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2019-2020 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 115 - College Algebra Units: 3
Equations and inequalities, functions, graphs, polynomials, exponential and logarithmic functions, conics, sequences and series, counting principles, binomial theorem, and systems of linear equations.
Note: Students who enter CSUSM in Mathematics/Quantitative Reasoning Placement Categories IV and who have completed MATH 101 with a grade of C (2.0) or better should take MATH 105 instead of this course.
Cross-listed: MATH 115, ESM 105 , and MATH 105 are cross-listed. Students may receive credit for only one of the courses. May not be taken for credit by students who have received credit for MATH 125 . Enrollment Restrictions: For students matriculating prior to Fall 2018: enrollment is restricted to students who have completed the Entry-Level Mathematics (ELM) requirement. For students matriculating in Fall 2018 or later: enrollment is restricted to students in Mathematics/Quantitative Reasoning Placement Categories I and II, or who have completed MATH 101 with a grade of C (2.0) or better.
Satisfies GE area: B4
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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. Students who have received credit for MATH 105 or MATH 115 may earn only three (3) credits toward graduation. Cross-listed: MATH 125 and MATH 126 . Students may not receive credit for both. Enrollment Restrictions: For students matriculating prior to Fall 2018, enrollment is restricted to students who have completed the Entry-Level Mathematics (ELM) requirement.
For students matriculating in Fall 2018 or later, enrollment is restricted to students in Mathematics/Quantitative Reasoning Placement Categories I or II, or who have completed MATH 105 with a grade of C (2.0) or better.
Satisfies GE area: B4
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MATH 126 - Transition to Calculus Units: 3
Designed as a bridge course between college algebra (MATH 105 or MATH 115 ) and calculus (MATH 160 ). Includes complex numbers, functions and their inverses, polynomial functions, polynomial division and inequalities, exponential and logarithmic functions, trigonometric functions and identities, sequences and series, systems of linear equations, and limits. May not be taken for credit by students who have received credit for MATH 125 .
Prerequisite(s): MATH 105 or MATH 115 with a grade of C (2.0) or better.
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 Restrictions: For students matriculating prior to Fall 2018, enrollment is restricted to students who have completed the Entry-Level Mathematics (ELM) requirement. For students matriculating in Fall 2018 or later, enrollment is restricted to students in Mathematics/Quantitative Reasoning Placement Categories I and II, or who have completed MATH 105 with a grade of C (2.0) or better. Enrollment Requirements: MATH 105 or MATH 115 with a grade of C (2.0) or better, or the equivalent.
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 Restrictions: For students matriculating prior to Fall 2018, enrollment is restricted to students who have completed the Entry-Level Mathematics (ELM) requirement. For students matriculating in Fall 2018 or later, enrollment is restricted to students in Mathematics/Quantitative Reasoning Placement Categories I and II, or who have completed MATH 101 or MATH 105 with a grade of C (2.0) or better.
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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.
Prerequisite(s): A passing score on the math placement test; or MATH 125 or MATH 126 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 Restrictions: For students matriculating prior to Fall 2018, enrollment is restricted to Pre-Nursing students who have completed the Entry-Level Mathematics (ELM) requirement. For students matriculating in Fall 2018 or later, enrollment is restricted to Pre-Nursing students in Mathematics/Quantitative Reasoning Placement Categories I and II, or who have completed MATH 101 or MATH 105 with a grade of C (2.0) or better.
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. Enrollment Restrictions: For students matriculating prior to Fall 2018, enrollment is restricted to students who have completed the Entry-Level Mathematics (ELM) requirement. For students matriculating in Fall 2018 or later, enrollment is restricted to students in Mathematics/Quantitative Reasoning Placement Categories I and II, or who have completed MATH 101 or MATH 105 with a grade of C (2.0) or better.
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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 Restrictions: 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. Enrollment Restrictions: For students matriculating prior to Fall 2018, enrollment is restricted to students who have completed the Entry-Level Mathematics (ELM) requirement. For students matriculating in Fall 2018 or later, enrollment is restricted to students in Mathematics/Quantitative Reasoning Placement Categories I and II, or who have completed MATH 105 with a grade of C (2.0) or better. Enrollment Requirements: MATH 105 or MATH 115 with a grade of C (2.0) or better, or an equivalent (or more advanced) course.
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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: 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: 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 Restrictions: 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 Restrictions: 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 Restrictions: 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 Restrictions: 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 toward the mathematics major. Grading Basis: Graded Credit / No Credit.
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 Restrictions: 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 342 - Probability and Statistics for Engineers and Scientists Units: 3
Introduction to probability and statistical methods applicable to engineering and science. Includes basic probability theory, special random variables and their uses, sampling distributions and the Central Limit Theorem, estimating parameters and finding confidence intervals, hypothesis testing, simple linear regression, and quality control. Cross-listed: MATH 342 and EE 342 are cross-listed. Students may not receive credit for both. May not be taken for credit by students who received credit for MATH 440 , or MATH 442 . Credit may not be counted toward the mathematics major.
