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762012-2014 General Catalog Course Supplement and Policies and Requirements Addendum498. Directed Group Study ManagementPracticum (1-12)Project. Prerequisite: consent of instructor; sponsorshipof a GSM Academic Senate faculty member,and approval of Graduate Adviser. Provides theopportunity for students to gain experience in applyingbusiness methodologies previously acquired inother GSM courses. (S/U grading only.)—I, II, III. (I,II, III.)(change in existing course—eff. winter 12)MathematicsNew and changed courses inMathematics (MAT)Lower Division12. Precalculus (3)Lecture—3 hours. Prerequisite: two years of highschool algebra, plane geometry, plane trigonometry;and obtaining required score on the PrecalculusDiagnostic Examination. Topics selected for their usein calculus, including functions and their graphs,slope, zeroes of polynomials, exponential, logarithmicand trigonometric functions, sketching surfacesand solids. Not open for credit to students who havecompleted any of courses 16A, 16B, 16C, 17A,17B, 17C, 21A, 21B, or 21C with a C- or better.GE credit: SciEng | QL, SE, SL.—I, II, III. (I, II, III.)(change in existing course—eff. winter 13)21AL. Emerging Scholars Program CalculusWorkshop (2)Workshop—6 hours. Prerequisite: concurrent enrollmentin course 21A. Functions, limits, continuity.Slope and derivative. Same course content as course21A. Enrollment for students in the Emerging ScholarsProgram by instructor's invitation only. Offeredirregularly. (P/NP grading only.) GE credit: SE.(change in existing course—eff. winter 13)21BL. Emerging Scholars Program CalculusWorkshop (2)Workshop—6 hours. Prerequisite: course 21A or21AH; concurrent enrollment in 21B. Continuationof course 21A. Same course content as 21B. Enrollmentfor students in the Emerging Scholars Programby instructor's invitation only. Offered irregularly. (P/NP grading only.) GE credit: SE.(change in existing course—eff. winter 13)21CL. Emerging Scholars Program CalculusWorkshop (2)Workshop—6 hours. Prerequisite: course 21B or21BH; concurrent enrollment in 21C. Continuationof course 21B. Same course content as course 21C.Enrollment for students in the Emerging Scholars Programby instructor's invitation only. (P/NP gradingonly.) Offered irregularly. GE credit: SE.(change in existing course—eff. winter 13)21D. Vector Analysis (4)Lecture—3 hours; discussion—1 hour. Prerequisite:course 21C or 21CH. Continuation of course 21C.Definite integrals over plane and solid regions in variouscoordinate systems. Line and surface integrals.Green's theorem, Stoke's theorem, divergence theorem.GE credit: SciEng | QL, SE.—I, II, III. (I, II, III.)(change in existing course—eff. winter 13)22A. Linear Algebra (3)Lecture—3 hours. Prerequisite: nine units of collegemathematics and Engineering 6 or knowledge ofMatlab or course 22AL (to be taken concurrently).Matrices and linear transformations, determinants,eigenvalues, eigenvectors, diagonalization, factorization.Not open for credit to students who havecompleted course 67. GE credit: SciEng | QL, SE.—I, II, III. (I, II, III.)(change in existing course—eff. winter 13)22AL. Linear Algebra Computer Laboratory(1)Laboratory—2-3 hours. Prerequisite: nine units ofcollege mathematics. Introduction to Matlab and itsuse in linear algebra. (P/NP grading only.) GEcredit: QL, SE.—I, II, III. (I, II, III.)(change in existing course—eff. winter 13)22B. Differential Equations (3)Lecture—3 hours. Prerequisite: courses 21C; 22A or67. Solutions of elementary differential equations.GE credit: SciEng | QL, SE.—I, II, III. (I, II, III.)(change in existing course—eff. winter 13)25. Advanced Calculus (4)Lecture/discussion—4 hours. Prerequisite: course21B. Introduction to the rigorous treatment ofabstract mathematical analysis. Proofs in mathematics,induction, sets, cardinality; real number system,theory of convergence of sequences. Not open forcredit to students who have completed former course127A. GE credit: SciEng | SE.