2016-2018 Catalog [ARCHIVED CATALOG]
Course Descriptions
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Course Numbering System
The first digit in each course designation is intended to indicate the level of the course. In addition, the first digit also roughly indexes the student’s year of study at the University.
Courses numbered 001 to 099 are non-baccalaureate developmental courses.
Courses numbered 100 to 299 are lower-division.
Courses numbered 300 to 499 are upper-division.
Courses numbered 500 to 599 are graduate level, and may be taken by advanced upper-division, post-baccalaureate, or graduate students for undergraduate or graduate credit.
Courses numbered 600 to 699 are graduate level. These courses may be taken by undergraduate students only on an individual basis, and only with prior, case-by-case approval of the program director of the program offering the course (or his/her designee).
Courses numbered 700 to 799 are doctoral level.
Courses numbered 1000 and above not listed in this catalog because these are professional-level courses carrying University credit, which do not typically apply to credentials or degrees offered by the University. These courses are recorded on student transcripts.
Students should consult relevant sections of this catalog, as well as college and program advising staff, in order to determine which courses are appropriate for their level of study, and which courses satisfy degree requirements for various programs of study.
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Mathematics |
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MATH 125 - Pre-Calculus Units: 4
Designed for students preparing to take MATH 160 . Equations and inequalities, functions, graphs, polynomial and rational functions, trigonometric functions, exponential and logarithmic functions, systems of linear equations, conics, sequences and series, and the binomial theorem. May not be taken for credit by students who have received credit for MATH 115 . Enrollment restricted to students who have completed the Entry-Level Mathematics (ELM) requirement.
Satisfies GE area: B4
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MATH 132 - Survey of Calculus Units: 3
Basic calculus concepts with applications to business, economics, and the social sciences. Differential calculus for algebraic, exponential, and logarithmic functions; optimization, linearization, and other applications of derivatives; introduction to integral calculus. Includes use of graphing calculators. Enrollment Requirements: Enrollment Requirement: MATH 115 with a grade of C (2.0) or better.
Satisfies GE area: B4
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MATH 142 - Basic Statistics Units: 3
Covers types of data; descriptive statistics; types of studies; probability and sampling distributions; statistical inference; correlation and linear regression; chi-square, t-tests, and F-test; interpretation of the relevance of the statistical findings. Includes the application of technology for statistical analysis from disciplines including business, social sciences, psychology, life science, health science, and education. Enrollment restricted to students who have completed the Entry-Level Mathematics (ELM) requirement.
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MATH 160 - Calculus with Applications, I Units: 5
Differential and integral calculus of functions of one variable: analytic geometry, limits, continuity, derivatives, analysis of curves, integrals, and applications; algebraic, trigonometric, logarithmic, and exponential functions; and historical perspectives. Includes a laboratory experience using either computers or graphing calculators. Enrollment Requirements: Enrollment Requirement: A strong background in high school mathematics (Algebra I and II, Geometry, and Trigonometry) or MATH 125 with a grade of C (2.0) or better.
Satisfies GE area: B4
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MATH 162 - Calculus with Applications,II Units: 4
A continuation of differential and integral calculus: inverse trigonometric and hyperbolic functions, integration methods, indeterminate forms, coordinate systems, planes and lines in space, sequences and series, applications, and historical perspectives. Includes a laboratory experience using either computers or graphing calculators.
Prerequisite(s): MATH 160 with a grade of C (2.0) or better.
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MATH 200 - Mathematical Statistics for Nursing Units: 3
Introduction to descriptive and inferential statistics and basic probability theory. Focuses on examples from life and health sciences. Includes histograms, stem- and dotplots, measuring center and spread, scatterplots, correlation, regression, two-way tables, parameter estimation, confidence intervals, t-test, and chi-square test. Introduces discrete and continuous probability model, random variables, normal, binomial, and Poisson distribution, and basic counting principles. Provides the necessary properties of exponential and logarithmic functions. Enrollment restricted to Pre-Nursing students who have completed the Entry-Level Mathematics (ELM) requirement.
Satisfies GE area: B4
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MATH 210 - Math for K-8 Teachers I: Number Sense Units: 3
Designed to reinforce mathematical concepts for those teaching in grades K-8. Emphasis on numeric concepts: sets, logic, counting numbers, integers, rational numbers, real numbers, some number theory, and measurement and estimation, appropriate use of technology, and historical/cultural perspectives. Credit may not be counted toward the mathematics major. Enrollment restricted to students who have completed the Entry-Level Mathematics (ELM) requirement.
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MATH 212 - Mathematics for K-8 Teachers II: Geometry, Measurement, and Reasoning Units: 3
Designed to reinforce mathematical concepts for those teaching in grades K-8. Emphasis on patterns and functional relationships; geometric concepts in two- and three-dimensional space: points, lines, planes, curves, triangles, convex figures, parallelism, congruence, similarity, symmetry, perimeter, area, and volume; problem-solving strategies; appropriate use of technology; and historical/cultural perspectives. Credit may not be counted toward the mathematics major. Enrollment restricted to students who have completed the Entry-Level Mathematics (ELM) requirement.
Prerequisite(s): MATH 210 with a grade of C (2.0) or better.
Satisfies GE area: B4
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MATH 242 - Introduction to Statistics Units: 3
Introduces basic concepts of probability theory such as sample space, discrete, and continuous probability models, counting principles, random variables, conditional probability, discrete probability distributions, normal probability distribution, joint and marginal distributions. Subjects in statistics include types of data, measures of central tendency and variations, visualizing data, tests for normality, sampling distribution, central limit theorem, hypothesis tests for means and proportions, correlation, and regression. May include computer software such as Excel, Minitab, or courseware. Credit may not be counted toward the mathematics major. Enrollment restricted to students who have completed the Entry-Level Mathematics (ELM) requirement. Enrollment Requirements: Enrollment Requirement: MATH 115 .
