# Course Offerings

## MATHEMATICS (MATH)

- 70. Fundamental Arithmetic
- Fundamental topics in arithmetic, including a preview of algebra. Units awarded for MATH 70 are not applicable to a baccalaureate degree. Graded A, B, C/no credit. (4 units)
- 75. Basic Mathematics
- A course designed for students who score at or in the lowest quartile on the Entry Level Mathematics examination. Units awarded for MATH 75 are not applicable to a baccalaureate degree. Graded credit/no credit.

- Arithmetic of integers, rational numbers and decimals, including the order of operations, percentages, fractions, ratio and proportion, linear equations. (4 units)
- Linear equations and their graphs, systems of linear equations, polynomials, factoring, integer exponents and factoring. (4 units)
- Integer exponents and factoring, systems of linear equations, solving rational equations, quadratic equations, the Pythogorean theorem, the distance formula. (4 units)

- 79. Algebra Workshop
- A laboratory based algebra workshop; to be taken with MATH 80 by students who would otherwise not qualify for admission to that course. Units awarded for MATH 79 are not applicable to a baccalaureate degree. Graded credit/no credit. Prerequisite: consent of instructor. (1 unit)
- 80. Fundamental Algebra (FWS)
- Arithmetic operations, linear and quadratic equations, applications and introduction to graphing. Units awarded for MATH 80 are not applicable to a baccalaureate degree. Graded A, B, C/no credit. (4 units)
- 90. Intermediate Algebra (FWS)
- Linear and quadratic equations and inequalities, algebraic fractions and rational equations, exponents, radicals and radical equations, applications to word problems. Units awarded for MATH 90 are not applicable to a baccalaureate degree. Graded A, B, C/no credit. Prerequisite: passage of the Entry Level Mathematics examination or a satisfactory score on the appropriate placement test. (4 units)

### Lower Division

- 110. College Algebra (FWS)
- Functional notation, graphs and inverses of linear, polynomial, and rational functions, rational exponents, arithmetic and geometric progressions, logarithmic and exponential functions, systems of linear equations. Graded A,B,C/no credit. Prerequisite: passing score on the Entry Level Mathematics examination or passage of MATH 90. (GE=B1) (4 units)
- 115. The Ideas of Mathematics (FWS)
- Sets and their applications to topics in discrete mathematics that will include enumeration techniques and finite probability spaces. Graded A, B, C/no credit. Prerequisite: passing score on the Entry Level Mathematics examination or passage of MATH 90. (GE=B1) (4 units)
- 120. Pre-Calculus Mathematics (FWS)
- Trigonometric functions, trigonometric identities, right angle trigonometry, complex numbers, conic sections, binomial theorem, induction. Graded A, B, C/no credit. Prerequisite: satisfactory score on the Entry Level Mathematics examination or passage of MATH 110. (GE=B1) (4 units)
- 180. Critical Thinking Through Applications of Mathematical Logic (FWS)
- Analysis of logical implication, logical equivalence and valid argument using symbolic logic. Applications drawn from a wide variety of practical examples. Emphasis on problem solving techniques. (GE=A4) (4 units)
- 192. Methods of Calculus (FWS)
- A short course in calculus with emphasis on applications. Prerequisite: satisfactory score on the Entry Level Mathematics examination, or passage of MATH 110. This course does not substitute for any course in the calculus sequence MATH 211, 212, 213, 251, 252 required for majors in chemistry, computer science, mathematics or physics. (GE=B1) (4 units)
- 199. Technology in Math Education through Problem Solving (WS)
- Exploration of central ideas in secondary school mathematics through problem solving using technology. Introduction to the use of three types of software: dynamic geometry, spreadsheet, and computer algebra systems. Materials fee required. Prerequisite: MATH 120 or equivalent (3 units)
- 211. Basic Concepts of Calculus (FWS)
- An introduction to limits and continuity, differentiation of functions in one variable (including trigonometric functions) and antiderivatives with applications. Prerequisite: satisfactory score on the Entry Level Mathematics examination or passage of MATH 120. (GE=B1) (4 units)
- 212. Calculus II (FWS)
- Techniques and applications of integration, differentiation and integration of transcendental functions. Prerequisite: MATH 211 with a grade of "C" or better. (4 units)
- 213. Calculus III (FWS)
- Sequences and series, numerical techniques, polar coordinates, parametric equations. Prerequisite: MATH 212 with a grade of "C" or better. (4 units)
- 229. Geometry in Two and Three Dimensions (S)
- Axiomatic foundations of Euclidean geometry and their relation to absolute, affine, and ordered geometry. Isometry and similarity in the Euclidean plane and three-space. Inversive transformations and construction of the real projective plane. Formerly MATH 129. Prerequisites: completion of the general education requirement in mathematics. (4 units)
- 241. Problem Solving in Calculus (FWS)
- An approach to solving calculus-based problems incorporating a computer algebra system. Projects will include interpolation, numerical methods, differential equations and graphical approaches. One hour lecture and three hours laboratory. Prerequisites: some programming experience and MATH 212. Recommended: MATH 213. (2 units)
- 251. Multivariable Calculus I (FWS)
- Vectors and vector geometry in two and three dimensions. Elementary linear algebra. Multivariable functions. Parametrization of space curves. Prerequisite: MATH 212 with a grade of "C" or better. (4 units)
- 252. Multivariable Calculus II (FWS)
- Differentiation and integration of vector functions with applications, multiple integration, line and surface integrals. Partial and directional derivatives. Theorems of Green and Stokes. Prerequisites: MATH 251, and 213 with a grade of "C" or better. (4 units)
- 262. Applied Statistics (FWS)
- Basic concepts of probability and statistics. Important probability models such as the binomial, Poisson and normal. Statistical procedures, particularly in relation to estimation, hypothesis testing and modeling. Computer simulations and computations. May not be taken for credit by students who have received credit for MATH 305. Prerequisite: MATH 120. Prerequisite or corequisite: MATH 211. (4 units)
- 270. Elementary Differential Equations (FS)
- First order equations, second order linear equations, linear equations with constant coefficients, variation of parameters, applications. Prerequisite: MATH 252. (4 units)
- 272. Discrete Mathematics (FWS)
- Boolean algebra. Computer arithmetic including hexadecimal, octal and binary numeration. Relations and functions. Vectors and matrices. Introduction to graph theory. Prerequisite: completion of the general education requirement in mathematics. (4 units)

