Apr 28, 2024  
2015-2016 Catalog 
    
2015-2016 Catalog [ARCHIVED CATALOG]

Course Descriptions


UNDERGRADUATE COURSES

Lower Division Courses numbered 1–99 are designed primarily for freshmen and sophomores but are open to all students for lower division credit. (Graduate students requesting to enroll in lower-division undergraduate courses will not receive unit credit nor will the course fulfill degree requirements.) Upper Division Courses courses numbered 100–199 are open to all students who have met the necessary prerequisites as indicated in the catalog course description. Preparation should generally include completion of one lower division course in the given subject or completion of two years of college work.

GRADUATE COURSES

Courses numbered 200–299 are open to graduate students. (Undergraduate students must obtain the signature of the instructor, School Dean, and the Dean of Graduate Studies. Graduate level units will count towards the required 120 units for graduation; however students are urged to meet with their academic advisor in order to determine if graduate course units may be used to fulfill a graduation requirement.)

CROSS-LISTED/CONJOINED COURSES

Cross-listed Courses are the same course offered under different course subjects at the same level (either undergraduate or graduate) that share the same meeting time, requirements, units, etc. Conjoined Courses are the same course but one is undergraduate and one is graduate.

COREQUISITE COURSE

A corequisite course is a course that must be taken at the same time as another course.

PREREQUISITES

Prerequisites for courses should be followed carefully; the responsibility for meeting these requirements rests on the student. If you can demonstrate that your preparation is equivalent to that specified by the prerequisites, the instructor may waive these requirements for you. The instructor also may request that a student who has not completed the prerequisites be dropped from the course. If the prerequisite for a course is not satisfied, students must obtain the approval of the instructor (or school designee) of the course they wish to take.

For all undergraduate courses a “C-” or better grade is required for a course to be used as a prerequisite for another course. If a course was taken for a “P/NP” grade then a “P” grade is required.

For all graduate courses a “B” or better grade is required for a course to be used as a prerequisite for another course. If a course was taken for a “S/U” grade then a “S” grade is required.

FOREIGN LANGUAGES

No credit is allowed for completing a less advanced course after successful completion (C-or better) of a more advanced course in the foreign languages. This applies only to lower division foreign language courses, not upper division courses. 

GRADING OPTIONS

Unless otherwise stated in the course description, each course is letter graded with a P/NP or S/U option (unless required for your major or graduate program). The policy regarding Grading Options , can be found in an alternate section of the catalog.

More information about Course Substitutions  and Course Materials and Services Fees  can be found in alternate areas of the catalog.

 

Mathematics

  
  • Syllabus

    MATH 005: Preparatory Calculus


    [4 units]

    Preparation for calculus. Analyzing data by means of functions (linear, quadratic, polynomial, logarithmic, exponential and trigonometric) and graphs with an emphasis on mathematical modeling of real-world applications.

    Course cannot be taken after successfully completing MATH 011  or MATH 021 . Normal Letter Grade only. Discussion included.


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  • Syllabus

    MATH 011: Calculus I


    [4 units]

    Introduction to differential and integral calculus of functions of one variable, including exponential, logarithmic and trigonometric functions, emphasizing conceptual understanding and applying mathematical concepts to real-world problems (approximation, optimization). Course does not lead to MATH 23, 24.

    Prerequisite: MATH 005  or equivalent score on the Placement (or equivalent) Exam. Not open to major(s): Applied Mathematical Sciences, Bioengineering, Materials Sci & Engineering, Undeclared Engineering, Physics, Undeclared Natural Sciences, Environmental Engineering, Mechanical Engineering, Computer Science & Engineering, Chemical Sciences. For majors that do not require more than two semesters of calculus courses. Course may not be taken for credit after obtaining credit for: MATH 021 . Normal Letter Grade only. Discussion included.


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  • Syllabus

    MATH 012: Calculus II


    [4 units]

    Continuation of MATH 011 . Introduction to integral calculus of functions of one variable and differential equations, emphasizing conceptual understanding and applying mathematical concepts to real-world problem. Course does not lead to Math 23, 24.