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MATH 260 - Calculus with Applications, III Units: 4
Differential and integral calculus of functions of several variables: three dimensional analytic geometry, vector calculus, partial derivatives, multiple integrals, line integrals, applications, and historical perspectives. Includes a computer laboratory experience.
Prerequisite(s): MATH 162 with a grade of C (2.0) or better.
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MATH 262 - Introduction to Differential Equations Units: 3
Models involving first-order equations, higher-order linear equations, systems of equations, numerical methods, and applications. Combines theoretical ideas with hands-on experience using appropriate computer software packages. This course is not currently offered at Cal State San Marcos. It is listed only for transfer credit and course equivalency purposes. Enrollment Requirements: Enrollment Requirement: MATH 162 with a grade of C (2.0) or better.
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MATH 264 - Introduction to Linear Algebra Units: 3
Matrix algebra, systems of linear equations, vector spaces, independence, linear transformations, eigenvalues and eigenvectors, and applications. This course is not currently offered at Cal State San Marcos. It is listed only for transfer credit and course equivalency purposes. Enrollment Requirements: Enrollment Requirement: MATH 115 with a grade of C (2.0) or better.
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MATH 270 - Basic Discrete Mathematics Units: 3
Exposure to fundamental discrete mathematical skills and knowledge: basic logic and applications in computer science, methods of proof, functions, relations, set, basic counting techniques, graphs, trees, and applications in computer science.
Prerequisite(s): MATH 160 with a grade of C (2.0) or better.
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MATH 303 - Themes for Society Units: 3
Descriptive overviews of selected areas of mathematics which play a visible role in the modern world. Topics include management science and operations research, political science, statistics, computer science, biology, and some late 20th Century advancements in pure mathematics. Credit may not be counted toward the mathematics major. Enrollment restricted to students who have completed the Lower-Division General Education requirement in Mathematics/Quantitative Reasoning (B4).
Satisfies GE area: BB
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MATH 304 - Women and Mathematics Units: 3
Examination of the social phenomena that have led to the small number of women in the mathematical profession. Exploration of the controversy concerning research on the comparative mathematical ability of boys and girls. Study of the lives, times, and works of women mathematicians. Enrollment restricted to students who have completed the Lower-Division General Education requirement in Mathematics/Quantitative Reasoning (B4).
Satisfies GE area: BB
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MATH 308 - Non-Statistical Mathematics in the Social Sciences Units: 3
Themes involving applications of mathematics in the social sciences such as: proportional representation, voting rules and aggregation of individual preferences, spatial models of election competition, power in weighted voting systems, power indices in politics, balance theory and social inequalities, measurement theory, game theory, static models of animal dominance, rumor and information networks. May not be taken for credit by students who have received credit for MATH 404. Enrollment restricted to students who have completed the Lower-Division General Education requirement in Mathematics/Quantitative Reasoning (B4).
Satisfies GE area: BB
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MATH 311 - Mathematics for K-8 Teachers III: Algebra, Probability, Statistics, and Data Analysis Units: 3
Designed to reinforce mathematical concepts for those teaching grades K-8. Emphasis on linear and quadratic equations and inequalities; collection, organization, and representation of data; inferences, predictions, and arguments based on data; basic notions of chance and probability; appropriate use of technology; and historical/cultural perspectives. May not be taken for credit by students who have received credit for MATH 311B . Credit may not be counted toward the mathematics major.
Prerequisite(s): MATH 212 with a grade of C (2.0) or better.
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MATH 311B - Mathematics for K-8 Teachers III: Algebra, Probability, Statistics, and Data Analysis Units: 3
Designed to reinforce mathematical concepts for those teaching grades K-8. Emphasis on linear and quadratic equations and inequalities; collection, organization, and representation of data; inferences, predictions, and arguments based on data; basic notions of chance and probability; appropriate use of technology; and historical perspectives. Credit may not be counted toward the mathematics major. May not be taken for credit by students who have received credit for MATH 311 . Enrollment restricted to students participating in the Integrated Credential Program.
Prerequisite(s): MATH 212 with a grade of C (2.0) or better.
Corequisite(s): EDMS 512B , EDMS 522B , EDMS 543B .
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MATH 314 - Workshop for Future Mathematics Educators Units: 2
Provides a discussion forum for students pursuing the Mathematics Single-Subject CSET Waiver Program, while co-enrolled in EDUC 350 - Foundations of Teaching as a Profession . Discussions focus on various mathematical subject matter typically presented in secondary-level classrooms, which students visit and observe in EDUC 350 . Students link their observations from the field experience to their own study of relevant mathematical skills and knowledge. Credit may not be counted towards the mathematics major.
Prerequisite(s): MATH 162 with a grade of C (2.0) or better.
Corequisite(s): EDUC 350 .
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MATH 315 - Finite Mathematics Units: 3
Sets, permutations, combinations, probability, linear equations and inequalities, matrices, linear programming, and finance. Credit may not be counted toward the mathematics major. May not be taken for credit by students who have received credit for MATH 130. Enrollment restricted to students who have completed the lower-division General Education requirement in Mathematics/Quantitative Reasoning (B4).
Satisfies GE area: BB
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MATH 330 - Introduction to the History of Mathematics Units: 3
Major currents in the evolution of mathematical thought from early civilization to modern times.
Prerequisite(s): MATH 160 with a grade of C (2.0) or better.