### Upper Division

- 301. Fundamental Concepts of Mathematics for Educators (FWS)
- A mathematics sequence for future teachers, containing fundamental concepts of number sense, algebra, and geometry. May not be counted toward fulfilling requirements in the mathematics major.
- Fundamental Concepts of Arithmetic and Geometry. Mathematical reasoning behind the structure and arithmetic of real numbers. Connections between numbers and geometry. Introduction to functions and graphs as a natural extension of arithmetic. May not be taken for credit by students who have completed MATH 301. Prerequisites: completion of MATH 115 and the general education requirements in written communication, oral communication and critical thinking. Graded ABC/no credit. (4 units)
- Transition from Concrete to Abstract in Algebra and Geometry. Algebra in context, algebraic techniques, proportion. Linear functions and their graphs. Angle, shape, size, polygons, and circles. Congruence and similarity. Graded ABC/no credit. Prerequisites: completion of MATH 301A (or 301), with a course grade of at least "C." (4 units)
- Further Developments in Algebra and Geometry. The arithmetic and graphs of polynomial and rational functions. Scientific notation, logarithmic and exponential functions. Polygons, tessellations, and transformations. Polyhedra, spheres, cylinders, cones. Transformations in graphs. Graded ABC/no credit. Prerequisite: completion of MATH 301B with a course grade of at least "C." (4 units)
- 302. Problem Solving in Mathematics (FWS)
- Use of heuristic techniques, such as analogy and induction, in problem solving. Elementary and recreational problems selected from algebra, logic, number theory, combinatorics and probability. May not be counted toward fulfilling requirements in the mathematics major. Prerequisites: completion of the general education requirements in mathematics, written communication, oral communication and critical thinking. (4 units)
- 303. Geometry in Two and Three Dimensions for Teachers
- Geometric figures, constructions and transformations in two and three dimensions. Development of axiomatic geometry and subsequent study of axiomatic systems from a historical perspective; students create proofs in solving geometry problems. Algebraic approach contrasted with Euclidean. Includes hands-on activities, emphasizes connection to disciplines such as art and geography. Teaching methods, integrated throughout, stress transition from concrete to abstract, use of geometric construction tools including computers where appropriate, visualization of transformations and their application in problem solving as well as assessment of student work. (6 units)
- 304. Algebra for Teachers
- Polynomials and rational functions, analogy between arithmetic and algebra. Linear, quadratic, and rational equations and inequalities and their graphs; rational exponents, geometric series, exponential functions and their graphs. Algebra presented more as a way of thinking than as a collection of algorithms. Emphasis on solution of verbally stated problems. Teaching methods, integrated throughout, focus on transition from concrete to abstract, pattern recognition and discovery, appropriate use of calculators and computers, and assessment of student work. Prerequisite: B.A. or B.S. degree from an accredited institution. (6 units)
- 305. Statistics: Hypothesis Testing and Estimation (FWS)
- After a brief introduction to descriptive statistics, course will emphasize hypothesis testing and estimation, using packaged computer programs. May not be taken for credit by students who have received credit for MATH 262. Prerequisite: completion of the general education requirement in mathematics or equivalent preparation. (4 units)
- 306. Mathematics, the Language of Science
- Introduction to basic calculus with emphasis on its role in the development of the life and physical sciences. Applications include rates of change, growth and velocity. Prerequisites: MATH 120 and at least one four unit college level course in both physics and biology. (4 units)
- 307. Mathematics in Science
- Differential equations applied to scientific questions of motion, growth and decay, and populations, including an overview of statistics and data analysis. Prerequisite: a minimum of one quarter of calculus (MATH 192, 211, 306 or equivalent). (4 units)
