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MATH 1000 - Quantitative Reasoning In Today’s World (also listed as MATH 1002)
(3)
Co-requisite: MATH 1001 if supported instruction is required (Math Placement Category III or IV). Units and unit conversion, proportional reasoning, descriptive statistics, basic probability and financial mathematics. Graded ABC-/NC.
GE B4
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MATH 1001 - Quantitative Reasoning in Today’s World Workshop
(1)
Co-requisite: MATH 1000. Mathematics skills development needed for success in MATH 1000 course content. Mathematics background, examination of learning principles, and effective mathematics study skills for becoming independent and self-motivated learners. Recommended for all students but mandatory if supported instruction is required and for those repeating MATH 1000. Graded: CR/NC.
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MATH 1002 - Quantitative Reasoning in Today’s World (also listed as MATH 1000)
(3)
Prerequisite: on Math Placement Category I or II (supported instruction is not required). Units and unit conversion, proportional reasoning, descriptive statistics, basic probability and financial mathematics.
GE B4
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MATH 1040 - Precalculus: Functions and Trigonometry
(6)
Prerequisite: Math Placement Category I or II (supported instruction is not required). Functions, exponential and logarithmic functions; polynomials and rational functions; systems of linear equations and matrices; sequences and series; trigonometric functions, identities, and equations; solution of triangles; inverse trigonometric functions; complex numbers, DeMoivre’s Theorem; parametric equations; polar coordinates; conic sections. Lecture 5 hours, activity 2 hours. Graded ABC-/NC.
CI-D MATH 155 or MATH 955:
The University course listed above articulates with any California Community College (CCC) course that is approved by the C-ID program and given the corresponding “C-ID Course” designation listed here. The articulation is one-way articulation, meaning the approved community college course will articulate for the indicated course credit at the four-year university. Articulation does NOT apply from the four-year institution to the community college or between the four-year institutions.
GE B4
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MATH 1081 - PreCalculus: Functions
(3)
Prerequisite: on Math Placement Category I or II (supported instruction is not required). Functions, exponential and logarithmic functions; polynomials and rational functions; systems of linear equations and matrices; sequences and series including arithmetic and geometric series. Graded ABC-/NC.
GE B4
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MATH 1082 - PreCalculus: Functions, with Lab
(4)
Functions, exponential and logarithmic functions; polynomials and rational functions; systems of linear equations and matrices; sequences and series including arithmetic and geometric series. This course includes a supported instruction component as required for Math Placement Category III or IV. Graded ABC-/NC.
GE B4
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MATH 1083 - Precalculus: Trigonometry
(4)
Prerequisites: Grade of C or better in any of ESM 1082, MATH 1081 or MATH 1082. Trigonometric functions, identities, and equations; solution of triangles; inverse trigonometric functions; complex numbers, DeMoivre’s Theorem; parametric equations; polar coordinates; conic sections. Graded ABCDF.
GE B4
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MATH 1085 - Discrete Mathematical Models
(3)
Prerequisites: Grade of C or better in any of MATH 1081, MATH 1082, or ESM 1082. Rudimentary knowledge of Microsoft Excel. Co-requisite: MATH 1086 if pre-requiste is graded below B-, or is repeating MATH 1085. Sinusoidal, exponential and logarithmic functions in a biological context. Formulation and analysis of basic discrete models in biology. Basic probability, including conditional probability and independence.
Intended for life sciences majors. Graded ABCDF.
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MATH 1086 - Discrete Mathematics Models workshop
(1)
Co-requisite: MATH 1085. Activity for MATH 1085 with focus on problem solving and applications. Recommended for all students, but mandatory for those with grade below B- in any prerequisite for MATH 1085 or those repeating MATH 1085. Graded: CR/NC.
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MATH 1090 - Quantitative Reasoning with Statistics (also listed as ECON 1090, EDFN 1090, EDFN 1092, MATH 1092)
(3)
Co-requisite: MATH 1091 if support instruction is required (Math Placement Category III or IV). Principles of quantitative reasoning, data presentation, descriptive statistics, correlation,probability, distributions of random variables, sampling distributions, interval estimation, and statistical inference, with multi-disciplinary applications. This course includes a supported instruction co-requisite as required for Math Placement Category III or IV. Graded ABC-/NC.