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MATH 340 - Stochastic Modeling in Business and Economics Units: 3
Introduction to stochastic modeling with emphasis on application in business and economics. Discrete probability distributions including uniform, Bernoulli, binomial, hypergeometric, multinomial, and geometric. Random variables, expected value, and standard deviation. Joint distributions, conditional distributions, independence, and conditional expected value. Laws of large numbers. Discrete time Markov chains and martingales. Applications to include queuing models, cash and inventory management models, and stock option pricing. May not be taken for credit by students who have received credit for MATH 440 , MATH 441 , or MATH 571 .
Prerequisite(s): MATH 132 or MATH 160 or MATH 264 and MATH 315 or MATH 374 with a grade of C (2.0) or better.
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MATH 346 - Mathematical Methods for Physics Units: 3
Survey of mathematical methods applicable to physics. Includes series, complex analysis, ordinary and partial differential equations, and special functions and transforms. Recommended Preparation: MATH 260 .
Prerequisite(s): MATH 162 with a grade of C (2.0) or better.
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MATH 350 - Foundations for Theoretical Mathematics Units: 3
Bridge course between computation-driven mathematics and theoretical mathematics. Designed to familiarize the student with the language and process of rigorous mathematical thought, speech, and writings through the introduction of typical and important examples from algebra, analysis, combinatorics, and geometry. Covers elementary logic, methods of proof, mathematical induction, sets, relations, equivalence relations, functions, inverse functions, binary operations and cardinality. Mathematics majors are encouraged to take this course as early as possible.
Prerequisite(s): MATH 160 with a grade of A- (3.7) or better, or MATH 162 with a grade of C (2.0) or better.
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MATH 362 - Differential Equations Units: 3
Analysis and application of ordinary differential equations: linear and nonlinear equations, existence and uniqueness theorems, analytic methods, qualitative analysis of solutions, and numerical methods. Combines theoretical ideas along with hands-on experience using appropriate computer software.
Prerequisite(s): MATH 162 with a grade of C (2.0) or better.
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MATH 374 - Linear Algebra Units: 3
Systems of linear equations, vector spaces, independence, bases, dimension, orthogonality, least squares, determinants, eigenvalues and eigenvectors, positive definiteness, computation, and linear programming. Combines theoretical ideas with hands-on experience using appropriate computer software packages.
Prerequisite(s): MATH 160 with a grade of C (2.0) or better.
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MATH 378 - Number Systems Units: 3
Numbers: natural, rational, real, and complex. Algebraic laws: commutative, associative, and distributive. Brief introduction to groups, rings, and fields. Divisibility and unique factorization for integers and polynomials. Integers modulo n as finite rings and fields. The rational numbers as a non-complete countable ordered field. The real numbers as a complete uncountable ordered field. Sequences and limits including Cauchy sequences, lim inf and lim sup. Complex numbers including De Moivre’s theorem and related trigonometric identities. Factoring polynomials over the various number systems. The Fundamental Theorem of Algebra.
Prerequisite(s): MATH 350 or MATH 370 with a grade of C (2.0) or better.
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MATH 390 - Mathematics Colloquium Units: 1
Guest lecturers present seminars on mathematical topics, e.g., recent advances in mathematics research, interesting applications of mathematics, or fun and challenging math problems. Students must attend each seminar, prepare a journal summarizing the content of each presentation, and write a follow up paper on one of the topics that they found particularly interesting. May be repeated for credit for a total of three (3) units. Grading Basis: Graded Credit/No Credit. Enrollment Requirements: Enrollment Requirement: MATH 162 with a grade of C (2.0) or better.
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MATH 410 - Modern Geometry Units: 3
Critical review of the foundations and basic structure of plane and solid Euclidean geometry, non-Euclidean geometries, incidence and affine geometries; convexity and applications.
Prerequisite(s): MATH 350 or 370 with a grade of C (2.0) or better.
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MATH 422 - Introduction to Number Theory Units: 3
Divisibility, Euclidean algorithm, unique factorization, congruences, and quadratic reciprocity. May also cover some of the following: included primitive roots and indices, continued fractions, sum of squares, introduction to Diophantine equations, prime numbers, pseudo-primes, the prime number theorem, and factorization and primality-testing algorithms. May not be taken for credit by students who have received credit for MATH 372.
Prerequisite(s): MATH 378 with a grade of C (2.0) or better.
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MATH 430 - Foundations of Analysis Units: 3
A classical treatment of the basic concepts of calculus of one variable: the real number system, limits, continuity, differentiability, the Riemann integral, and sequences and series of numbers and functions. May not be taken for credit by students who have received credit for MATH 360.
Prerequisite(s): MATH 378 with a grade of C (2.0) or better.
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MATH 440 - Introduction to Mathematical Probability and Statistics Units: 4
Basic concepts of probability: axiomatic formulation, combinatorics, conditional probability, independence, standard discrete and continuous random variables, expectation, variance, joint distributions, limit theorems. Statistical inference: tests of significance, point estimation methods, confidences intervals, simple linear regression. Combines theoretical ideas with hands-on experience using appropriate computer software packages. May not be taken for credit by students who received credit for MATH 441 .
Prerequisite(s): MATH 260 with a grade of C (2.0) or better.
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MATH 441 - Introduction to Probability Units: 3
Discrete and continuous probability spaces, axiomatic formulation, combinatorics, conditional probability and independence, standard discrete and continuous probability distributions (including uniform, Bernoulli, binomial, Poisson, geometric, normal, and exponential), random variables, expectation and variance, joint distributions, and limit theorems. Emphasis on modeling. Simple proofs required. Additional topics may include random walks, branching processes, and generating functions. May not be taken for credit by students who received credit for MATH 440 .