Prerequisite(s): MATH 260 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. Enrollment Requirements: for graduate students MATH 160 with a grade of A- (3.7) or better, or MATH 162 with a grade of C (2.0) or better.
Prerequisite(s): for undergraduates 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. Enrollment Requirements: for graduate students MATH 162 with a grade of C (2.0) or better.
Prerequisite(s): for undergraduates 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. Enrollment Requirements: for graduate students MATH 160 with a grade of C (2.0) or better.
Prerequisite(s): for undergraduates 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. Enrollment Requirements: for graduate students MATH 350 or MATH 370 with a grade of C (2.0) or better.
Prerequisite(s): for undergraduates MATH 350 or MATH 370 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. Enrollment Requirements: for graduate students MATH 350 or MATH 370 with a grade of C (2.0) or better.
Prerequisite(s): for undergraduates MATH 350 or MATH 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. Enrollment Requirements: for graduate students MATH 378 with a grade of C (2.0) or better.
Prerequisite(s): for undergraduates: 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. Enrollment Requirements: for graduate students MATH 378 with a grade of C (2.0) or better.
Prerequisite(s): for undergraduates 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 . Enrollment Requirements: for graduate students MATH 260 with a grade of C (2.0) or better.
Prerequisite(s): for undergraduates 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 . Enrollment Requirements: for graduate students MATH 260 with a grade of C (2.0) or better.
Prerequisite(s): for undergraduates: 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): for undergraduates and enrollment requirement(s) for graduate students: 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: 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, interpolating polynomials, numerical integration, error analysis, and computational effort of numerical algorithms. Combines theoretical ideas with hands-on laboratory experience.
Prerequisite(s): CS 111 and MATH 162 .
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MATH 465 - Introduction to Numerical Linear Algebra Units: 3
Uses results from linear algebra to derive and analyze numerical methods for the solution of linear equation systems and related problems. Includes algorithms for matrix multiplications, complexity of algorithms, singular value decomposition, triangular systems and the LU decomposition, condition numbers of matrices, the least square problem, and use of software to implement and test matrix algorithms.
Prerequisite(s): CS 111 and either MATH 264 or MATH 374 .
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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. Enrollment Requirements: for graduate students MATH 378 with a grade of C (2.0) or better.
Prerequisite(s): for undergraduates 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. Enrollment Requirements: for graduate students MATH 350 or MATH 370 with a grade of C (2.0) or better.
Prerequisite(s): for undergraduates MATH 350 or MATH 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. Enrollment Requirements: for graduate students MATH 350 or MATH 370 with a grade of C (2.0) or better.
Prerequisite(s): for undergraduates MATH 350 or MATH 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. Cross-listed: MATH 480 and CS 480 are cross-listed. Students may not receive credit for both. Enrollment Requirements: for graduate students MATH 374 with a grade of C (2.0) or better.
Prerequisite(s): for undergraduates MATH 374 with a grade of C (2.0) or better.
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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: 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: 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 Restrictions: 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 Restrictions: Enrollment restricted to students who have obtained consent of instructor. Enrollment Requirements: 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 Restrictions: Enrollment restricted to students who have obtained consent of instructor. Enrollment Requirements: 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 Restrictions: Enrollment restricted to students who have obtained consent of instructor. Enrollment Requirements: 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 Restrictions: Enrollment restricted to students who have obtained consent of instructor. Enrollment Requirements: 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 Restrictions: Enrollment restricted to students who have obtained consent of instructor. Enrollment Requirements: 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 Restrictions: Enrollment restricted to students who have obtained consent of instructor. Enrollment Requirements: 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: At least nine (9) other units of upper-division mathematics.
Prerequisite(s): for undergraduates and enrollment requirement(s) for graduate students: MATH 350 with a grade of C (2.0) or better.
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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(s) for graduate students: MATH 470 with a grade of C (2.0) or better.
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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(s) for graduate students: MATH 430 with a grade of C (2.0) or better.
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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 with a grade of C (2.0) or better.
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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: 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: 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(s) for graduate students: MATH 430 with a grade of C (2.0) or better.
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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(s) for graduate students: MATH 362 , MATH 374 , and MATH 430 with grades of C (2.0) or better.
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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: 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(s) for graduate students: MATH 430 with a grade of C (2.0) or better.
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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(s) for graduate students: MATH 374 with a grade of C (2.0) or better.
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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(s) or graduate students: MATH 374 or MATH 480 or CS 480 with a grade of C (2.0) or better.
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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 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 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 Restrictions: 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 Restrictions: 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 Restrictions: 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 Restrictions: 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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Media Studies |
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MDIA 301 - Media Theory Units: 3
Introduction to the theories of mediated communication, including theories based on normative, critical/cultural, and social scientific approaches. Explores the historical development of the major Western philosophical perspectives regarding the media and their role and impact in society.