- 308. Problem Solving Through Theory and Practice (FWS)
- Heuristic techniques in solving contextual problems from algebra, number theory, geometry, logic, probability and statistics. May not be counted toward fulfilling requirements in the mathematics major. May not be taken for credit by students who have completed MATH 302. Two hours seminar. Prerequisite: MATH 301C with a grade of at least "C" or consent of instructor. (2 units)
- 320. Mathematical Interest Theory (S)
- Development of the mathematical theory of interest in both finite and continuous time, including the accumulation function and special cases of simple and compound interest, valuation of the discrete and continuous streams of payments, and nominal and effective interest and discount rates. Application of the theory, with computer applications, to actuarial science, including amortization of lump sums, fixed income securities, and depreciation. Three hours lecture and two hours laboratory. Prerequisites: MATH 213 and 241. (4 units)
- 329. Transformation Geometry (FWS)
- Development of Euclidean plane geometry in terms of congruence and similarity transformations. Classification of affine transformations with applications to classical theorems. Introduction to inversive transformations and related constructions. Prerequisites: MATH 251 and high school geometry or equivalent. (4 units)
- 331. Linear Algebra (FWS)
- Vector spaces over a field, linear dependence, dimension; matrices and systems of linear equations; the theory of linear transformations; characteristic values and vectors; applications. Prerequisite: MATH 251 or consent of instructor. (4 units)
- 345. Number Theory and Proof (FWS)
- Introduction to ideas and techniques of proof and historical topics in classical number theory. Theory of divisibility, primes and linear congruences. Theorems of Fermat, Euler and Wilson. Primitive roots and indices. Number theoretic functions. Prerequisite: MATH 213. (4 units)
- 355. Analysis and Proof (FWS)
- Introduction to ideas and techniques of proof with an emphasis on analysis. Topics chosen from: logic, set theory, functions, cardinality and analysis. Prerequisite: MATH 213. (4 units)
- 372. Combinatorics (FWS)
- Permutations and combinations, recurrence relations with applications and topics in graph theory. Prerequisite: MATH 213; or MATH 211, 262 and 272. (4 units)
- 395. Directed Study
- Reading and library research in mathematics conducted under the direction of a faculty member. A total of four units may apply toward the major. Prerequisites: consent of instructor and departmental approval of a written proposal of a project submitted on a standard application filed in advance of the quarter in which the course is to be taken. (1-4 units)
- 399. Service Learning Experience in Mathematics (FW)
- Supervised learning experience in the secondary mathematics classroom. Observation and participation that provides future teachers with first-hand experience and the opportunity to link their undergraduate mathematics course work with classroom experience. Includes weekly meetings on campus (one hour per week) and observation in a secondary classroom (20 hours). Graded A, B, C/no credit. Prerequisite: MATH 329. (2 units)
- 411. Introduction to Mathematical Logic
- Propositional and quantificational logic, completeness and consistency results, formal systems, Peano arithmetic, recursive functions, Godel's incompleteness theorem. Prerequisite: MATH 345. (4 units)
- 455. Fourier Analysis
- Fourier series and the Fourier transform. Convergence properties and orthogonality. Applications to differential equations. Prerequisites: MATH 270 and 355. (4 units)
- 465. Probability Theory (FWS)
- Probability spaces, independence, conditional probability, densities, mass and distribution functions, moments, joint and marginal distributions, moment generating functions, Chebychev's inequality, law of large numbers and other topics. Prerequisites: MATH 252 and 372. (4 units)
- 470. Ordinary Differential Equations (W)
- Topics from among: first order equations, linear equations, systems of equations, iterative methods, series solutions, Laplace transformations, applications. Prerequisites: MATH 270 and 331. (4 units)
- 474. Numerical Methods