Prerequisite(s): MATH 260 with a grade of C (2.0) or better.
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MATH 442 - Introduction to Mathematical Statistics Units: 3
Data analysis and inferential statistics: random samples, estimation, sufficient statistics, confidence intervals, hypothesis tests, curve fitting, linear regression, least squares, and goodness of fit. Covers both theory and applications, with emphasis on applications. Simple proofs required.
Prerequisite(s): MATH 441 with a grade of C (2.0) or better.
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MATH 448 - MathematicalModels and Methods in Biology Units: 3
Introduces mathematical models in Biology and their analysis. Both one dimensional models, including the Malthusian Model and the logistic model, and multi-dimensional models, including structured population models and predator-prey models, are studied, as are matrix models for base substitution in DNA, phylogenetic trees, and sequence alignment. Mathematical concepts and methods to formulate and analyze these models include limits, derivatives, matrix algebra, eigenvectors, probability theory, and dynamic programming. Software is used to simulate models and visualize the numerical results. Enrollment Requirements: Enrollment Requirement: MATH 160 with a grade of C (2.0) or better.
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MATH 464 - Numerical Analysis and Computing Units: 3
Computer arithmetic, solution of a single algebraic equation, solution of systems of equations interpolating polynomials, numerical integration, numerical solution of ordinary differential equations, error analysis, and computational effort of numerical algorithms. Combines theoretical ideas with hands-on laboratory experience. Also offered as CS 464 . Students may not receive credit for both.
Prerequisite(s): CS 111 and MATH 162 .
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MATH 470 - Introduction to Abstract Algebra Units: 3
An introduction to the theory of groups, rings, and fields, with abstract ideas reinforced by concrete and important examples, such as permutation groups, polynomial rings, and finite fields. The power of the axiomatic systems introduced will be illustrated via several applications to concrete and classical problems.
Prerequisite(s): MATH 378 with a grade of C (2.0) or better.
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MATH 472 - Introduction to Graph Theory Units: 3
Fundamental concepts of undirected and directed graphs, trees, connectivity and traversability, planarity, colorability, networks, and matchings; emphasis on modern applications.
Prerequisite(s): MATH 350 or 370 with a grade of C (2.0) or better.
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MATH 474 - Introduction to Combinatorics Units: 3
Introduction of the basic tools of combinatorics and their applications. Permutations, combinations, occupancy problems, generating functions, recurrences, inclusion/ exclusion, graph theory, pigeonhole principle, experimental design, and coding theory.
Prerequisite(s): MATH 350 or 370 with a grade of C (2.0) or better.
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MATH 480 - Introduction to Optimization Units: 3
Modern study of linear programming with an emphasis on model formulation, solution, and interpretation of software output. Applications in work-scheduling, diet, capital budgeting, blending, production process, transportation, assignment, transshipment, and flow problems. Programming methods include the simplex method and its specialized variations, Big M Method, goal programming, and integer programming. Theoretical aspects include optimality conditions, sensitivity analysis, and duality. Requires using industry-standard software to strengthen the ideas and concepts. Also offered as CS 480 . Students may not receive credit for both.
Prerequisite(s): MATH 374 .
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MATH 490 - Senior Seminar Units: 3
Presentation and discussion of selected areas of mathematics in order to supplement available offerings. Sample areas include differential forms, complex variables, partial differential equations, and a second course in analysis, abstract algebra, or discrete math. May be repeated twice as course content changes, with consent of the program, for a maximum of nine (9) units of credit from MATH 490 and MATH 491 . Enrollment Requirements: Enrollment Requirement: Twelve (12) units of upper-division mathematics. Other requirements to be determined by instructor.
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MATH 491 - Senior Seminar with Lab Units: 3
Presentation and discussion of selected areas of mathematics in order to supplement available offerings. Sample areas include mathematical modeling and a second course in numerical analysis, optimization, or statistics. This course meets for four hours per week. May be repeated for a maximum of nine (9) units of credit for MATH 490 and 491. Enrollment Requirements: Enrollment Requirement: Twelve (12) units of upper-division mathematics. Other requirements to be determined by instructor.
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MATH 495 - Internship in Mathematics Units: 1-3
Faculty-sponsored academic internship in business, industrial, government, research firm, or university labs and centers. Enrollment restricted to students who have obtained consent of instructor.
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MATH 498A - Individual Study in Mathematics Units: 1
Individually directed reading and study in mathematical sciences literature. May be repeated for a maximum of three (3) units. Enrollment restricted to students who have obtained consent of instructor. Enrollment Requirements: Enrollment Requirement: Twelve (12) units of upper-division Mathematics.
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MATH 498B - Individual Study in Mathematics Units: 2
Individually directed reading and study in mathematical sciences literature. May be repeated for a maximum of three (3) units. Enrollment restricted to students who have obtained consent of instructor. Enrollment Requirements: Enrollment Requirement: Twelve (12) units of upper-division Mathematics.
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MATH 498C - Individual Study in Mathematics Units: 3
Individually directed reading and study in mathematical sciences literature. May be repeated for a maximum of three (3) units. Enrollment restricted to students who have obtained consent of instructor. Enrollment Requirements: Enrollment Requirement: Twelve (12) units of upper-division Mathematics.
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MATH 499A - Independent Research in Mathematics Units: 1
Designed for students capable of independent and original research. May be repeated for a maximum of three (3) units. Enrollment restricted to students who have obtained consent of instructor. Enrollment Requirements: Enrollment Requirement: Twelve (12) units of upper-division mathematics.
