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Mathematics Course Descriptions

(MATH) College-Program: 17-10 Check with department for quarter when quarter courses are offered. Read each course description for prerequisites.

106 MATHEMATICS FOR ELEMENTARY TEACHERS I (4 credits). The first of three courses providing the background for teaching contemporary mathematics in the elementary school. The use of mathematics manipulatives for modeling the basic operations will be emphasized. Set theory; numeration; and the systems of whole numbers, integers and rational numbers will be considered. Prerequisite: Elementary education major or consent of instructor.

107 MATHEMATICS FOR ELEMENTARY TEACHERS II (4 credits). One of three courses providing the background for teaching contemporary mathematics in the elementary school. The use of mathematics manipulatives for modeling the basic operations for the rational and real number systems will be emphasized. Ratio and proportion, percentiles, elementary functions and solutions of linear equations will be considered. Prerequisite: MATH 106.

108 GEOMETRY FOR ELEMENTARY TEACHERS (4 credits). Provides background for teaching Geometry in the elementary classroom. Topics to be considered include geometric shapes, measurement, triangle congruence and similarity, coordinate geometry, and transformational geometry. Prerequisite: MATH 106. NOTE: MATH 107 is not a prerequisite.

112 BEGINNING COLLEGE ALGEBRA (4 credits). Algebraic concepts including linear, quadratic, and absolute value equations and inequalities; rational inequalities, complex numbers, graphs of lines, parabolas, and other relations; functions. Prerequisites: Two years of high school algebra and an appropriate score on the Mathematics Placement Test or completion of MATH 080 with a grade of C or better. (Applies to Liberal Education Area II ).

113 COLLEGE ALGEBRA (4 credits). Functions including polynomial, rational, inverse, exponential, and logarithmic functions; systems of equations and inequalities, matrices, sequences and series, binomial theorem, permutations and combinations. Prerequisites: Three years of high school mathematics (including two years of algebra) and an appropriate score on the Mathematics Placement test or successful completion of MATH 112. (Applies to Liberal Education Area II ).

114 MODERN TRIGONOMETRY (4 credits). Trigonometric functions, identities, equations and applications. Prerequisite: MATH 113. (Applies to Liberal Education Area II ).

141 PRE-CALCULUS MATHEMATICS I (5 credits). The first of a two course sequence dealing with algebra, functions (including polynomial, rational, exponential and logarithmic), and discrete algebra topics. A graphics calculator is required. Prerequisites: Three years of high school mathematics (including two years of algebra) and an appropriate score on the Mathematics Placement Test or completion of MATH 112 with a grade of B or better.

142 PRE-CALCULUS MATHEMATICS II (5 credits). The second of a two-course sequence dealing with trigonometric functions, inverse trigonometric functions, identities, applications of trigonometry, parametric equations, systems of linear and non-linear equations, and matrices. A graphics calculator is required. Prerequisites: Successful completion of MATH 141. A half year of trigonometry is strongly recommended.

145, 146 ACCELERATED PRE-CALCULUS MATHEMATICS A,B (5,2 credits). Concurrent enrollment is required for these two courses which are offered fall quarter only. The topics are the same as those listed for MATH 141, 142 and a graphics calculator is required. Prerequisites: Three years of high school mathematics (including two years of high school algebra and a half year of trigonometry) and an appropriate score on the Mathematics Placement Test. NOTE: Not open to students who are concurrently enrolled in or who have successfully completed MATH 113, 114, 141 or 142. (Applies to Liberal Education Area II ).

211 CONCEPTS OF CALCULUS I (4 credits). A broad overview of both differential and integral calculus with less rigor than MATH 241-242. For students majoring in non-mathematically oriented disciplines needing a survey of calculus. Prerequisite: A grade of C or better in MATH 113 or MATH 142 or MATH 145 and 146. (Not open to majors in mathematics, computer science, physics, or chemistry, or students who have successfully completed 241, 242 or equivalent.) (Applies to Liberal Education Area II ).

