Natural Science Division

Course Descriptions: Math (MATH)

MATH 99. Intermediate Algebra (4)
A study of the algebraic operations related to polynomial, exponential, logarithmic, rational and radical functions, systems of equations, inequalities, and graphs. Designed for students who have had from one to two years of high school algebra, but who are unprepared for MATH 103/104 (College Algebra/Trigonometry). Grades are A, B, C, NC. The course grade is not calculated into the student’s GPA and does not count toward fulfilling any requirements for a degree, including total units for the degree.

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MATH 103. College Algebra (3)
A study of the real number system, equations and inequalities, polynomial and rational functions, exponential and logarithmic functions, complex numbers, systems of linear and nonlinear equations and inequalities, matrices, and introduction to analytic geometry. The emphasis of this course will be on logical implications and the basic concepts rather than on symbol manipulations. Prerequisite: MATH 99 or appropriate score on math placement exam.

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MATH 104. Trigonometry (2)
Trigonometric functions, functional relations, solution of right and oblique triangles with applications, identities, inverse functions, trigonometric equations, and vectors. Prerequisite: MATH 103 or concurrent enrollment.

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MATH 120. The Nature of Mathematics (3)
An exploration of the vibrant, evolutionary, creative, practical, historical, and artistic nature of mathematics, while focusing on developing reasoning ability and problem-solving skills. Core material includes logic, probability/statistics, and modeling, with additional topics chosen from other areas of modern mathematics. (GE)

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MATH 130. Colloquium in Mathematics (1)
Designed to introduce entering math majors to the rich field of study available in mathematics. Required for all math majors during their first year at Pepperdine. One lecture period per week. Cr/NC grading only.

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MATH 140. Calculus for Business and Economics (3)
Derivatives: definition using limits, interpretations and applications such as optimization. Basic integrals and the fundamental theorem of calculus. Business and economic applications such as marginal cost, revenue and profit, and compound interest are stressed. Prerequisites: Two years of high school algebra and appropriate score on math placement exam, or Math 103. (GE)

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MATH 141. Probability, Linear Systems, and Multivariable Optimization (3)
Functions of several variables, partial derivatives, multivariable optimization, matrices, systems of linear equations, discrete probability theory, conditional probability, Bayes’ Theorem, random variables, expected value, variance, normal distributions. Business and economic applications stressed. Prerequisite: MATH 140 or MATH 150 or equivalent (AP Calculus AB or BC). (GE)

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MATH 150. Calculus I (4)
Limits of functions and their associated geometry, parametric equations, derivatives of algebraic and transcendental functions, and applications of differentiation. The definite integral and basic applications; the fundamental theorem of calculus. Prerequisite: MATH 103 and MATH 104 or equivalent, or appropriate score on math placement exam. (GE)

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MATH 151. Calculus II (4)
Integration techniques, improper integrals; additional applications of integration; an introduction to differential equations; infinite sequences and series; an introduction to vector algebra. Prerequisite: MATH 150 or equivalent (AP Calculus AB) (GE).

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MATH 220. Formal Methods (3)
Formal logic as a tool for mathematical proofs. Propositional calculus: Boolean expressions, logic connectives, axioms, and theorems. Predicate calculus: universal and existential quantification, modeling English propositions. Application to computer program specification, verification, and derivation. Prerequisite: MATH 103 and MATH 104 or equivalent, or appropriate score on math placement exam.

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MATH 221. Discrete Structures (3)
Application of formal methods to discrete analysis, mathematical induction, the correctness of loops, relations and functions, combinatorics, and analysis of algorithms. Application of formal methods to the modeling of discrete structures of computer science–sets, binary trees. Prerequisite: MATH 220.

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MATH 250. Calculus III (4)
Vectors, analytic geometry and calculus of curves and surfaces in three-dimensional space, functions of several variables, partial derivatives, gradient, multiple integration. Vector calculus, including fields, line and surface integrals, Green’s, Stokes’, and Divergence Theorems. Prerequisite: MATH 151 or equivalent (AP Calculus BC) (GE).

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MATH 260. Linear Algebra (4)
Systems of linear equations and linear transformations; matrix determinant, inverse, rank, eigenvalues, eigenvectors, factorizations, diagonalization, singular value decomposition; linear independence, vector spaces and subspaces, bases, dimension; inner products and norms, orthogonal projection, Gram-Schmidt process, least squares; applications; numerical methods, as time allows. Prerequisite: MATH 250 or concurrent enrollment.