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MATH 499B - Independent Research in Mathematics Units: 2
Designed for students capable of independent and original research. May be repeated for a maximum of three (3) units. Enrollment restricted to students who have obtained consent of instructor. Enrollment Requirements: Enrollment Requirement: Twelve (12) units of upper-division mathematics.
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MATH 499C - Independent Research in Mathematics Units: 3
Designed for students capable of independent and original research. May be repeated for a maximum of three (3) units. Enrollment restricted to students who have obtained consent of instructor. Enrollment Requirements: Enrollment Requirement: Twelve (12) units of upper-division mathematics.
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MATH 503 - Cryptography Units: 3
Fundamentals of protecting confidentiality, integrity and availability of information in computer systems. This course covers the fundamentals of cryptographic concepts and methods. Several encryption/decryption algorithms will be discussed. The topics include an introduction to the mathematics behind cryptography including number theory, group theory, and probability theory; cryptographic algorithms including classical methods, symmetric key systems, public key systems, hash functions, digital signatures and certificates; cryptanalysis and attacks; and access control including authentication and authorization.orization. Assignments include programming labs to apply public keys, dictionary attacks, digital signatures, and certificates. May not be counted towards the Master’s degree in Mathematics.
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MATH 505 - Readings from Original Sources Units: 3
Mathematics studied through the reading, analysis, and discussion of original papers. May be repeated once for credit with consent of instructor. Enrollment Requirements: Enrollment requirements to be determined by instructor.
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MATH 510 - Mathematical Communication Units: 3
Selected topics in advanced mathematics chosen to demonstrate appropriate use of technology and effective organization and presentation of mathematics in oral and written form. Includes three aspects of mathematical writing: writing expository mathematics, writing formal mathematics, and writing as a tool to learn; preparation of mathematical lectures; and development software modules/notebooks. Enrollment Requirements: Additional enrollment requirement for all students: At least nine (9) other units of upper-division mathematics.
Prerequisite(s): For undergraduates and enrollment requirement For graduate students: MATH 350 .
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MATH 520 - Algebra Units: 3
Review and continuation of the study of algebra begun in MATH 470. Covers some of the following: the theory of finite group theory including the Sylow Theorems, polynomial ring, unique factorization, number fields, and finite fields. The latter half of the course will cover field extensions and Galois Theory, including the classic theorems on the unsolvability of the general quintic and the impossibility of certain ruler and compass constructions, such as trisecting an angle.
Prerequisite(s): For undergraduate students and enrollment requirement For graduate students: MATH 470 with a grade of C (2.0) or better.
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MATH 521 - Computational and Applied Algebra Units: 3
Introduction to algebraic tools and ideas that have applications in such fields as cryptography, coding theory, number theory, algebraic geometry, integer programming, computing modeling, and robotics. Includes some of the following: finite fields, Gröbner bases, resultants, algebraic curves, and their codes.
Prerequisite(s): For undergraduate students and enrollment requirement For graduate students: MATH 470 .
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MATH 522 - Number Theory Units: 3
Introduction to number theory from the algebraic and/or analytic point of view. Includes some of the following: congruences, finite fields and rings, and quadratic reciprocity; quadratic forms and Diophantine equations; elliptic curves; the Gaussian integers, the Eisenstein integers, and unique factorization in these rings; other quadratic and cyclotomic fields and ideal factorization; and introduction to analytic number theory, primes in arithmetic progressions, and the prime number theorem.
Prerequisite(s): For undergraduate students and enrollment requirement For graduate students: MATH 470 with a grade of C (2.0) or better.
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MATH 523 - Cryptography and Computational Number Theory Units: 3
Algorithms for factorization and primality testing: pseudo-primes, quadratic sieve, Lucas Test, continued fractions, factorization using elliptic curves, and public key cryptosystems such as RSA, which is widely used for secure transfer of data on the internet. Additional background material (such as the rudiments of elliptic curves) will be introduced as needed. Combines theoretical ideas with computer lab experimentation and implementation. Some familiarity with a computer language is useful but not required.
Prerequisite(s): For undergraduates and enrollment requirement For graduate students: MATH 350 or 370 with a grade of C (2.0) or better.
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MATH 528 - Advanced Linear Algebra Units: 3
Vector spaces; dual spaces; linear transformations; bilinear forms and their matrix representations; Jordan and other canonical forms; finite-dimensional spectral theory; and connections to other branches of mathematics.
Prerequisite(s): For undergraduates and enrollment requirement For graduate students: MATH 374 with a grade of C (2.0) or better.
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MATH 530 - Measure Theory Units: 3
Lebesgue measure, measurable functions, the Lebesgue integral, Fubini’s Theorem, Lp-spaces, and differentiation.
Prerequisite(s): For undergraduates and enrollment requirement For graduate students: MATH 430 .
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MATH 532 - Ordinary Differential Equations Units: 3
Theory and applications of ordinary differential equations. Existence and uniqueness of solutions, methods for solving equations, linear differential equations, singularities, qualitative analysis of solutions, and systems of equations.
Prerequisite(s): For undergraduates and enrollment requirement For graduate students: MATH 374 and MATH 430 .
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MATH 534 - Partial Differential Equations Units: 3
Theory and applications of partial differential equations. Cauchy problems, boundary problems, the Cauchy-Kovalevsky Theorem, Fourier Series, harmonic functions, elliptic equations, and hyperbolic equations. Enrollment Requirements: Enrollment Requirement: MATH 260 and MATH 362 .
Prerequisite(s): For undergraduates and enrollment requirement For graduate students: MATH 374 and MATH 430 .