    Prerequisite: MATH 011  or MATH 021  or equivalent score on the Competency Exam. Not open to major(s): Bioengineering, Applied Mathematical Sciences, Materials Sci & Engineering, Undeclared Engineering, Undeclared Natural Sciences, Physics, Environmental Engineering, Mechanical Engineering, Computer Science & Engineering, Chemical Sciences. For majors that do not require more than two semesters of calculus courses. Course may not be taken for credit after obtaining credit for: MATH 022 . Normal Letter Grade only. Discussion included.


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  • Syllabus

    MATH 015: Introduction to Scientific Data Analysis


    [2 units]

    Fundamental analytical and computational skills to find, assemble and evaluate information, and to teach the basics of data analysis and modeling using spreadsheets, statistical tool, scripting languages, and high-level mathematical languages. This course is not intended for students from the School of Engineering.

    Prerequisite: MATH 005 , which may be taken concurrently, or MATH 011  or MATH 021  or equivalent score on the Competency (or equivalent) Exam. Not open to major(s): Materials Sci & Engineering, Bioengineering, Undeclared Engineering, Environmental Engineering, Mechanical Engineering, Computer Science & Engineering. Normal Letter Grade only. Laboratory included.


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  • Syllabus

    MATH 018: Statistics for Scientific Data Analysis


    [4 units]

    Analytical and computational methods for statistical analysis of data. Descriptive statistics, graphical representations of data, correlation, regression, causation, experiment design, introductory probability, random variables, sampling distributions, inference and significance.

    Prerequisite: (MATH 005  or MATH 011  or MATH 021  or equivalent score on the Competency (or equivalent) Exam) and (MATH 015  or CSE 020  or CSE 005  or ENVE 105 ). Course cannot be taken after successfully completing MATH 032 . Normal Letter Grade only. Discussion included.


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  • Syllabus

    MATH 021: Calculus I for Physical Sciences and Engineering


    [4 units]

    An introduction to differential and integral calculus of functions of one variable. Elementary functions such as the exponential and the natural logarithm, rates of change and the derivative with applications to physical sciences and engineering.

    Prerequisite: MATH 005  or equivalent score on the Placement (or equivalent) Exam. Open only to major(s): Applied Mathematical Sciences, Materials Sci & Engineering, Bioengineering, Undeclared Engineering, Earth Systems Science, Physics, Undeclared Natural Sciences, Environmental Engineering, Mechanical Engineering, Chemical Sciences, Computer Science & Engineering. Course may not be taken for credit after obtaining credit for: MATH 011 . Normal Letter Grade only. Discussion included.


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  • Syllabus

    MATH 022: Calculus II for Physical Sciences and Engineering


    [4 units]

    Continuation of MATH 021 . Analytical and numerical techniques of integration with applications, infinite sequences and series, first order ordinary differential equations.

    Prerequisite: MATH 021  or equivalent score on the Competency Exam. Open only to major(s): Bioengineering, Applied Mathematical Sciences, Materials Sci & Engineering, Earth Systems Science, Undeclared Engineering, Undeclared Natural Sciences, Physics, Environmental Engineering, Mechanical Engineering, Chemical Sciences, Computer Science & Engineering. Course may not be taken for credit after obtaining credit for: MATH 012 . Normal Letter Grade only. Discussion included.


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  • Syllabus

    MATH 023: Vector Calculus


    [4 units]

    Calculus of several variables. Topics include parametric equations and polar coordinates, algebra and geometry of vectors and matrices, partial derivatives, multiple integrals, and introduction to the theorems of Green, Gauss, and Stokes.

    Prerequisite: MATH 022  or equivalent score on the Competency Exam. Normal Letter Grade only. Discussion included.


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  • Syllabus

    MATH 024: Linear Algebra and Differential Equations


    [4 units]

    Introduces ordinary differential equations, systems of linear equations, matrices, determinants, vector spaces, linear transformations and linear systems of differential equations.

    Prerequisite: MATH 022  or equivalent score on the Competency Exam. Normal Letter Grade only. Discussion included.


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  • Syllabus

    MATH 032: Probability and Statistics


    [4 units]

    Concepts of probability and statistics. Conditional probability, independence, random variables, distribution functions, descriptive statistics, transformations, sampling errors, confidence intervals, least squares and maximum likelihood. Exploratory data analysis and interactive computing.