212 CONCEPTS OF CALCULUS II (4 credits). Applications of differential and integral calculus for students majoring in non-mathematically oriented disciplines. Applications to problems in the areas of business, life, and behavioral sciences. Prerequisites: Successful completion of MATH 211. (Applies to Liberal Education Area II ).

213 CONCEPTS OF CALCULUS III (4 credits). Investigates Taylor series, approximations using Taylor series, indeterminate forms and L'Hospitals Rule; numerical techniques, root approximations, interpolating polynomials, numerical integration; discrete and continuous probability functions, simulation and applications. Prerequisites: Successful completion of MATH 212.

241 CALCULUS I (5 credits). Limits, differentiation and integration of algebraic and trigonometric functions, applications of the derivative, and curve sketching. A graphics calculator is required. An appropriate score on the Mathematics Placement Test or a grade of C or better in MATH 141 and 142, or MATH 145 and 146. (Applies to Liberal Education Area II ).

242 CALCULUS II (5 credits). Differentiation and integration of transcendental functions, techniques of integration, applications of integration. A graphics calculator is required. Prerequisite: Successful completion of MATH 241. (Applies to Liberal Education Area II ).

243 CALCULUS III (5 credits). Parametric equations, polar coordinates, analytic geometry, infinite sequences and series. A graphics calculator is required. Prerequisites: Successful completion of MATH 242. (Applies to Liberal Education Area II ).

244 CALCULUS IV (5 credits). Three dimensional analytic geometry, spherical, and cylindrical coordinate systems, vectors, partial derivatives, and multiple integrals. A graphics calculator is required. Prerequisites: Successful completion of MATH 243. (Applies to Liberal Education Area II ).

245 DIFFERENTIAL EQUATIONS (5 credits). Ordinary differential equations including first order, second order linear, series solutions, Laplace transformations, existence and uniqueness theory, applications. Prerequisite: Successful Completion of MATH 243. (Applies to Liberal Education Area II ).

260 APPLIED STATISTICS I (4 credits). A nontheoretical introduction to statistics with an emphasis on applications in a variety of disciplines. Topics include measures of central tendency, position and dispersion; basic probability; hypothesis testing; estimation; analysis of variance; linear correlation and regression. Prerequisite: MATH 113 or 141, or 145 and 146.

275 APPLIED MATHEMATICS: FOR BUSINESS, ECONOMICS, TECHNOLOGY, LIFE SCIENCES, AND SOCIAL SCIENCES (4 credits). Investigates linear models, matrices, non-linear models, probabilistic models, linear programming, and stochastic processes and their applications. Prerequisites: MATH 113 or MATH 141.

300 MATH MODELS, GAMES AND ACTIVITIES FOR THE PRIMARY GRADES (2 credits). For teachers of grades K-3. Mathematical background including teaching-aids, games, projects and activities that relate to the primary level will be presented. The basic mathematical operations will be presented from a "concrete" standpoint.

301 MATH MODELS, GAMES AND ACTIVITIES FOR THE INTERMEDIATE GRADES (2 credits). For teachers of grades 3-6. Mathematical background including teaching-aids, games, projects and activities that relate to the intermediate level will be presented. The basic mathematical operations will be presented from a "concrete" standpoint.

302 MATH MODELS, GAMES, AND ACTIVITIES FOR THE ELEMENTARY CLASSROOM (4 credits). An intensive introduction to activities, models, projects, and ideas needed to effectively teach using contemporary text materials. Materials usable at every ability level will be included. Prerequisite: Teaching experience or consent of instructor.

304 MATH ACTIVITIES FOR THE JUNIOR HIGH/MIDDLE SCHOOL CLASSROOM (4 credits). Presents and analyzes mathematical activities, models, games, and related background material that can be used to supplement textbook instruction.

306 MATH ACTIVITIES FOR THE SECONDARY CLASSROOM (4 credits). Presents and analyzes mathematical activities, games, models, and related background material that can be used to supplement textbook instruction.

307 NUMBER CONCEPTS FOR ELEMENTARY TEACHERS w (4 credits). Designed to provide the student with a background in special number concepts which are pertinent to elementary school mathematics. Topics include: properties of integers, prime and composite numbers, GCD's, LCM's, the Euclidean Algorithm, Famous Unsolved Problems, and congruences. Prerequisite: MATH 107 or equivalent.