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Math 270. Foundations of Elementary Mathematics I (4)
This course is designed primarily for liberal arts majors, who are multiplesubject classroom teacher candidates, to study the mathematics standards for the Commission on Teacher Credentialing. Taught from a problem-solving perspective, the course content includes sets, set operations, basic concepts of functions, number systems, number theory, and measurement. (GE for liberal arts majors.)

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Math 271. Foundations of Elementary Mathematics II (3)
This course includes topics on probability, statistics, geometry, and algebra. The course is part of the liberal arts major in continuing study to meet mathematics standards for the Commission on Teacher Credentialing. (Students who have previous approved math courses or who select the math concentration must check with the liberal arts or math advisor for course credit.)

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MATH 292. Selected Topics (1-4)

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MATH 299. Directed Studies (1-4)
Consent of the divisional chairperson is required.

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MATH 316. Biostatistics (3)
Statistics for the biological sciences. Random sampling; measures of central tendency; dispersion and variability; probability; normal distribution; hypothesis testing (one-sample, two-sample, and paired-sample) and confidence intervals; multi-sample hypotheses and the one- and two-factor analysis of variance; linear and multiple regression and correlation; other chi-square tests; nonparametric statistics. Prerequisite: Prerequisite: MATH 150 or permission of instructor. (GE)

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MATH 317. Statistics and Research Methods Laboratory (1)
A study of the application of statistics and research methods in the areas of biology, sports medicine, and/or nutrition. The course stresses critical thinking ability, analysis of primary research literature, and application of research methodology and statistics through assignments and course projects. Also emphasized are skills in experimental design, data collection, data reduction, and computer-aided statistical analyses. One two-hour session per week. Corequisite: MATH 316 or consent of instructor. (PS, RM)

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MATH 320. Transition to Abstract Mathematics (4)
Bridges the gap between the usual topics in elementary algebra, geometry, and calculus and the more advanced topics in upper division mathematics courses. Basic topics covered include logic, divisibility, the Division Algorithm, sets, an introduction to mathematical proof, mathematical induction and properties of functions. In addition, elementary topics from real analysis will be covered including least upper bounds, the Archimedean property, open and closed sets, the interior, exterior and boundary of sets, and the closure of sets. Prerequisite: MATH 151. (PS, RM, WI)

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MATH 325. Mathematics for Secondary Education. (4)
Covers the development of mathematical topics in the K-12 curriculum from a historical perspective. Begins with ancient history and concludes with the dawn of modern mathematics and the development of calculus. Considers contributions from the Hindu-Arabic, Chinese, Indian, Egyptian, Mayan, Babylonian and Greek people. Topics include number systems, different number bases, the Pythagorean Theorem, algebraic identities, figurate numbers, polygons and polyhedral, geometric constructions, the Division Algorithm, conic sections and number sequences. Course also covers the NCTM standards for K-12 content instruction and how to build mathematical understanding into a K-12 curriculum. Prerequisite: MATH 320 or concurrent enrollment.

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MATH 335. Combinatorics (4)
Topics include basic counting methods and theorems for combinations, selections, arrangements, and permutations, including the Pigeonhole Principle, standard and exponential generating functions, partitions, writing and solving linear, homogeneous and inhomogeneous recurrence relations and the principle of inclusion-exclusion,. In addition, the course will cover basic graph theory, including basic definitions, Eulerian and Hamiltonian circuits and graph coloring theorems. Throughout the course, learning to write clear and concise combinatorial proofs will be stressed. Prerequisite: MATH 151 and MATH 320 or concurrent enrollment in MATH 320 or consent of the instructor.

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MATH 340. Differential Equations (4)
A study of ordinary differential equations, including linear, separable, and exact first-order differential equations; linear second-order and nth-order differential equations; linear and nonlinear systems of equations; Laplace transforms and power series methods; existence and uniqueness properties, growth and decay models, logistic models and population dynamics; Euler’s method, Runge-Kutta methods if time allows. Prerequisite: MATH 260.

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MATH 345. Numerical Methods (4)
Numerical methods and error analysis; methods for finding roots of single-variable functions; interpolation and extrapolation; numerical differentiation and integration; iterative methods for linear and nonlinear systems; approximation of general functions with polynomials or trigonometric functions; methods for initial-value problems for ordinary differential equations; finite difference methods for boundary value problems including ordinary and partial differential equations, as time allows. Prerequisite: MATH 260.