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MATH 535 - Multivariable Advanced Calculus Units: 3
Analysis in several variables including multivariable derivatives and integrals, inverse function theorem, implicit function theorem, and generalizations of the fundamental theorem of calculus (e.g., Stokes’ Theorem). Some of these topics may be presented from the point of view of differential forms. Enrollment Requirements: Enrollment Requirement: MATH 260 .
Prerequisite(s): For undergraduates and enrollment requirement For graduate students: MATH 374 and MATH 430 .
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MATH 536 - Complex Analysis Units: 3
Study of functions of a complex variable, including analytic functions, contour integrals, Cauchy’s Theorem, poles and residues, Liouville’s Theorem, Laurent Series, the Residue Theorem, analytic continuation, and conformal mappings.
Prerequisite(s): For undergraduates and enrollment requirement For graduate students: MATH 430 .
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MATH 537 - Calculus of Variations Units: 3
Study of the theory of maximum and minimum values of functions defined on spaces of infinite dimension. Includes topics such as Euler’s equation, geodesics, the isoperimetric problem, optimization constrained by subsidiary conditions, and the Weierstrass-Erdman corner conditions. Emphasis to be on both theory and application.
Prerequisite(s): For undergraduates and enrollment requirement For graduate students: MATH 362 , MATH 374 , and MATH 430 .
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MATH 538 - Applicable Analysis Units: 3
Foundations of functional analysis; linear and metric spaces; different modes of convergence; Hilbert Space; and applications. May include topics such as calculus of variations, fixed point theorems, and operator theory.
Prerequisite(s): For undergraduates and enrollment requirement For graduate students: MATH 362 , MATH 374 , and MATH 430 .
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MATH 540 - Concrete Mathematics Units: 3
Blend of continuous and discrete topics including sums, recurrences, elementary number theory, binomial coefficients, generating functions, discrete probability, and asymptotic methods.
Prerequisite(s): For undergraduates and enrollment requirement For graduate students: MATH 350 or 370 or MATH 470 or MATH 472 or MATH 474 .
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MATH 541 - Structural Graph Theory Units: 3
Material covered will be selected from a subset of the following subjects: trees and cycles; independence and matching; graph partitioning, packing, and covering; tournaments; flows; algorithmic aspects; topological graph theory; and facility location.
Prerequisite(s): For undergraduates and enrollment requirement For graduate students: MATH 350 or 370 or MATH 470 or MATH 472 or MATH 474 .
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MATH 542 - Advanced Graph Theory Units: 3
Graphs and digraphs; traversability; factorization; planarity and embedding; coloring; graph Ramsey theory; probabilistic methods; extremal graph theory; and algebraic graph theory.
Prerequisite(s): For undergraduates and enrollment requirement For graduate students: MATH 350 or 370 or MATH 470 or MATH 472 or MATH 474 .
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MATH 544 - Advanced Combinatorics Units: 3
Enumeration; combinatorial set systems; combinatorial designs; Ramsey theory; combinatorial optimization; matroids; and axiomatic social choice.
Prerequisite(s): For undergraduates and enrollment requirement For graduate students: MATH 350 or 370 or MATH 470 or MATH 472 or MATH 474 .
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MATH 550 - Geometry Units: 3
Geometric ideas selected from the following fields: euclidean geometry, hyperbolic geometry, projective geometry, introductory algebraic geometry, and computational geometry. Combines theoretical ideas with hands-on laboratory experience.
Prerequisite(s): For undergraduates and enrollment requirement For graduate students: MATH 374 and MATH 470 .
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MATH 552 - Introduction to Differential Topology and Geometry Units: 3
Introduction to curves, surfaces, and possibly higher dimensional manifolds from the point of view of differential topology and/or differential geometry. Includes some of the following: Curves (e.g., Frenet-Serret Theorem and its consequences, isoperimetric inequality, four-vertex theorem, line integrals, Fenchel’s Theorem); the topological classification of surfaces, vector fields, and curvature on surfaces (leading up to some of the following: geodesics, minimal surfaces, Gauss’s theorema egregium, and the Gauss-Bonnet Theorem); and introduction to higher dimensional manifolds, differential forms, and integration (possibly including Stokes’ Theorem and global invariants such as the Euler characteristic and de Rham cohomology). Enrollment Requirements: Enrollment Requirement: MATH 260 .
Prerequisite(s): For undergraduates and enrollment requirement For graduate students: MATH 374 and MATH 430 .
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MATH 555 - General Topology Units: 3
Topological spaces, open and closed sets, metric spaces, continuity, compactness, and connectedness. Other subjects may include separation axioms, fundamental groups, classification of surfaces, and completion of metric spaces.
Prerequisite(s): For undergraduates and enrollment requirement For graduate students: MATH 430 .
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MATH 561 - Computational Linear Algebra Units: 3
Provides a thorough background in the formulation and analysis of algorithms for numerical linear algebra. Includes fundamentals of scientific computation, subspaces, rank-revealing matrix factorizations, numerical solutions of linear systems, linear least squares, regularization, perturbation theory, and iterative methods. Combines theoretical ideas with laboratory experience. Knowledge of computer language is required.
Prerequisite(s): For undergraduates and enrollment requirement For graduate students: MATH 374 .
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MATH 563 - Numerical Solution of Ordinary Differential Equations Units: 3
Survey of numerical methods for the solution of ordinary differential equations including Runge-Kutta, Taylor’s, Voterra, and multistep methods. Analysis of convergence and implementation of various methods using numerical software. Covers the stability of differential equations and stability regions for numerical schemes. Subjects include the method of lines, two-point boundary value problems, and Volterra integral equations.
Prerequisite(s): MATH 362 and MATH 374 with a grade of C (2.0) or better.