- Introduction to numerical methods for finding solutions of non-linear equations, systems of linear equations and ordinary differential equations. Discussion of errors and numerical instabilities; numerical differentiation; numerical integration. Prerequisites: CSE 201 and MATH 331. (4 units)
- 480. Topics in History of Mathematics (FWS)
- Exploration of the historical and topical development of interconnected areas of mathematics, such as algebra, geometry and analysis. Discussion of the influence of culture and society on the development of mathematical ideas and discovery will be included. Prerequisites: MATH 252, 329, 345 and 355. (4 units)
- 499. Mathematics in the Secondary Classroom (WS)
- Instruction in the methods and materials for teaching mathematics in the secondary classroom, with emphasis on algebra and geometry. Each student will complete and present a project relating advanced mathematics to the high school curriculum that implements ideas and strategies presented in this course. May not be counted toward fulfilling requirements of the B.A. (Non-Teaching Track), B.S., M.A. or M.A. in Teaching, Mathematics. Prerequisites: MATH 329, 331 and 399. (4 units)
- 510. Topics in Mathematics
- Study of selected areas of advanced mathematics. May be repeated for credit with consent of instructor as topics change. Prerequisite: senior or graduate standing. (4 units)
- 529. Advanced Geometry (FWS)
- Topics in affine and projective geometry with applications to Euclidean 2 and 3 space and to modern algebra. Prerequisites: MATH 329, 331 and 345. (4 units)
- 531. Advanced Linear Algebra
- Inner product spaces; duality of vector spaces; canonical forms; spectral theory; quadratic forms. Formerly a topic under MATH 510. Prerequisite: MATH 331. (4 units)
- 545. Abstract Algebra I (FWS)
- An introduction to algebraic structures, including groups, rings and fields. Prerequisites: MATH 331, 345 and 355. (4 units)
- 546. Abstract Algebra II (S)
- Continuation of MATH 545. Prerequisite: MATH 545. (4 units)
- 553. Analysis I (FWS)
- Continuous and differentiable functions, infinite series. Uniform convergence, computation with series, functions represented by integrals, theory of integration. Prerequisites: MATH 252 and 355. (4 units)
- 554. Analysis II (S)
- Continuation of MATH 553. Prerequisite: MATH 553. (4 units)
- 555. Introduction to Point-Set Topology
- Topics to include topological and metric spaces, compactness, product spaces, connectedness, separation properties. Prerequisite: MATH 355. (4 units)
- 557. Complex Variables
- Analytic and harmonic functions, power series, Cauchy's Theorem and Cauchy's Formula. Prerequisites: MATH 252 and 355. (4 units)
- 565. Mathematical Statistics
- Likelihood ratio, estimators, distributions of estimators, theory of hypothesis testing, linear statistical models. Prerequisite: MATH 465. (4 units)
- 570. Partial Differential Equations
- Classification of partial differential equations; heat equation, Laplace's equation, boundary value-problems; separation of variables. Applications of Fourier and Laplace transforms, numerical methods. Prerequisites: MATH 270 and 355. MATH 241 recommended. (4 units)
- 576. Introduction to Mathematical Models
- Topics from linear and probabilistic models, computer simulation, difference and differential equation models. Prerequisites: CSE 201, MATH 331 and 465. (4 units)
- 595. Independent Study
- An independent study course for senior mathematics majors. A total of four units may apply toward the major. Prerequisites: MATH 331 and 553, a minimum overall grade point average of 3.0, consent of instructor and departmental approval of a written proposal of a project submitted in advance of the quarter in which the course is to be taken. (1-4 units)
- 599. Senior Seminar for Future Mathematics Educators (FS)
- Summative assessment of subject matter competence for prospective mathematics teachers. Each student will complete and present a project relating advanced mathematics to the high school curriculum, and complete and submit a portfolio of their undergraduate work in mathematics for assessment. Meets four hours per week during the first week and the last four weeks of the quarter. Graded A,B,C/no credit. Prerequisites: MATH 199, 480 and 499. (2 units)

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