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MDIA 303 - Histories of Media Technologies Units: 3
A critical and historical examination of 19th, 20th, and 21st century analog and digital media/communication technologies. Introduces the role of media technology in human creative activity and examines the contexts in which new technologies come into use. Examines economic and political issues that have (and do) influence the selection of some technologies and standards over others. Students may have the opportunity to create media projects applying course concepts.
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MDIA 304 - Global Media Units: 3
An exploration of “globalization” as an historical — as well as a contested — process, and of cultural, social, technological economic, and political processes at work in “media globalization.” Case studies link discussions of specific forms (i.e., music, radio, video, journalism, internet, mobile phones, broadcast satellites, and points of origin) to old and new audiences. These case studies are contextualized in a consideration of specific communication processes associated with trade, war, community development, policy making and reform, and privatization/deregulation.
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MDIA 322 - Media Power Units: 3
Illustrates how media power operates in culture through discourse in local and global contexts. Students examine the power dynamics among producers, subjects and audiences in and around the media: who makes what for whom and how. Readings and discussions will explore power-inflected relations in media, along with discovering possibilities in how to reclaim media power. What happens when historical others make work about themselves, their cultures and communities?
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MDIA 365 - New Media and Everyday Life Units: 3
Explores various new media technologies and the role they play in our everyday lives. Takes a critical media studies approach in surveying the social, cultural, and political issues raised by the deployment and adoption of digital media. Will engage the implications of new media technologies on society and conduct everyday life. May not be taken for credit by students who have received credit for MASS 470-2.
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MDIA 403 - Critical Approaches to Children’s Media Units: 3
Examines the landscape of children’s media from a critical media and cultural studies perspective. Explores the complexities of children’s media through the communication circuit of production, text, and audience. Content introduces students to the major debates surrounding the role of media in the lives of children in the U.S. and around the globe. May not be taken for credit by students who have received credit for MDIA 470 -3. Recommended Preparation: Recommend concurrent enrollment in MDIA 301 .
Prerequisite(s): COMM 360 .
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MDIA 451 - Media, Religion, Popular Culture Units: 3
A study of the theoretical foundations and the process of constructing religiosity and spirituality on electronic media. Explores construction of religiosity in religious media. Examines construction of spirituality in secular media. Investigates the commodification of religiosity and spirituality in popular culture.
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MDIA 452 - Media Ethics Units: 3
Examination of ethical standards and practices of the media. Focuses on the conduct as a future media practitioner and the impact students will have on others in particular and society in general. Includes development of ethical decision-making skills.
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MDIA 460 - Political Economy of the Media Units: 3
Theories and problems concerning systems of support and control of the media, with special reference to the role of special-interest groups and the political state. Emphasis on allocations of spectrum, time, money, energy, materials, and human resources among agencies of media systems. Consideration is given to questions of access to media institutions and the operations of such institutions in light of governmental regulations and policies. Some focus on the significance of the media in conducting foreign affairs, as well as the role of the media in developing nations.
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MDIA 470 - Topics in Media Studies Units: 3
Focuses on a specific aspect of media studies. Topics vary by semester. Students should check the Class Schedule for listing of individual topics. May be repeated for credit as topics change for a total of six (6) units.
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MDIA 495 - Media Studies Internship Units: 3
Provides students with opportunities to connect classroom learning with real-world experience through media-related work activities in private and public enterprises. Students complement classroom and laboratory learning with that of the work world. Internships may be paid or unpaid. Students majoring in MDIA strongly advised to enroll in MDIA 495 (not COMM 495). May be repeated for credit for a total of six (6) units toward the MDIA major in any combination from MDIA 495 and MDIA 499A , MDIA 499B , MDIA 499C . Cross-listed: MDIA 495 and COMM 495 are cross-listed. Students may not receive credit for both. Enrollment Restrictions: Enrollment restricted to Communication or Media Studies majors who have been placed in an internship. Recommended Preparation: COMM 355 or MDIA 301 or MDIA 304 .
Prerequisite(s): COMM 100 .
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MDIA 499A - Independent Study Units: 1
May be used by students who desire to do individualized projects with a professor. May be repeated for a total of six (6) units. MDIA 495 and MDIA 499A, MDIA 499B , MDIA 499C may total no more than six (6) units applied toward the major. Enrollment Restrictions: Enrollment restricted to students who have obtained consent of instructor.
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MDIA 499B - Independent Study Units: 2
May be used by students who desire to do individualized projects with a professor. May be repeated for a total of six (6) units. MDIA 495 and MDIA 499A , MDIA 499B, MDIA 499C may total no more than six (6) units applied toward the major. Enrollment Restrictions: Enrollment restricted to students who have obtained consent of instructor.
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MDIA 499C - Independent Study Units: 3
May be used by students who desire to do individualized projects with a professor. May be repeated for a total of six (6) units. MDIA 495 and MDIA 499A , MDIA 499B , MDIA 499C may total no more than six (6) units applied toward the major. Enrollment Restrictions: Enrollment restricted to students who have obtained consent of instructor.
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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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