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MATH 564 - Nonlinear Programming Units: 3
Theory and techniques for solving constrained and unconstrained nonlinear programming problems. Techniques include Quasi-Newton Secant Methods, Broyden’s Method, conjugate gradient methods, and line search methods. Theoretical aspects include convexity, Lagrangian Multipliers, optimality conditions, convergence, primal problem, duality, saddle points, and line searches.
Prerequisite(s): For undergraduates and enrollment requirement For graduate students: MATH 374 or MATH 480 or CS 480 .
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MATH 570 - Introduction to Stochastic Processes Units: 3
Elements of stochastic processes, discrete-time and continuous-time Markov chains, random walks, branching processes, birth and death processes, and Poisson point processes. Applications to queues and stochastic networks, resource management, biology, and physics. May include optimal stopping, hidden Markov models, renewal processes, martingales, Brownian motion, and Gaussian processes.
Prerequisite(s): For undergraduates and enrollment requirement(s) for graduate students: MATH 430 and either MATH 440 or MATH 441 with grades of C (2.0) or better.
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MATH 571 - Probability and Random Processes Units: 3
Framework for probability theory: probability spaces as measure spaces, random variables, expectation and conditional probability. Major results such as limit theorems for sums of random variables, zero-one laws, and ergodic theorems. Applications may include branching processes, Markov Chains, Markov Random Fields, martingales, percolation, Poisson Processes, queuing theory, random walks, and renewal processes. Combines theoretical ideas with hands-on laboratory experience using appropriate computer software packages.
Prerequisite(s): For undergraduates and enrollment requirement(s) for graduate students: MATH 430 or MATH 440 or MATH 441 with a grade of C (2.0) or better.
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MATH 620 - Seminar in Advanced Mathematics Units: 3
Advanced mathematics chosen from areas represented in the program faculty and intended to build on 500-level material. Covers the following: algebra and number theory, analysis, combinatorics and graph theory, computational mathematics, geometry, and probability. May be repeated for a maximum of twelve (12) units of credit for MATH 620 and MATH 621 . Enrollment restricted to students who have obtained consent of instructor.
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MATH 621 - Seminar in Advanced Mathematics with Lab Units: 3
Advanced mathematics chosen from areas represented in the program faculty and intended to build on 500-level material. Covers the following: algebra and number theory, analysis, combinatorics and graph theory, computational mathematics, geometry, and probability. This course meets for four hours per week. May be repeated for a maximum of twelve (12) units of credit for MATH 620 and 621. Enrollment restricted to students who have obtained consent of instructor.
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MATH 697 - Workshop in the Teaching of Mathematics Units: 1
Discussion of syllabus construction, lecture preparation, assignment and grading of homework, construction and grading of exams, and resolution of classroom problems. May be repeated, but credit will not be counted toward the Master of Science degree. Grading Basis: Graded Credit/No Credit. Enrollment restricted to students with graduate standing in mathematics.
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MATH 698 - Preparation for Graduate Comprehensive Examination Units: 3
Independent preparation for taking the Master of Science in Mathematics Comprehensive Examination. May be repeated for credit for a total of nine (9) units, but students may enroll in only one section per semester, a maximum of three (3) units will be counted toward the Master of Science in Mathematics degree. Grading Basis: Credit / No Credit. Enrollment restricted to students with graduate student standing in mathematics who have advanced to candidacy under the Comprehensive Exam Option, and requires the approval of the Graduate Coordinator.
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MATH 699 - Thesis Units: 3
Preparation of a thesis for the master’s degree. May be repeated for a total of six 6 units, but students may enroll in only one section per semester. Grading Basis: Graded Credit/No Credit. Enrollment Requirements: Enrollment requires approval of the graduate coordinator.
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Military Science |
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MILS 101 - Introduction to Leadership I Units: 3
Structure, organization and mission of the U.S. Army. Development of leadership styles. Preparation and development for officer status.
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MILS 102 - Introduction to Leadership II Units: 3
Officer leadership, development and functions emphasizing command responsibilities for basic foundation of military fundamentals. Skills and techniques required to be an effective leader in today’s rapidly changing world.
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MILS 201 - Foundations of Leadership I Units: 3
Scientific approach to leadership theory and its applicability to military settings through study of human behavior and leadership models at individual and group levels using simulations, case studies, and diagnostic instruments.
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MILS 202 - Foundations of Leadership II Units: 3
Leadership at organizational level with applications to military settings with an emphasis on developing leader skills and examination of civil-military relations. Individual leadership development in different training environments utilizing different leadership doctrine, professionalism, standard of ethical conduct, motivation, counseling, team development, and organizational climate. Uses simulations, case studies, and diagnostic instruments.
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MILS 301 - Military Decision-Making Process Units: 3
Emphasizes the study, practice, and application of the fundamentals of Army leadership, Officership, Army values and ethics, personal development, and small unit tactics at the team and squad level. Enrollment Requirements: Enrollment Requirements: MILS 101 , MILS 102 , MILS 201 , MILS 202 , prior military service or successful completion of Cadet Initial Entry Training (CIET).
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MILS 302 - Adaptive Team Leadership Units: 3
Emphasizes the application of the basic tenets of small-unit leadership and mission-accomplishment. Challenging scenarios related to small unit tactical operations are used to develop self-awareness and critical thinking skills. Enrollment Requirements: Enrollment Requirements: MILS 301 , and prior military service or successful completion of Cadet Initial Entry Training (CIET).