C-ID MATH 110:
The University course listed above articulates with any California Community College (CCC) course that is approved by the C-ID program and given the corresponding “C-ID Course” designation listed here. The articulation is one-way articulation, meaning the approved community college course will articulate for the indicated course credit at the four-year university. Articulation does NOT apply from the four-year institution to the community college or between the four-year institutions.
GE B4
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MATH 1091 - Quantitative Reasoning With Statistics Workshop
(1)
Co-requisite: ECON 1090 or MATH 1090. Mathematics skills development needed for success in ECON/MATH 1090 course content. Mathematics background, examination of learning principles, and effective mathematics study skills for becoming independent and self-motivated learners. Recommended for all students but mandatory if supported instruction is required for those repeating ECON/MATH 1090. Graded: CR/NC.
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MATH 1092 - Quantitative Reasoning with Statistics (also listed as ECON 1090, EDFN 1090, EDFN 1092, MATH 1090)
(3)
Prerequisite: on Math Placement Category I or II (Supported instruction is not required). Principles of quantitative reasoning, data presentation, descriptive statistics, correlation,probability, distributions of random variables, sampling distributions, interval estimation, and statistical inference, with multi-disciplinary applications. Graded ABC-/NC.
C-ID MATH 110:
The University course listed above articulates with any California Community College (CCC) course that is approved by the C-ID program and given the corresponding “C-ID Course” designation listed here. The articulation is one-way articulation, meaning the approved community college course will articulate for the indicated course credit at the four-year university. Articulation does NOT apply from the four-year institution to the community college or between the four-year institutions.
GE B4
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MATH 1100 - Foundations of the Real Number System for Elementary and Middle School Teachers
(3)
Co-requisite: MATH 1101 if support instruction is required (Math Placement Category III or IV). Integers and elementary number theory, rational numbers, decimals and percent, ratio and proportion, alternate bases, and word problems. Restricted to students in multiple subjects credential programs. Graded ABC-/NC.
C-ID MATH 120:
The University course listed above articulates with any California Community College (CCC) course that is approved by the C-ID program and given the corresponding “C-ID Course” designation listed here. The articulation is one-way articulation, meaning the approved community college course will articulate for the indicated course credit at the four-year university. Articulation does NOT apply from the four-year institution to the community college or between the four-year institutions.
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MATH 1101 - Foundations of the Real Number System Workshop
(1)
Co-requisite: MATH 1100. Mathematics skills development needed for success in MATH 1100 course content. Mathematics background, examination of learning principles, and effective mathematics study skills for becoming independent and self-motivated learners. Recommended for all students but mandatory if supported instruction is required for those repeating Math 1100. Graded: CR/NC.
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MATH 1150 - Elements of Algebra and Statistics for Elementary and Middle School Teachers
(3)
Prerequisite: MATH 1100. Functions, relations, sequences, discrete structures, probability, data analysis, and descriptive statistics. Restricted to students in multiple subjects credential and education specialist credential programs. Graded ABC-/NC.
GE B4
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MATH 1540 - Selected Topics in Mathematics
(1-3)
Prerequisite: As needed for specific topic. Current topics of interest to students in Mathematics as announced in the Schedule of Classes. May be repeated for credit as subject matter changes. Graded CR/NC.
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MATH 2041 - Applied Calculus I: Workshop
(1)
Activity for MATH 2040 with focus on problem solving and applications. Recommended for all students, but mandatory for those with grade below B- in any prerequisite for MATH 2040 or those repeating MATH 2040.
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MATH 2051 - Applied Calculus II: Workshop
(1)
Activity for MATH 2050 with focus on problem solving and applications. Recommended for all students enrolled in MATH 2050, but mandatory for those with grade below B- in Math 2040 or those repeating MATH 2050.