    Prerequisite: MATH 023 , which may be taken concurrently. Normal Letter Grade only. Discussion included.


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  • Syllabus

    MATH 050: Beginning MATLAB Programming


    [2 units]

    This half-semester minicourse introduces students to the writing, implementing, and testing of MATLAB algorithms to solve mathematical problems. Topics include programming syntax, data visualization, debugging, and coding aesthetics.

    Prerequisite: MATH 022  or equivalent score on the Competency Exam. Normal Letter Grade only.


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  • MATH 091: General Topics in Applied Mathematics


    [1 unit]

    Introduction to a variety of concepts useful in applied mathematics. Topics covered included floating point arithmetic, methods of proofs, random walks, stereographic projections, transforms, etc. Students are exposed to advanced mathematical topics in preparation for their ongoing studies.

    Prerequisite: MATH 023  and MATH 024 , both of which may be taken concurrently. Pass/Fail only.


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  • MATH 095: Lower Division Undergraduate Research


    [1-6 units]

    Supervised research in mathematics.

    Permission of instructor required. Normal Letter Grade only.


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  • MATH 098: Lower Division Directed Group Study


    [1-5 units]

    Permission of instructor required. Pass/Fail only. Course may be repeated for credit.


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  • MATH 099: Lower Division Individual Study


    [1-5 units]

    Permission of instructor required. Pass/Fail only. Course may be repeated for credit.


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  • MATH 101: Real Analysis


    [4 units]

    Introduction to rigorous mathematical proofs and concepts pertaining to real numbers. The class will cover the structure of real numbers, sequences, series and functions of real numbers, and, time permitting, concepts of abstract algebra.

    Prerequisite: MATH 023 . Normal Letter Grade only. Discussion included.


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  • MATH 122: Complex Variables and Applications


    [4 units]

    Introduction to complex variables, analytic functions, contour integration and theory of residues. Mappings of the complex plane. Introduction to mathematical analysis.

    Prerequisite: MATH 023  and MATH 024 . Normal Letter Grade only. Discussion included.


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  • Syllabus

    MATH 125: Intermediate Differential Equations


    [4 units]

    An introduction of advanced solution techniques for ordinary differential equations (ODE) and elementary solution techniques for partial differential equations (PDE). Specific topics include higher-order linear ODE, power series methods, boundary value problems, Fourier series, Sturm-Liouville theory, Laplace transforms, Fourier transforms, and applications to one-dimensional PDE.

    Prerequisite: MATH 023  and MATH 024 . Normal Letter Grade only. Discussion included.


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  • MATH 126: Partial Differential Equations


    [4 units]

    An introduction to the theory of boundary value and initial value problems for partial differential equations with emphasis on linear equations. Topics covered include Laplace’s equation, heat equation, wave equation, application of Sturm-Liouville’s theory, Green’s functions, Bessel functions, Laplace transform, method of characteristics.

    Prerequisite: MATH 125 . Normal Letter Grade only. Discussion included.


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  • Syllabus

    MATH 131: Numerical Analysis I


    [4 units]

    Introduction to numerical methods with emphasis on algorithm construction, analysis and implementation. Programming, round-off error, solutions of equations in one variable, interpolation and polynomial approximation, approximation theory, direct solvers for linear systems, numerical differentiation and integration, initial-value problems for ordinary differential equations.

    Prerequisite: MATH 024 . Normal Letter Grade only. Discussion included.


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  • MATH 132: Numerical Analysis II


    [4 units]

    Initial-value problems for ordinary differential equations, interactive techniques for solving linear systems, numerical solutions of nonlinear systems of equations, boundary-value problems for ordinary differential equations, numerical solutions to partial differential equations.

    Prerequisite: MATH 131  and MATH 125 . Normal Letter Grade only. Discussion included.


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  • MATH 140: Mathematical Methods for Optimization


    [3 units]

    Linear programming and a selection of topics from among the following: matrix games, integer programming, semidefinite programming, nonlinear programming, convex analysis and geometry, polyhedral geometry, the calculus of variations and control theory.

    Prerequisite: MATH 023 . Normal Letter Grade only. Discussion included.