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MILS 401 - Developmental Leadership Units: 3
Focuses on duties and responsibilities cadets need to become Army staff officers. Includes applying the Military Decision Making Process, Army writing style, and the Army’s Training Management and METL Development processes during weekly Training Meetings that plan, execute, and assess battalion training events. Enrollment Requirements: Enrollment Requirements: MILS 301 and MILS 302 , prior military service or successful completion of Cadet Initial Entry Training (CIET) would waive the following lower-division requirements: MILS 101 , MILS 102 , MILS 201 , MILS 202 .
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MILS 402 - Leadership in a Complex World Units: 3
Explores the dynamics of leading in complex situations of current military operations in full spectrum operations (FSO). Enrollment Requirements: Enrollment Requirements: MILS 401 , prior military service or successful completion of Cadet Initial Entry Training (CIET) would waive the following lower division requirements: MILS 101 , MILS 102 , MILS 201 , MILS 202 .
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Modern Language Studies |
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MLAN 101 - Beginning Study of a Second Language Units: 4
Basic concepts of a language other than English, Spanish, French, German, Chinese, or Japanese. Designed to develop oral and written communication skills and enhance cultural knowledge. This course is not currently offered at Cal State San Marcos. It is listed only for transfer-credit and course equivalency purposes. May be repeated for credit as language changes.
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MLAN 102 - Beginning Study of a Second Language Units: 4
Continuation of MLAN 101 . Further study of basic concepts of a language other than English, Spanish, French, German, Chinese, or Japanese. Designed to develop oral and written communication skills and enhance cultural knowledge. This course is not currently offered at Cal State San Marcos. It is listed only for transfer-credit and course equivalency purposes. May be repeated for credit as language changes. Enrollment Requirements: Enrollment Requirement: MLAN 101 (in the same language).
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MLAN 115 - Introduction to Literatures of the World in Translation: Beginnings to 1600 Units: 3
Introduction to literature as a universal artistic human expression, found throughout all times and all cultures. Readings from several broad regions of the world, and from before the 16th century, will be studied to determine what is both particular and universal about literature, how literature is an interpretation of life, and how that interpretation provides meaning.
Satisfies GE area: C2
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MLAN 116 - Introduction to Literatures of the World in Translation: 1600 to Present Units: 3
Introduction to literature as a universal artistic human expression, found throughout all times and all cultures. Readings from several broad regions of the world, from 15th century to the present time, will be studied to determine what is both particular and universal about literature, how literature is an interpretation of life, and how that interpretation provides meaning.
Satisfies GE area: C2
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MLAN 201 - Intermediate Study of a Foreign Language I Units: 3
Further study of a language other than English, Spanish, French, German, Chinese, or Japanese. Emphasis on development of the skills of reading, listening, comprehension, speaking, and writing. This course is not currently offered at Cal State San Marcos. It is listed only for transfer-credit and course equivalency purposes. Conducted in the appropriate language other than English. May be repeated for credit as language changes. Enrollment Requirements: Enrollment Requirement: MLAN 102 (in the same language).
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MLAN 202 - Intermediate Study of a ForeignLanguage II Units: 3
Continuation of MLAN 201 . Further development of the four skills in a language other than English, Spanish, French, German, Chinese, or Japanese. Emphasis on oral and written composition, communication, and review of grammatical structures. Conducted in the appropriate language other than English. This course is not currently offered at Cal State San Marcos. It is listed only for transfer-credit and course equivalency purposes. May be repeated for credit as language changes. Enrollment Requirements: Enrollment Requirement: MLAN 201 (in the same language).
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MLAN 216 - Intermediate Second Language for Special Purpose Units: 1-6
Intermediate study of a language other than English, Spanish, French, German, Chinese, or Japanese. Designed to develop oral and written communication skills, with special emphasis on vocabulary, conversational practice, and cultural background necessary for successful communication within a specialized context. This course does not fulfill the graduation requirement for a language other than English. Course maybe repeated for credit as language and/or subject matter changes. Enrollment Requirements: Enrollment Requirement: MLAN 102 .
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MLAN 220 - English and Cross-Cultural Skills for University Success for International Students Units: 3
Develops oral and written communication skills, allowing international students to compare and contrast diverse cultures for the development of cross-cultural understanding in individual institutional, and global contexts. Emphasizes the values, customs and practices within U.S. academic culture. Enrollment restricted to students who have obtained consent of instructor.
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MLAN 316 - Advanced Second Language for Special Purpose Units: 1-6
Advanced-level study of a language other than English, Spanish, French, German, Chinese, or Japanese. Designed to develop oral and written communication skills, with special emphasis on vocabulary, conversational practice, and cultural background necessary for successful communication within a specialized context. Course may be repeated for credit as language and/or subject matter changes. Enrollment Requirements: Enrollment Requirement: MLAN 216 .
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MLAN 331 - World Languages and Their Speakers Units: 3
Designed to introduce students to the variety of language and linguistic phenomena in the world today, this course examines the history, pronunciation, alphabets, and speakers of languages greater and lesser known that have helped to shape the contemporary sociopolitical context. This course requires no knowledge of any language other than English and can be a great introduction to future second language study. Recommended Preparation: Recommended Preparation: A course in Introductory Linguistics.
Satisfies GE area: DD
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MLAN 350 - The Origins and Contemporary Aspects of Latino Culture Units: 3
Influences and results of mixed background are examined in the literature, the arts and the ideas of major figures throughout the centuries. The course seeks to allow students to make connections, examine and question theories, and draw conclusions about heritage and the meaning of self. It also seeks to educate Latinos and non-Latinos as to major artistic and literary movements, and important historical developments as manifested in writings, arts and music so they can reach their own conclusions about what it means to be Latino.
Satisfies GE area: CC
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