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MATH 2110 - Calculus I
(4)
Prerequisites: Graded C or better in MATH 1040 or (in MATH 1081 and MATH 1083) or (in MATH 1082 and MATH 1083)or (in ESM 1082 and MATH 1083), or satisfactory score on placement examination; co-requisite: MATH 2111 when any of the captioned prerequisite courses is graded below B-. Functions, graphs, limits, continuity, derivatives, applications of the derivative, anti-differentiation, definite integral, Fundamental Theorem of Calculus, integration by substitution, applications of the integral. Graded ABCDF.
(GE B4, Not to list as GE B4 , but can be double counted to meet major requirement,)
CI-D MATH 210/MATH 211/MATH 900S:
To receive full transfer credit, student must take both MATH 2110 and MATH 2120.
The University course listed above articulates with any California Community College (CCC) course that is approved by the C-ID program and given the corresponding “C-ID Course” designation listed here. The articulation is one-way articulation, meaning the approved community college course will articulate for the indicated course credit at the four-year university. Articulation does NOT apply from the four-year institution to the community college or between the four-year institutions.
GE B4
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MATH 2111 - Calculus I Workshop
(1)
Co-requisite: MATH 2110. Activity for MATH 2110 students with an emphasis on problem solving. Graded CR/NC.
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MATH 2120 - Calculus II
(4)
Prerequisites: MATH 2110 with minimum C grade; students with a grade of less then B- in MATH 2110 must enroll concurrently in MATH 2121. Integration of transcendental functions, methods of integration, limits of sequences and series, power series, Taylor series, three dimensional analytic geometry.
CI-D MATH 220/MATH 221/MATH 900S:
To receive full transfer credit, students must take both MATH 2110 and MATH 2120.
The University course listed above articulates with any California Community College (CCC) course that is approved by the C-ID program and given the corresponding “C-ID Course” designation listed here. The articulation is one-way articulation, meaning the approved community college course will articulate for the indicated course credit at the four-year university. Articulation does NOT apply from the four-year institution to the community college or between the four-year institutions.
GE B4
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MATH 2121 - Calculus II Workshop
(1)
Co-requisite: MATH 2120. Open to all MATH 2120 students but mandatory for students whose grade in MATH 2110 is less than B-. Graded CR/NC.
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MATH 2130 - Calculus III
(3)
Prerequisites: MATH 2120 with a minimum C grade; students with a grade of less than B- in MATH 2120 must enroll concurrently in MATH 2131. Partial differentiation, multiple integration, vector calculus, line integrals.
CI-D MATH 230:
The University course listed above articulates with any California Community College (CCC) course that is approved by the C-ID program and given the corresponding “C-ID Course” designation listed here. The articulation is one-way articulation, meaning the approved community college course will articulate for the indicated course credit at the four-year university. Articulation does NOT apply from the four-year institution to the community college or between the four-year institutions.
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MATH 2131 - Calculus III Workshop
(1)
Co-requisite: MATH 2130. Open to all MATH 2130 students but mandatory for students whose grade in MATH 2120 is less than B-. Graded CR/NC.
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MATH 2150 - Differential Equations
(3)
Prerequisite: MATH 2130. Ordinary differential equations with concentration on methods of finding solutions; applications in science and engineering.
CI-D MATH 240 or MATH 910S:
To receive full transfer credit, students must take both MATH 2150 and MATH 2550.
The University course listed above articulates with any California Community College (CCC) course that is approved by the C-ID program and given the corresponding “C-ID Course” designation listed here. The articulation is one-way articulation, meaning the approved community college course will articulate for the indicated course credit at the four-year university. Articulation does NOT apply from the four-year institution to the community college or between the four-year institutions.
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MATH 2170 - Introduction to Computer Algebra Systems
(3)
Prerequisites: MATH 2110 graded C or better. Introduction to computer algebra systems such as Mathematica, Matlab or Maple; overview of built-in functions; 2-D and 3-D graphs; basic programming structures; flow control; development and implementation of algorithms.
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MATH 2250 - Explorations in Geometry for Elementary and Middle School Teachers
(3)
Prerequisite: A college level mathematics course graded C or better. Topics include properties of two and three dimensional figures, measurement, constructions, structure, spatial relationships, transformations, and graph theory presented through multiple teaching modes. No credit for mathematics majors.