308 MATHEMATICAL FOUNDATIONS FOR ELEMENTARY TEACHERS w (4 credits). Designed to provide the elementary teacher with a background in the foundations of mathematics. Content includes: finite mathematical systems; modular arithmetic; elementary statistics; probability and elementary algebraic structures. Prerequisite: MATH 107 or equivalent.

310 PROBLEM SOLVING AND CALCULATORS IN THE ELEMENTARY CLASSROOM w (4 credits). An analysis of problem solving strategies and the use of calculators in the elementary classroom. Prerequisite: MATH 106 or equivalent.

320 FOUNDATIONS OF MATHEMATICS (4 credits). Symbolic logic, quantifiers, predicate calculus, methods of proof, set theory, relations and functions. Prerequisites: sophomore status and MATH 242, or consent of the instructor.

322 MATHEMATICAL CONCEPTS FOR MIDDLE SCHOOL / JUNIOR HIGH TEACHERS (4 credits). A study of mathematics concepts pertaining to middle school or junior high based on the current Curriculum and Evaluation Standards established by the National Council of Teachers of Mathematics. Prerequisite MATH 320.

326 DISCRETE MATHEMATICS (4 credits). A variety of topics that have applications in mathematical modeling and in computer science. Topics include: graphs, trees, networks, mathematical induction, recurrence relations, and complexity of alogrithms. Prerequisites: MATH 212 or 242.

327 MATHEMATICAL PROBLEM SOLVING (4 credits). Investigation of problems and the process of problem solving across a variety of mathematical areas. Development and application of strategies used to solve problems with emphasis on multistep and nonroutine problems. Application of the process of mathematical modeling to real world problem situations. Prerequisites: MATH 320 or MATH 326.( Prerequisites updated from 96-98 hard copy catalog.)

332, 333 LINEAR ALGEBRA I, II (4,4 credits). Systems of linear equations, matrices and determinants, vector spaces; linear transformations, eigenvalues and eigenvectors, inner product spaces, canonical forms, and applications. Prerequisites: MATH 243 and MATH 320 or 326.

338 MATRIX ALGEBRA (4 credits). Operations with matrices; determinants; systems of equations; orthogonalization, canonical forms. (May not be offered every year.) Prerequisite: MATH 243 and either MATH 320 or 326.

340 INTRODUCTION TO FRACTALS & CHAOS (4 credits). An introduction into the topics of fractal geometry, chaos, and dynamic mathematical systems. Topics included are iteration, fractals and fractal dimension, iterated function systems, Julia set, Mandelbrot set, bifurcation, and chaos. Prerequisites: MATH 243, MATH 320.

347 COMPLEX VARIABLES I w (4 credits). Complex number system, polar form, analytic functions, differentiation and integration, series, and residues. Prerequisites: MATH 244 and 320.

348 COMPLEX VARIABLES II (4 credits). Theory of residues, conformal mapping, Schwarz-Christoffel transformations, and applications. (May not be offered every year.) Prerequisites: MATH 347.

352 ADVANCED EUCLIDEAN GEOMETRY (4 credits). A rigorous examination of secondary school geometry, the interaction of definitions, postulates, and theorems in the study of the structure of geometries. Prerequisite: MATH 320.

361 PROBABILITY THEORY (4 credits). Probability of finite sample spaces; discrete and continuous random variables; Chebyshev's inequality; independence. Prerequisites: MATH 243 and either MATH 320 or 326.

362 MATHEMATICAL STATISTICS (4 credits). Moment generating functions; the Law of Large Numbers; Central Limit Theorems; sampling distributions; estimations of parameters; testing hypotheses. Prerequisite: MATH 361 and MATH 244.

370 MATHEMATICS OF FINANCE (4 credits). A thorough and modern treatment of mathematics of investment, incorporating both theory and applications. Topics to be converted are the measurement of interest; annuities; yield rates; amortization schedules and sinking funds; and bonds and other securities. Prerequisites: MATH 212 or MATH 242.