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  • Syllabus

    MATH 141: Linear Analysis I


    [4 units]

    Applied linear analysis of finite dimensional vector spaces. Review of matrix algebra, vector spaces, orthogonality, least-squares approximations, eigenvalue problems, positive definite matrices, singular value decomposition with applications in science and engineering.

    Prerequisite: MATH 131 , which may be taken concurrently. Normal Letter Grade only. Discussion included.


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  • MATH 142: Linear Analysis II


    [4 units]

    Applied linear analysis of infinite dimensional vector spaces. Inner product spaces, operators, adjoint operators, Fredholm alternative, spectral theory, Sturm-Liouville operators, distributions and Green’s functions with applications in science and engineering.

    Prerequisite: MATH 141 . Normal Letter Grade only. Discussion included.


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  • Syllabus

    MATH 146: Numerical Linear Algebra


    [4 units]

    Matrix factorization and iterative methods for solving systems of linear equations. Topics include floating point arithmetic, eigenvalue problems, conditioning and stability, LU factorization, QR factorization, and SVD with applications in science and engineering.

    Prerequisite: MATH 141  and MATH 131 , both of which may be taken concurrently. Normal Letter Grade only. Laboratory included.


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  • MATH 150: Mathematical Modeling


    [4 units]

    Introduction to the basics of mathematical modeling emphasizing model construction, analysis and application. Using examples from a variety of fields such as physics, biology, chemistry and economics, students will learn how to develop and use mathematical models of real-world systems.

    Prerequisite: MATH 131  and (MATH 125  or MATH 141 ). Normal Letter Grade only. Discussion included.


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  • MATH 171: Mathematical Logic


    [4 units]

    Introduction to the meta-theory of first-order logic. Topics include the consistency, compactness, completeness and soundness proofs for propositional and first-order logic; model theory; the axiomatization of number theory; Gödel’s incompleteness theorems and related results.

    Prerequisite: PHIL 005 . Discussion included. Cross-Listed with PHIL 160 .


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  • MATH 180: Modern Applied Statistics


    [4 units]

    Introduction to modern applied statistics emphasizing computational methods to deal with high-dimensional data. Multivariate linear and nonlinear regression, model selection, overfitting, cross-validation, bootstrapping and quantification of uncertainty in model parameters and predictions, principal component analysis, and classification.

    Prerequisite: MATH 024  and MATH 032 . Normal Letter Grade only. Laboratory included.


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  • MATH 181: Stochastic Processes


    [4 units]

    Introduction to stochastic processes with emphasis on problem-solving using both analytical and computational techniques. Markov chains in discrete and continuous time, martingales, branching processes, renewal processes, and Brownian motion.

    Prerequisite: MATH 024  and MATH 032 . Normal Letter Grade only. Discussion included.


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  • MATH 195: Upper Division Undergraduate Research


    [1-5 units]

    Supervised research.

    Permission of instructor required. Course may be repeated for credit.


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  • MATH 198: Upper Division Directed Group Study


    [1-5 units]

    Permission of instructor required. Pass/Fail only. Course may be repeated for credit.


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  • MATH 199: Upper Division Individual Study


    [1-5 units]

    Permission of instructor required. Pass/Fail only. Course may be repeated for credit.


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  • Syllabus

    MATH 201: Teaching and Learning in the Sciences


    [1 unit]

    Students will be introduced to ‘scientific teaching’ - an approach to teaching science that uses many of the same skills applied in research. Topics will include how people learn, active learning, designing, organizing and facilitating teachable units, classroom management, diversity in the classroom and assessment design.

    Satisfactory/Unsatisfactory only. Cross-Listed with PHYS 201 .


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  • Syllabus

    MATH 221: Partial-Differential Equations I


    [4 units]

    Partial differential equations (PDEs) of applied mathematics. Topics include modeling physical phenomena, linear and nonlinear first-order PDEs, D’Alembert’s solution, second-order linear PDEs, characteristics, initial and boundary value problems, separation of variables, Sturm-Liouville problem, Fourier series, Duhamel’s Principle, linear and nonlinear stability.

    Prerequisite: MATH 122 . Normal Letter Grade only. Discussion included.