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MATH 2450 - Foundations of Mathematics I: Discrete Mathematics
(3)
Prerequisite: MATH 2110. Preliminary introduction to the basic mathematical notation, vocabulary, and reasoning used in advanced mathematics courses. Logic; elementary set theory; proof techniques; recursion; induction; equivalence relations; counting techniques; graphs and trees.
CI-D COMP 152 or MATH 160:
The University course listed above articulates with any California Community College (CCC) course that is approved by the C-ID program and given the corresponding “C-ID Course” designation listed here. The articulation is one-way articulation, meaning the approved community college course will articulate for the indicated course credit at the four-year university. Articulation does NOT apply from the four-year institution to the community college or between the four-year institutions.
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MATH 2540 - Selected Topics in Mathematics
(1-4)
Prerequisite: As needed for specific topic. Current topics of interest to students in mathematics, as announced in Schedule of Classes. May be repeated for credit.
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MATH 2550 - Introduction to Linear Algebra
(3)
Prerequisite: MATH 2120. Vector spaces, linear transformations, linear equations, matrices, determinants, eigenvectors and eigenvalues, canonical forms.
CI-D MATH 240 or MATH 910S:
To receive full transfer credit, students must take both MATH 2150 and MATH 2550.
The University course listed above articulates with any California Community College (CCC) course that is approved by the C-ID program and given the corresponding “C-ID Course” designation listed here. The articulation is one-way articulation, meaning the approved community college course will articulate for the indicated course credit at the four-year university. Articulation does NOT apply from the four-year institution to the community college or between the four-year institutions.
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MATH 2740 - Introduction to Statistics
(3)
Prerequisites: Any of ESM 1082, MATH 1040, MATH 1081 or MATH 1082. Graphical display of data, measures of variation, correlation, least-squares regression, design of samples and experiments, basic rules of probability, normal distribution, central limit theorem, sampling distributions, confidence intervals, hypothesis tests. Graded ABCDF.
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MATH 3200 - Selected Topics in History of Mathematics
(3)
Pre/co-requisite: MATH 2120. Traces development of fundamental concepts and techniques in fields of algebra, geometry, trigonometry, and calculus.
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MATH 3450 - Foundations of Mathematics II: Mathematical Reasoning
(4)
Prerequisite: MATH 2450. Set families; equivalence relations; modular arithmetic; functions; combinatorial reasoning; cardinality; linearly and partially ordered sets; abstract binary operations; standard number systems as groups, rings, or fields; and limits of sequences. 3 units lecture, 1 unit recitation.
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MATH 3540 - Selected Topics in Mathematics
(1-4)
Prerequisite: As needed for specific topic. Current topics of interest to students in mathematics as announced in the Schedule of Classes. May be repeated for credit.
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MATH 3950 - Field Experience I: Introduction to Classroom Strategies
(2)
Prerequisite: MATH 2130. Introduction to effective teaching techniques, common core standards, California frameworks and education laws; analysis of strategies to prepare mathematics teaching candidates for urban schools. Service learning required. Graded CR/NC. Field Experience I.
(cl) (wi)
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MATH 4010 - Ordinary Differential Equations
(3)
Prerequisites: Graded C or better in MATH 2130, MATH 2150, MATH 2550, MATH 3450. Ordinary differential equations with concentration on properties of solutions. Introduction to dynamical systems and bifurcation theory.
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MATH 4021 - Advanced Mathematics I for Engineers and Physicists
(3)
Prerequisite: MATH 2150 or MATH 4010. Vector analysis to include line and surface integrals, orthogonal curvilinear coordinates, complex variables to include contour integration and conformal mapping, Laplace transformation.
*All 4000-level courses may be applied toward master’s degree requirements except the following, subject to limits established by department and approval of graduate adviser: MATH 4021, 4550, 4650, 4900, 4950.
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MATH 4030 - Partial Differential Equations
(3)
Prerequisite: MATH 2150 or MATH 4010. Orthogonal sets of functions; Fourier series and integrals, with applications to the equations of mathematical physics; first order equations, Cauchy’s method of characteristics.
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MATH 4100 - Vector Analysis
(3)
Prerequisites: MATH 2130 and MATH 2550. Vector algebra and calculus, vector fields, gradient, divergence, curl, divergence theorem, Stokes’ theorem, applications to geometry and mathematical physics.