371 NUMERICAL ANALYSIS I (4 credits). Root finding techniques, fixed point iteration, polynomial interpolation, solution of systems of equations, numerical integration and differentiation. Prerequisites: MATH 243 and programming competency.

372 NUMERICAL ANALYSIS II (4 credits). A continued study of numerical methods, numerical solutions of differential and partial differential equations, eigenvalues and eigenvectors. (May not be offered every year.) Prerequisites: MATH 244 and 371 or consent of instructor.

376 LINEAR PROGRAMMING (4 credits). Mathematical models applicable to linear programming; systems of linear equations and inequalities; graphical methods; the simplex method; game theory. (May not be offered every year.) Prerequisite: MATH 211 or MATH 241. NOTE: Not open to students who have taken CS 330.

381 HISTORY OF MATHEMATICS (3 credits). Historical presentation of the source and growth of mathematical knowledge and principles. (May not be offered every year.) Prerequisite: Junior or senior status and consent of the instructor.

411 ACTUARIAL MATHEMATICS I (2 credits). Investigation of topics from calculus and linear algebra that are covered on the Course 100 examination, as jointly administered by the Society of Actuaries and the Casualty Actuarial Society. Prerequisites: MATH 244, MATH 332 .

412 ACTUARIAL MATHEMATICS II (2 credits). Investigation of topics from probability and statistics that are covered on the Course 110 examination, as jointly administered by the Society of Actuaries and the Casualty Actuarial Society. Prerequisites: MATH 362.

423 Set Theory w (4 credits). Investigation of the various types of sets including: finite and infinite, countable and uncountable, and well-ordered; cardinal numbers; Peano's axioms and Zermelo-Fraenkel's axioms; the Axiom of Choice and Russell's Paradox. Prerequisite: MATH 320.

425 NUMBER THEORY w (4 credits). Elementary properties of integers; prime and composite numbers; the Euclidean Algorithm; congruences; finite algebras; Diophantine equations; quadratic reciprocity; numerical functions. Prerequisite: MATH 320.

431 ABSTRACT ALGEBRA FOR SECONDARY TEACHERS w (4 credits). For secondary school mathematics teachers. Designed to deepen the algebraic background of the student through the study of the real number system, applications of deduction, functional concepts, and other concepts of an algebraic nature. Prerequisite: MATH 320, MATH 332.

434 ABSTRACT ALGEBRA (4 credits). A study of abstract algebraic systems with emphasis on rings, integral domains, and fields. Not open to students who have taken MATH 436. Prerequisite: MATH 320.

435, 436 MODERN ALGEBRA I, II (4,4 credits). Theory of groups, homomorphisms, rings, integral domains and fields, polynomial rings, algebraic field extensions, and other topics in abstract algebra. (May not be offered every year.) Prerequisite: MATH 320, MATH 332.

441, 442 ADVANCED CALCULUS I, II (4,4 credits). Functions, sequences, limits, properties of continuous functions, mean value theorems, the definite integral, improper integrals, infinite series, convergence, power series. (May not be offered every year.) Prerequisites: MATH 244 and 320.

451 GEOMETRY OF CURVES AND SURFACES (4 credits). An introduction to the geometry of hypersurfaces with the goal of introducing the basic notions of differential geometry through examples of curves and surfaces. These include vector fields, orientation, Gauss map, geodesics, curvature, surface area and volume, Stoke's Theorem and the Gauss-Bonnet Theorem. Prerequisites: MATH 244 and MATH 332 or consent of instructor.

475 METHODS OF OPTIMIZATION (4 credits). N-dimensional vector space, convexity, classical methods of optimization of functions of one or more variables, global and local extremes, various search techniques for functions of several variables. (May not be offered every year.) Prerequisites: MATH 332, programming competency, and MATH 244 or consent of instructor.

489 SEMINAR IN MATHEMATICS (1-4 credits). Lecture, group discussion, readings in an area or field of mathematics. Prerequisite: MATH 320 or consent of instructor.