—I, III. (I, III.)(change in existing course—eff. winter 13)Upper Division108. Introduction to Abstract Mathematics(4)Lecture/discussion—4 hours. Prerequisite: course21B. A rigorous treatment of mathematical conceptswith emphasis on developing the ability to understandabstract mathematical ideas, to read and writemathematical concepts, and to prove theorems.Designed to serve as preparation for the more rigorousupper division courses. GE credit: SciEng,Wrt | SE.—I, II. (I, II.)(change in existing course—eff. winter 13)111. History of Mathematics (4)Lecture—3 hours; term paper or discussion. Prerequisite:eight units of upper division Mathematics; oneof the following: course 25, 67, 108, 114, 115A,141, or 145. History of mathematics from ancienttimes through the development of calculus. Mathematicsfrom Arab, Hindu, Chinese and other cultures.Selected topics from the history of modernmathematics. GE credit: SciEng | SE.—II. (II.)(change in existing course—eff. winter 13)114. Convex Geometry (4)Lecture/discussion—4 hours. Prerequisite: courses21C; 22A or 67. Topics selected from the theory ofconvex bodies, convex functions, geometric inequalities,combinatorial geometry, and integral geometry.Designed to serve as preparation for the more rigorousupper-division courses. Offered in alternateyears. GE credit: SciEng | SE.—(II.)(change in existing course—eff. winter 13)115A. Number Theory (4)Lecture/discussion—4 hours. Prerequisite: course21B. Divisibility and related topics, diophantineequations, selected topics from the theory of primenumbers. Designed to serve as preparation for themore rigorous upper division courses. GE credit:SciEng | QL, SE.—I. (I.)(change in existing course—eff. winter 13)115B. Number Theory (4)Lecture—3 hours; extensive problem solving. Prerequisite:courses 67, 115A. Euler function, Moebiusfunction, congruences, primitive roots, quadratic reciprocitylaw. Offered in alternate years. GE credit:SciEng | QL, SE.—II.(change in existing course—eff. winter 13)116. Differential Geometry (4)Lecture—3 hours; extensive problem solving. Prerequisite:course 125A. Vector analysis, curves, and surfacesin three dimensions. Offered in alternateyears. GE credit: SciEng | SE.—(III.)(change in existing course—eff. winter 13)118A. Partial Differential Equations:Elementary Methods (4)Lecture—3 hours; extensive problem solving. Prerequisite:courses 21D; 22B; 22A or 67.Derivation ofpartial differential equations; separation of variables;equilibrium solutions and Laplace's equation;Fourier series; method of characteristics for the onedimensional wave equation. Solution of nonhomogeneousequations. GE credit: SciEng | QL, SE.—I. (I.)(change in existing course—eff. winter 13)118B. Partial Differential Equations:Eigenfunction Expansions (4)Lecture—3 hours; extensive problem solving. Prerequisite:course 118A. Sturm-Liouville Theory; selfadjointoperators; mixed boundary conditions; partialdifferential equations in two and three dimensions;Eigenvalue problems in circular domains;nonhomogeneous problems and the method ofeigenfunction expansions; Poisson’s Equations. GEcredit: SciEng | QL, SE.—II. (II.)(change in existing course—eff. winter 13)118C. Partial Differential Equations:Green’s Functions and Transforms (4)Lecture—3 hours; extensive problem solving. Prerequisite:course 118B. Green’s functions for one-dimensionalproblems and Poisson’s equation; Fouriertransforms; Green’s Functions for time dependentproblems; Laplace transform and solution of partialdifferential equations. Offered irregularly. GE credit:SciEng | QL, SE.(change in existing course—eff. winter 13)119A. Ordinary Differential Equations (4)Lecture—3 hours; extensive problem solving. Prerequisite:courses 21D; 22B; 22A or 67. Scalar andplanar autonomous systems; nonlinear systems andlinearization; existence and uniqueness of solutions;matrix solution of linear systems; phase plane analysis;stability analysis; bifurcation theory; Liapunov'smethod; limit cycles; Poincare Bendixon theory. GEcredit: SciEng | QL, SE.