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MATH 4200 - Mathematical Logic
(3)
Prerequisites: MATH 3450 graded C or better. The statement calculus, the predicate calculus, mathematical structures, and the deduction of valid consequences; the completeness theorem.
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MATH 4300 - Modern Geometry
(3)
Prerequisites: MATH 3450 graded C or better. Topics selected from advanced Euclidean geometry, non-Euclidean geometry, projective geometry. May be repeated once for credit with approval of instructor as subject matter changes.
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MATH 4460 - Theory of Numbers
(3)
Prerequisites: MATH 3450 graded C or better. Divisibility, Euclidean algorithm, prime numbers, fundamental theorem of arithmetic, distribution of primes, congruences, Fermat-Euler and Wilson theorems, residues and quadratic reciprocity law. Bernoulli numbers, quadratic forms, Diophantine equations.
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MATH 4540 - Selected Topics in Advanced Mathematics
(1-4)
Prerequisite: As needed for specific topic. Current topics of interest to students in mathematics, as announced in Schedule of Classes. May be repeated for credit.
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MATH 4550 - Modern Algebra I
(3)
Prerequisites: MATH 2550, MATH 3450 graded C or better. Groups and rings, including normal subgroups, quotient groups, ideals, quotient rings, group and ring homomorphisms and isomorphisms.
*All 4000-level courses may be applied toward master’s degree requirements except the following, subject to limits established by department and approval of graduate adviser: MATH 4021, 4550, 4650, 4900, 4950.
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MATH 4560 - Modern Algebra II
(3)
Prerequisite: MATH 4550. Additional topics in groups and rings, field extensions, modules.
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MATH 4570 - Linear Algebra
(3)
Prerequisites: MATH 2550, MATH 3450, both graded C or better. Vector spaces linear transformations, eigenvalues and eigenvectors, canonical forms, scalar product spaces.
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MATH 4650 - Analysis I
(3)
Prerequisites: MATH 2130, MATH 3450 with minimum C grade. Real number system; topology of Euclidean space including compactness and completeness; sequences and series, including limit inferior and limit superior; continuity.
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MATH 4660 - Analysis II
(3)
Prerequisite: MATH 4650. Differentiation and integration of functions of a real variable; sequences of functions.
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MATH 4670 - Multivariate Analysis
(3)
Prerequisites: MATH 2550, MATH 4650. Functions of several variables; partial derivatives; generalized chain rule; inverse and implicit function theorems; line and surface integrals.
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MATH 4680 - Introduction to Complex Analysis
(3)
Prerequisite: MATH 4650. Complex variables, analytic functions, complex integration, conformal mappings, applications.
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MATH 4690 - Introduction to Topology
(3)
Prerequisite: MATH 4650. Introduction to point set topology, including continuity, product spaces, compactness, Tyconoff theorem, connectedness, metric spaces, and Urysohn lemma.
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MATH 4700 - Numerical Analysis I
(3)
Prerequisites: MATH 2120, (MATH 2170 or equivalent programming experience), and MATH 2550. Errors in floating point representation, nonlinear equations, systems of linear equations, polynomial interpolation, numerical integration and differentiation.
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MATH 4710 - Numerical Analysis II
(3)
Prerequisites: MATH 2150, MATH 4700. Numerical solution of ordinary and partial differential equations, spline and least square approximation, fast Fourier transform.
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MATH 4720 - Linear Optimization
(3)
Prerequisite: MATH 2550. Geometric solutions, simplex method, the transportation problem, elementary game theory.
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MATH 4740 - Theory of Probability
(3)
Prerequisites: MATH 2130. Highly recommended MATH 2450. General probability spaces, discrete and continuous random variables, conditional probability, joint distributions, random sampling, law of large numbers, normal, gamma, Poisson and binomial distributions.
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MATH 4750 - Introduction to Mathematical Statistics
(3)
Prerequisite: MATH 4740. Estimation and tests of hypotheses, decision theory and Bayes solutions.