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MATH 350. Mathematical Probability (4)
The theory of probability from counting and from axioms, conditional probability, independence, random variables, important discrete and continuous distributions, properties of expected value and variance, moment generating functions, law of large numbers, and central limit theorem. Other topics may include stochastic processes, random walks, hazard functions, Shannon entropy and information theory, game theory, expected time complexity of algorithms, probabilistic proofs, empirical versus Bayesian interpretations of probability, risk analysis, and applications to genetics, statistics, economics, and queuing theory. Prerequisites: MATH 250 and either MATH 221 or MATH 320.

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MATH 355. Complex Variables (4)
An introduction to the theory and applications of complex numbers and complex-valued functions. Topics include the complex number system, Cauchy-Riemann conditions, analytic functions and their properties, complex integration, Cauchy’s theorem, Laurent series, conformal mapping and the calculus of residues. Prerequisite: MATH 250 and MATH 320 or concurrent enrollment in MATH 320 or consent of the instructor.

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MATH 365. Automata Theory (3)
Theoretical models of computation. Finite automata: regular expressions, Kleene’s theorem, regular and nonregular languages. Pushdown automata: context-free grammars, Chomsky normal form, parsing. Turing machines: the halting problem. NP-complete problems. Prerequisite: MATH 221 or MATH 320.

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MATH 370. Real Analysis I (4)
Rigorous treatment of the foundations of real analysis; metric space topology, including compactness, completeness and connectedness; sequences, limits, and continuity in metric spaces; differentiation, including the main theorems of differential calculus; the Riemann integral and the fundamental theorem of calculus; sequences of functions and uniform convergence. Prerequisites: MATH 250 and MATH 320 or consent of the instructor.

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MATH 380. Algebraic Structures I (4)
The fundamental properties of groups and subgroups; factor groups and homomorphism theorems; direct products and finite abelian groups; permutation groups; rings, domains, and ideals; introduction to quotient rings, polynomial rings and fields. Prerequisites: MATH 260 and MATH 320.

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MATH 440. Partial Differential Equations (4)
A study of partial differential equations including development of the heat, wave and Laplace equations and the associated initial and boundary conditions. Solutions using separation of variables, Fourier series and Fourier transforms; Sturm-Liouville problems; numerical techniques such as finite differences, forward Euler, backward Euler and Crank-Nicholson. Linear and nonlinear discrete and continuous dynamical systems; bifuraction theory. Prerequisite: MATH 340.

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MATH 450. Mathematical Statistics (4)
Sampling, standard error, methods of finding estimates (such as method of moments and maximum likelihood) and analyzing their accuracy through analysis of bias, standard errors and confidence intervals, use of normal, t, chi square, and F distributions, large sampling methods, hypothesis testing, linear least-squares regression and correlation. Common errors and problems in statistical reasoning and experimental design. Other topics may include: bootstrap and jackknife methods of analyzing standard errors, multilinear and non- linear regression, tests for normality, graphical aspects of data presentation, and nonparametric methods. Prerequisite: MATH 350.

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MATH 470. Real Analysis II (4)
Convergence and other properties of series of real-valued functions, including power and Fourier series; differential and integral calculus of several variables, including the implicit and inverse function theorems, Fubini’s theorem, and Stokes’ theorem; Lebesgue measure and integration; special topics (such as Hilbert spaces). Prerequisite: MATH 370.

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MATH 480. Algebraic Structures II (4)
Finite, algebraic, and transcendental field extensions; Galois theory, including normality and separability, counting principles, field automorphisms, and the Galois correspondence. Applications including: solvable and simple groups, Cauchy’s theorem, and Sylow theorems; special topics (such as solution by radicals, insolvability of the quintic, and impossibility of certain ruler-and-compass constructions, advanced linear algebra, Burnsides’s theorem.) Prerequisite: MATH 380.

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MATH 490. Research in Mathematics (1-4)
Research in the field of mathematics. May be taken with the consent of a selected faculty member. The student will be required to submit a written research paper to the faculty member.

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MATH 492. Selected Topics (1-4)

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MATH 499. Directed Studies (1-4)
Consent of the instructor and the divisional chairperson is required.

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Although the above are excerpted from the 2012-2013 Seaver catalog this is not an official binding document. To view the actual catalog visit: http://seaver.pepperdine.edu/academics/catalog/