—II. (II.)(change in existing course—eff. winter 13)119B. Ordinary Differential Equations (4)Lecture—3 hours; extensive problem solving. Prerequisite:course 119A. Lorentz equations; Poincaremaps; center manifolds and normal forms; scalarand planar maps; phase space analysis for iteratedmaps; period-doubling bifurcation; Lyapunov exponent;chaos and symbolic dynamics; strange attractors;fractals. GE credit: SciEng | QL, SE.—III. (III.)(change in existing course—eff. winter 13)124. Mathematical Biology (4)Lecture—3 hours; project. Prerequisite: courses 22Aor 67; 22B. Methods of mathematical modeling ofbiological systems including difference equations,ordinary differential equations, stochastic anddynamic programming models. Computer simulationmethods applied to biological systems. Applicationsto population growth, cell biology, physiology, evolutionaryecology and protein clustering. MATLABprogramming required. Offered in alternate years.GE credit: SciEng | QL, SE.—(III.)(change in existing course—eff. winter 13)125A. Real Analysis (4)Lecture/discusssion—4 hours. Prerequisite: course25. Functions, limits of functions, continuity and uniformcontinuity, sequences of functions, series of realnumbers, series of functions, power series. Not openfor credit to students who have completed formercourse 127B. GE credit: SciEng | SE.—I, II. (I, II.)(change in existing course—eff. winter 13)125B. Real Analysis (4)Lecture/discusssion—4 hours. Prerequisite: course67 and 125A. Theory of the derivative, Taylorseries, integration, partial derivatives, Implicit Func-Quarter Offered: I=Fall, II=Winter, III=Spring, IV=Summer; 2013-2014 offering in parenthesesPre-Fall 2011 General Education (GE): ArtHum=Arts and Humanities; SciEng=Science and Engineering; SocSci=Social Sciences; Div=Domestic Diversity; Wrt=Writing ExperienceFall 2011 and on General Education (GE): AH=Arts and Humanities; SE=Science and Engineering; SS=Social Sciences;ACGH=American Cultures; DD=Domestic Diversity; OL=Oral Skills; QL=Quantitative; SL=Scientific; VL=Visual; WC=World Cultures; WE=Writing Experience
2012-2014 General Catalog Course Supplement and Policies and Requirements Addendum77tion Theorem. Not open for credit to students whohave completed former course 127C. GE credit:SciEng | SE.—II, III. (II, III.)(change in existing course—eff. winter 13)128A. Numerical Analysis (4)Lecture—3 hours; project. Prerequisite: ComputerScience: Engineering 30 or equivalent; course 21C;Error analysis, approximation, interpolation, numericaldifferentiation and integration. Programming inlanguage such as Pascal, Fortran, or BASICrequired. GE credit: SciEng | QL, SE.—I. (I.)(change in existing course—eff. winter 13)128B. Numerical Analysis in Solution ofEquations (4)Lecture—3 hours; project. Prerequisite: ComputerScience: Engineering 30 or equivalent; courses21C; 22A or 67. Solution of nonlinear equationsand nonlinear systems. Minimization of functions ofseveral variables. Simultaneous linear equations.Eigenvalue problems. Linear programming. Programmingin language such as Pascal, Fortran, or BASICrequired. GE credit: SciEng | QL, SE.—II. (II.)(change in existing course—eff. winter 13)128C. Numerical Analysis in DifferentialEquations (4)Lecture—3 hours; project. Prerequisite: ComputerScience: Engineering 30 or equivalent; courses 22Aor 67; 22B. Difference equations, operators, numericalsolutions of ordinary and partial differentialequations. Programming in language such as Pascal,Fortran, or BASIC required. GE credit:SciEng | QL, SE.—III. (III.)(change in existing course—eff. winter 13)129. Fourier Analysis (4)Lecture—3 hours; extensive problem solving. Prerequisite:courses 21D; 22A or 67; 22B; 25 or consentof instructor. Fourier series and integrals, orthogonalsets of functions. Topics selected from trigonometricapproximation, orthogonal polynomials, applicationsto signal and image processing, numericalanalysis, and differential equations. GE credit:SciEng | QL, SE.—III. (III.)