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MATH 4800 - Modeling Biological Systems (also listed as BIOL 4800)
(3)
Prerequisites: MATH 2050 or (MATH 2150 and MATH 2550), all graded C or better. Modeling techniques applied to biological systems. Topics include nonlinear dynamics, stochastic models, compartmental and spatial models, parameter estimation, methods of model evaluation, modeling complexities.
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MATH 4840 - Graph Theory
(3)
Prerequisites: MATH 2450 and MATH 3450 with minimum C grade. Introduction to graph theory and its applications: graphs, trees, and directed graphs; isomorphism; connectivity; network flows; Hamiltonian graphs; planar graphs; coloring problems; matchings; Ramsey theory.
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MATH 4900 - Senior Seminar in Mathematics
(4)
Prerequisites: MATH 2450, MATH 4650, (MATH 4550 or MATH 4570). Capstone course in mathematics including written and oral exposition Expository writing on mathematical topics selected by the instructor, including a technical report. Writing-intensive.
Grade of C or better in this course satisfies the Graduation Writing Assessment Requirement.
*All 400-level courses may be applied toward master’s degree requirements except the following, subject to limits established by department and approval of graduate adviser: MATH 4021, 4550, 4650, 4900, 4950.
(wi) GWAR
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MATH 4901 - Capstone Course for Teachers of Mathematics
(4)
Prerequisites: MATH 3960, MATH 4300, MATH 4650. Oral and written expositions including technical reports connecting advanced mathematics and high school mathematics, math education articles analyses, field-work analysis, pedagogical content knowledge analysis and a final report. Writing intensive.
Grade of C or better in this course satisfies the Graduation Writing Assessment Requirement.
*All 400-level courses may be applied toward master’s degree requirements except the following, subject to limits established by department and approval of graduate adviser: MATH 4021, 4550, 4650, 4900, 4901, 4950, 4960.
(wi) GWAR
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MATH 4950 - College Instruction I: Introduction to Instructional Strategies in College Mathematics
(2)
Prerequisite: Graduate standing or permission of instructor. Teaching strategies and learning styles in lower division mathematics courses. Course organization; syllabus and exam preparation; instructional techniques; dealing with special problems; University policies and procedures. Graded CR/NC.
*All 400-level courses may be applied toward master’s degree requirements except the following, subject to limits established by department and approval of graduate adviser: MATH 4021, 4550, 4650, 4900, 4950.
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MATH 4960 - College Instruction II: Application and Analysis of Instructional Strategies in College Mathematics
(2)
Prerequisite: MATH 4950; co-requisite: Math department graduate teaching assignment. Oral and written expositions including analyses of peer observation and interviews, discussion of emerging classroom issues, instructional planning and student learning; reflection paper on first college teaching experience and portfolio. May be repeated for credit. GRADED CR/NC
College instruction II
*All 400-level courses may be applied toward master’s degree requirements except the following, subject to limits established by department and approval of graduate adviser: MATH 4021, 4550, 4650, 4900, 4901, 4950, 4960.
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MATH 4990 - Undergraduate Directed Study
(1-3)
Prerequisite: Consent of an instructor to act as sponsor. Project selected in conference with sponsor before registration; progress meetings held regularly, and a final report submitted. May be repeated for credit.
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Math (Graduate) All 4000-level courses may be applied toward master’s degree requirements except the following, subject to limits established by department and approval of graduate adviser: MATH 4020, 4550 4650 4900, 4950. Classified graduate standing is required for enrollment in 5000-level courses.
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MATH 5021 - Applied Linear Analysis I
(3)
Prerequisites: MATH 2150 or MATH 4010; MATH 2550 and MATH 4650. Recommended: MATH 4570 and MATH 4660. Function spaces, convergence, inner product, bounded linear operators, integral operators and integral equations, adjoint operators, expansion in eigenfunctions, resolvent, kernel.
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MATH 5022 - Applied Linear Analysis II
(3)
Prerequisite: MATH 5021. Unbounded operators, differential operators of second order, Sturm-Liouville operators, eigenvalues and eigenfunctions, Green’s Functions, and additional topics.