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  • MATH 222: Partial-Differential Equations II


    [4 units]

    Continuation of MATH 221 . Topics include integral transforms, asymptotic methods for integrals, integral equations, weak solutions, point sources and fundamental solutions, conservation laws, Green’s functions, generalized functions, variational properties of eigenvalues and eigenvectors, Euler-Lagrange equations, Maximum principles.

    Prerequisite: MATH 221 . Normal Letter Grade only. Discussion included.


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  • MATH 223: Asymptotics and Perturbation Methods


    [4 units]

    Asymptotic evaluation of integrals, matched asymptotic expansions, multiple scales, WKB, and homogenization. Applications are made to ODEs, PDEs, difference equations, and integral equations to study boundary and shock layers, nonlinear wave propagation, bifurcation and stability, and resonance.

    Prerequisite: MATH 221 . Normal Letter Grade only. Discussion included.


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  • Syllabus

    MATH 231: Numerical Solution of Differential Equations I


    [4 units]

    Examines fundamental methods typically required in the numerical solution of differential equations. Topics include direct and indirect methods for linear systems, nonlinear systems, interpolation and approximation, eigenvalue problems, ordinary-differential equations (IVPs and BVPs), and finite differences for elliptic partial-differential equations. A significant amount of programming is required.

    Prerequisite: MATH 132 . Normal Letter Grade only. Discussion included.


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  • MATH 232: Numerical Solution of Differential Equations II


    [4 units]

    Fundamental methods presented in MATH 231  are used as a base for discussing modern methods for solving partial-differential equations. Numerical methods include variational, finite element, collocation, spectral, and FFT. Error estimates and implementation issues are discussed. A significant amount of programming is required.

    Prerequisite: MATH 231 . Normal Letter Grade only. Discussion included.


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  • MATH 233: Scientific Computing


    [4 units]

    Theoretical and practical introduction to parallel scientific computing. Survey of hardware and software environments, and selected algorithms and applications. Topics include linear systems, N-body problems, FFTs, and methods for solving PDEs. Practical implementation and performance analysis are emphasized in the context of demonstrative applications in science and engineering.

    Prerequisite: MATH 232 . Normal Letter Grade only. Discussion included.


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  • MATH 270: Academic Writing in Graduate Studies


    [3 units]

    Designed to increase the writing proficiency of graduate students, with a focus on strategies for reading critically, organizing and developing thoughts, choosing appropriate vocabulary, and generating and revising writing in a given scientific field. Topics address scientific disciplines. Projects may include writing abstracts, research reports, literature reviews, posters, and grant proposals.

    Open only to major(s): Applied Mathematics, Chemistry and Chemical Biology, Physics, Quantitative and Systems Biology. Cross-Listed with CHEM 270 , PHYS 270 , QSB 270 .


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  • MATH 291: Applied Mathematics Seminar


    [1 unit]

    Seminar series covering various topics in applied mathematics presented by faculty, graduate students, and visiting speakers.

    Permission of instructor required. Satisfactory/Unsatisfactory only. Course may be repeated for credit.


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  • Syllabus

    MATH 292: Special Topics in Applied Mathematics


    [1-4 units]

    Treatment of a special topic or theme in applied mathematics at the graduate level. May be repeated for credit in a different subject area.

    Permission of instructor required. Students may choose grading option with consent of instructor. Course may be repeated for credit.


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  • MATH 295: Graduate Research


    [1-12 units]

    Supervised research.

    Permission of instructor required. Satisfactory/Unsatisfactory only. Course may be repeated for credit. Laboratory included.


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  • MATH 298: Directed Group Study


    [1-12 units]

    Group project under faculty supervision.

    Permission of instructor required. Course may be repeated for credit. Laboratory included.


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  • MATH 299: Directed Independent Study


    [1-6 units]

    Permission of instructor required. Course may be repeated for credit. Laboratory included.


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  • Syllabus

    MATH 399: University Teaching


    [1 unit]

    Centered on a student’s classroom experiences as a Teaching Assistant in an undergraduate Applied Mathematics course. Provides a faculty-directed opportunity to implement teaching practices presented in the course Teaching and Learning in the Sciences. Involves video-taping of teaching, peer review, and weekly meetings with faculty.

    Permission of instructor required. Satisfactory/Unsatisfactory only. Course may be repeated 1 time for credit. Discussion, Laboratory included.


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