). The pedagogical approach will emphasize problem solving, use of technology, communication and hands-on materials.
May be repeated:  for credit 5 times (maximum 6 enrollments).
Usually offered:  Fall.

MATH 597T -- Professional Development Workshop in Teaching Mathematics  (1 unit)
Description:  Introduction to the theory and practice of teaching lower-division college mathematics courses. This course is required of and intended only for Math and Applied Math graduate student GATs who are teaching in the Math Department for the first time.
Prerequisite(s):  Math/Applied Math GAT - first semester teaching in the Math Department.
Usually offered:  Fall.

MATH 599 -- Independent Study  (1-6 units)
Description:  Qualified students working on an individual basis with professors who have agreed to supervise such work. Graduate students doing independent work which cannot be classified as actual research will register for credit under course number 599, 699, or 799.
May be repeated:  an unlimited number of times, consult your department for details and possible restrictions.
Usually offered:  Fall, Spring, Summer.

MATH 603 -- Interdisciplinary Biological Training Laboratory  (3 units)
Description:  Study of modern experimental techniques in biological physics including microscopy, optical trapping, electro-physiology, biological pattern formation; and quantification of experimental data through image analysis, mathematical methods and physical reasoning.
Typical structure:  6 hours laboratory, 1 hour lecture.
May be repeated:  for credit 1 time (maximum 2 enrollments).
Identical to:  PHYS 603; PHYS is home department.
Usually offered:  Fall.

MATH 636 -- Information Theory  (3 units)
Description:  Definition of a measure of information and study of its properties; introduction to channel capacity and error-free communications over noisy channels; rate distortion theory; error detecting and correcting codes.
Prerequisite(s):  ECE 503.
Identical to:  ECE 636; ECE is home department.
Usually offered:  Spring.

MATH 697A -- Problems in Computational Science  (3 units)
Description:  The practical application of theoretical learning within a group setting and involving an exchange of ideas and practical methods, skills, and principles.
May be repeated:  for credit 1 time (maximum 2 enrollments).
Identical to:  PHYS 697A.
Usually offered:  Fall, Spring.

MATH 697B -- Applied Mathematics Laboratory  (3 units)
Description:  The practical application of theoretical learning within a group setting and involving an exchange of ideas and practical methods, skills, and principles.
Prerequisite(s):  applied math core or equivalent.
Identical to:  PHYS 697B.
Usually offered:  Spring, Summer.

MATH 699 -- Independent Study  (1-6 units)
Description:  Qualified students working on an individual basis with professors who have agreed to supervise such work. Graduate students doing independent work which cannot be classified as actual research will register for credit under course number 599, 699, or 799.
May be repeated:  an unlimited number of times, consult your department for details and possible restrictions.
Usually offered:  Fall, Spring.

MATH 900 -- Research  (2-8 units)
Description:  Individual research, not related to thesis or dissertation preparation, by graduate students.
May be repeated:  an unlimited number of times, consult your department for details and possible restrictions.
Usually offered:  Fall, Spring, Summer.

MATH 910 -- Thesis  (3-6 units)
Description:  Research for the master's thesis (whether library research, laboratory or field observation or research, artistic creation, or thesis writing). Maximum total credit permitted varies with the major department.
May be repeated:  an unlimited number of times, consult your department for details and possible restrictions.
Usually offered:  Fall, Spring, Summer.

MATH 920 -- Dissertation  (1-9 units)
Description:  Research for the doctoral dissertation (whether library research, laboratory or field observation or research, artistic creation, or dissertation writing).
May be repeated:  an unlimited number of times, consult your department for details and possible restrictions.
Usually offered:  Fall, Spring, Summer.

MATH 930 -- Supplementary Registration  (1-9 units)
Description:  For students who have completed all course requirements for their advanced degree programs. May be used concurrently with other enrollments to bring to total number of units to the required minimum.
May be repeated:  an unlimited number of times, consult your department for details and possible restrictions.
Usually offered:  Fall, Spring, Summer.

 

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