(change in existing course—eff. winter 13)133. Mathematical Finance (4)Lecture—3 hours; extensive problem solving. Prerequisite:courses 67; 135A. Analysis and evaluation ofdeterministic and random cash flow streams, yieldand pricing of basic financial instruments, interestrate theory, meanvariance portfolio theory, capitalasset pricing models, utility functions and generalprinciples. MATLAB programming required. Offeredin alternate years. GE credit: SciEng | QL, SE, SL.—III.(change in existing course—eff. winter 13)135A. Probability (4)Lecture/discussion—4 hours. Prerequisite: course125A. Probability space; discrete probability, combinatorialanalysis; independence, conditional probability;random variables, discrete and continuousdistributions, probability mass function, joint andmarginal density functions; expectation, moments,variance, Chebyshev inequality; sums of randomvariables, random walk, large number law, centrallimit theorem. Not open for credit to students whohave completed former course 131. GE credit:SciEng | QL, SE.—I, II. (I, II.)(change in existing course—eff. winter 13)135B. Stochastic Processes (4)Laboratory/discussion—4 hours. Prerequisite:courses 135A; 22A or 67. Generating functions,branching processes, characteristic function; Markovchains; convergence of random variables, law ofiterated logarithm; random processes, Brownianmotion, stationary processes, renewal processes,queueing theory, martingales. Not open for credit tostudents who have completed former course 132A.GE credit: SciEng | QL, SE.—III. (III.)(change in existing course—eff. winter 13)141. Euclidean Geometry (4)Lecture/discussion—4 hours. Prerequisite: courses21B; 22A or 67. An axiomatic and analytic examinationof Euclidean geometry from an advancedpoint of view. In particular, a discussion of its relationto other geometries. Designed to serve as preparationfor the more rigorous upper division courses.GE credit: SciEng | SE, VL.—III. (III.)(change in existing course—eff. winter 13)145. Combinatorics (4)Lecture/discussion—4 hours. Prerequisite: course21B. Combinatorial methods using basic graph theory,counting methods, generating functions, andrecurrence relations. Designed to serve as preparationfor the more rigorous upper division courses. GEcredit: SciEng | QL, SE.—II. (II.)(change in existing course—eff. winter 13)146. Algebraic Combinatorics (4)Lecture/discussion—4 hours. Prerequisite: courses25; 22A or 67; 145. Enumeration, Polya theory,generating functions, current topics in algebraiccombinatorics. Not open for credit to students whohave completed former course 149A. GE credit:SciEng | SE.—III. (III.)(change in existing course—eff. winter 13)147. Topology (4)Lecture—3 hours; extensive problem solving. Prerequisite:courses 67, 125A. Basic notions of point-setand combinatorial topology. GE credit:SciEng | SE.—III. (III.)(change in existing course—eff. winter 13)148. Discrete Mathematics (4)Lecture/discussion—4 hours. Prerequisite: course67; or courses 22A and 25. Coding theory, errorcorrecting codes, finite fields and the algebraic conceptsneeded in their development. Not open forcredit to students who have completed former course149B. GE credit: SciEng | QL, SE.—II. (II.)(change in existing course—eff. winter 13)150A. Modern Algebra (4)Lecture/discussion—4 hours. Prerequisite: course67. Basic concepts of groups, symmetries of theplane. Emphasis on the techniques used in the proofof the ideas (Lemmas, Theorems, etc.) developingthese concepts. Precise thinking, proof writing, andthe ability to deal with abstraction. GE credit:SciEng | SE.—I. (I.)(change in existing course—eff. winter 13)150B. Modern Algebra (4)Lecture/discussion—4 hours. Prerequisite: course150A. Bilinear forms, rings, factorization, modules.GE credit: SciEng | SE.—II. (II.)(change in existing course—eff. winter 13)150C. Modern Algebra (4)Lecture/discussion—4 hours. Prerequisite: course150B. Group representations, fields, Galois theory.GE credit: SciEng | SE.—III. (III.)