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MATH 5210 - Mathematical Modeling
(3)
Prerequisites: MATH 2170 (or equivalent programming experience), MATH 2150 or MATH 4010, MATH 2550, MATH 4740, Recommended: MATH 4030. Modeling techniques with difference and differential equations and stochastic models, with applications in fields such as biology, physics, and engineering.
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MATH 5220 - Optimization
(3)
Prerequisites: MATH 2170 (or equivalent programming experience), MATH 2550, MATH 4650. Selected topics from unconstrained, constrained, least squares, and parametric optimization.
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MATH 5401 - Abstract Algebra I
(3)
Prerequisite: MATH 4550. Theory of groups, introduction to rings.
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MATH 5402 - Abstract Algebra II
(3)
Prerequisite: MATH 5401. Theory of rings and fields.
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MATH 5500 - Advanced Topics in Algebra and Number Theory
(3)
Prerequisite: Approval of instructor. Advanced topics selected from group theory, ring theory, linear algebra, combinatorial group theory, simple groups of Lie type, representation theory, and number theory. May be repeated to maximum of 6 units with approval of graduate advisor.
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MATH 5510 - Advanced Topics in Analysis
(3)
Prerequisite: Approval of instructor. Advanced topics selected from real analysis, complex analysis, functional analysis, Fourier analysis, and applied analysis. May be repeated to maximum of 6 units with approval of graduate advisor.
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MATH 5520 - Advanced Topics in Topology and Geometry
(3)
Prerequisite: Approval of instructor. Advanced topics selected from knot theory, algebraic topology, differential topology, combinatorial topology, algebraic geometry, and differential geometry. May be repeated to maximum of 6 units with approval of graduate advisor.
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MATH 5530 - Advanced Topics in Applied Mathematics
(3)
Prerequisite: Approval of instructor. Advanced topics selected from various fields in applied mathematics, such as mathematical biology, mathematical modeling, applied probability, dynamical systems, and numerical analysis. May be repeated to maximum of 6 units with approval of graduate advisor.
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MATH 5540 - Advanced Topics in Combinatorics and Graph Theory
(3)
Prerequisite: Approval of instructor. Advanced topics selected from combinatorics, graph theory and its applications, combinatorial optimization, and game theory. May be repeated to maximum of 6 units with approval of graduate advisor.
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MATH 5680 - Advanced Complex Analysis
(3)
Prerequisite: MATH 4680. Laurent series, singularities, residue problems, contour integration, conformal mappings, and additional topics.
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MATH 5690 - Topology
(3)
Prerequisite: MATH 4690. Basic concepts of point set topology: mappings, compactness, connectedness, separation properties, and metrization.
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MATH 5700 - Numerical Linear Algebra
(3)
Prerequisites: MATH 2170 or equivalent programming experience; MATH 4570, MATH 4700. Numerical solutions of linear systems of equations, and eigenvalue problems, direct solutions, interactive solutions, with additional topics in linear algebra as time permits.
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MATH 5710 - Numerical Solutions of Partial Differential Equations
(3)
Prerequisites: MATH 2170 (or equivalent programming experience), MATH 4700. Numerical solutions of partial differential equations; finite-difference approximations, consistency, convergence, stability.
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MATH 5740 - Applied Probability Theory
(3)
Prerequisite: MATH 4740. Recommended: MATH 2170. Characteristic functions. Modes of convergence. Law of large numbers. Martingale convergence theorem. Markov chains. Monte Carlo method. Poisson processes. Random walk. Gaussian processes. Brownian motion. Applications in related areas.
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MATH 5800 - Real Analysis
(3)
Prerequisite: MATH 4660. Theory of Lebesgue measure on the real line; theory of the Lebesgue integral and related convergence theorems.
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MATH 5960 - Comprehensive Examination
(0)
See the Comprehensive Examination in the requirements for the Masters Degree section of this catalog.
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MATH 5980 - Graduate Directed Study
(1-4)
Prerequisite: Instructor consent. Independent study of advanced topics in mathematics; regular conferences with instructor. May be repeated once.
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MATH 5990 - Thesis
(1-3)
Prerequisites: Advancement to Candidacy, instructor consent to act as sponsor, departmental approval of topic prior to registration. Independent research resulting in a thesis. May be repeated to maximum of 4 units. Graded CR/NC.
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