(change in existing course—eff. winter 13)160. Mathematical Foundations ofDatabase Theory, Design and Performance(4)Lecture—3 hours; project. Prerequisite: course 22Aor 67; one of the following courses: 25, 108, 114,115A, 141, or 145. Relational model; relationalalgebra, relational calculus, normal forms, functionaland multivalued dependencies. Separability. Costbenefit analysis of physical database design andreorganization. Performance via analytical modeling,simulation, and queueing theory. Blockaccesses; buffering; operating system contention;CPU intensive operations. Offered irregularly. GEcredit: SciEng | QL, SE.(change in existing course—eff. winter 13)165. Mathematics and Computers (4)Lecture—3 hours; project. Prerequisite: ComputerScience Engineering 30 or equivalent; course 22Band one of the following courses: 25, 67, 108,114, 115A, 141 or 145. Introduction to computationalmathematics, symbolic computation, and computergenerated/verified proofs in algebra, analysisand geometry. Investigation of rigorous new mathematicsdeveloped in conjunction with modern computationalquestions and the role that computers playin mathematical conjecture and experimentation. GEcredit: SciEng | QL, SE.—I. (I.)(change in existing course—eff. winter 13)167. Applied Linear Algebra (4)Lecture—3 hours; extensive problem solving. Prerequisite:course 22A or 67; knowledge of a programminglanguage. Applications of linear algebra; LUand QR matrix factorizations, eigenvalue and singularvalue matrix decompositions. GE credit:SciEng | QL, SE.—I, II, III. (I, II, III.)(change in existing course—eff. winter 13)168. Optimization (4)Lecture—3 hours; extensive problem solving. Prerequisite:Computer Science: Engineering 30 or equivalent;courses 21C or 25; 22A or 67. Linearprogramming, simplex method. Basic properties ofunconstrained nonlinear problems, descent methods,conjugate direction method. Constrained minimization.Programming language required. GE credit:SciEng | QL, SE.—III. (III.)(change in existing course—eff. winter 13)180. Special Topics (3)Lecture—3 hours. Prerequisite: courses 25 and 67,or consent of instructor. Special topics from variousfields of modern, pure, and applied mathematics.Some recent topics include Knot Theory, General Relativity,and Fuzzy Sets. May be repeated for creditwhen topic differs. Not offered every year. GEcredit: SciEng | SE.—I, II, III. (I, II, III.)(change in existing course—eff. winter 13)185A. Complex Analysis (4)Lecture—3 hours; extensive problem solving. Prerequisite:courses 67, 125A. Complex number system,analyticity and the Cauchy-Riemann equations, elementaryfunctions, complex integration, power andLaurent series expansions, residue theory. GE credit:SciEng | SE.—II. (II.)(change in existing course—eff. winter 13)185B. Complex Analysis (4)Lecture—3 hours; extensive problem solving. Prerequisite:course 185A. Analytical functions, elementaryfunctions and their mapping properties, applicationsof Cauchy's integral theorem, conformal mappingand applications to heat flow and fluid mechanics.Offered in alternate years. GE credit:SciEng | SE.—III.(change in existing course—eff. winter 13)189. Advanced Problem Solving (3)Lecture—3 hours. Prerequisite: courses 21D; 22A or67; 25. Solution and presentation of advancedproblem solving techniques. Solve and present interestingand challenging problems of all areas ofmathematics. Not offered every year. GE credit: Sci-Eng, Wrt | OL, QL, SE, WE.—II.(change in existing course—eff. winter 13)Quarter Offered: I=Fall, II=Winter, III=Spring, IV=Summer; 2013-2014 offering in parenthesesPre-Fall 2011 General Education (GE): ArtHum=Arts and Humanities; SciEng=Science and Engineering; SocSci=Social Sciences; Div=Domestic Diversity; Wrt=Writing ExperienceFall 2011 and on General Education (GE): AH=Arts and Humanities; SE=Science and Engineering; SS=Social Sciences;ACGH=American Cultures; DD=Domestic Diversity; OL=Oral Skills; QL=Quantitative; SL=Scientific; VL=Visual; WC=World Cultures; WE=Writing Experience
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