









Mathematics Course Descriptions


 Math 099: Intermediate Algebra (4)
 (remedial) 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
and Math 104 (College
Algebra/Trigonometry). Grades are A, B, C, NC.
Does not fulfill any requirements for a degree. The
course grade is not calculated into the student's grade
point average and does not count toward fulfilling any
requirements for a degree, including total units for the
degree.
 Math 103: College Algebra (3)
 A study of the real number system, equations and
inequalities, 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. Prerequisites: Math 99 or appropriate
score on math placement exam.
 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.
 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 problemsolving
skills. Core material includes logic, probability/statistics, and
modeling, with additional topics chosen from other areas of modern
mathematics. Prerequisites: two years of high school algebra.
Satisfies general education requirement in
mathematics.
 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.
 Math 140: Calculus for Business (3)
 Derivatives: definition using limits, interpretations
and applications with 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. Satisfies general
education requirement in mathematics. Note that class
meets 4 hours a week.
 Math 141: Probability and Linear Algebra (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 are stressed. Prerequisite: Math 140 or
Math 150 or equivalent (AP Calculus AB or BC). Note
that class meets 4 hours a week.
 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 score on math placement exam. Satisfies general education
requirement in mathematics. Note that 4 hours does not include computer
lab.
 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. Weekly computer lab. Prerequisite:
Math 150 or equivalent (AP Calc. AB). Note that
4 hours does not include computer lab.
 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 program specification, verification, and
derivation.
 Math 221: Discrete Structures (3)
 Application of formal methods to discrete analysis: mathematical
induction, the correctness of loops, relations and functions, combinatorics,
analysis of algorithms. Application of formal methods to the modeling of
discrete structures of computer science: sets, binary trees. Prerequisite:
Math 220. Math 221 is the computer science equivalent
to Math 320.
 Math 250: Calculus III (4)
 Vectors, analytic geometry and calculus of curves and surfaces in threedimensional
space, functions of several variables, partial derivatives, gradient,
multiple integration. Vector calculus, including fields, line and surface integrals,
GreenÕs, StokesÕ, and Divergence Theorems. Weekly computer lab. Prerequisite:
Math 151 or equivalent (AP Calc. BC). Note that
4 hours does not include computer lab.
 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, GramSchmidt
process, least squares; applications; numerical methods, as time allows.
Prerequisite: Math 250 or
concurrent enrollment.
 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
problemsolving perspective, the course content includes sets, set operations,
basic concepts of functions, number systems, number theory, and measurement. Continued in Math 271.
Math 270 satisfies the general education requirement
for teacher education majors only.
 Math 271: Foundations of Elementary Mathematics II
(4)
 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.)
 Math 292: Special topics (14)
 Varies.
 Math 299: Directed Studies (14)
 Varies. Consent of divisional chairperson is required.
 Math 316: Biostatistics (3)
 Statistics for the biological sciences. Random sampling; measures of central
tendency; dispersion and variability; probability; normal distribution; hypothesis
testing (onesample, twosample, and pairedsample) and confidence intervals;
multisample hypotheses and the one and twofactor analysis of variance; linear
and multiple regression and correlation; other chisquare tests; nonparametric
statistics. Prerequisite:
Math 150 or permission of instructor.
 Math 317: Statistical 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 computeraided statistical analyses. One twohour session per week. Corequisite: Math 316 or consent of instructor.
 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.
 Math 325: Math for Secondary Education (4)
 Covers the development of mathematics topics in the K12
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 HinduArabic, Chinese, Indian,
Egyptian, Mayan, Babylonian and Greek people. Topics
include number systems, different number bases, the
Pythagorean theorem, algebraic identities, figurate numbers,
polygons and polyhedra, geometric constructions, the
Division Algorithm, conic sections and number sequences.
Course also covers the NCTM standards for K12 content
instruction and how to build mathematical understanding into
a K12 curriculum. Prerequisite: Math
320 or concurrent enrollment.
 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 solivng
linear, homogeneous and inhomogeneous recurrence relations
and the principle of inclusionexclusion. 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.
 Math 340: Differential Equations (3)
 A study of ordinary differential equations, including
linear, separable, and exact first order differential
equations, linear second order and nthorder
differential equations, linear and nonlinear systems of differential equations, Laplace transforms and power series methods, existence and uniqueness properties, growth and decay models, logistic models and population dynamics, Euler's method, RungeKutta methods if time allows. Prerequisite: Math 260.
 MATH 345: Numerical Methods (4)
 Numerical methods and error analysis; methods for finding roots of singlevariable
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 initialvalue problems for ordinary differential equations; finite difference
methods for boundary value problems including ordinary and partial differential
equations, as time allows. Prerequisite: MATH 260.
 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.
 MATH 355: Complex Variables (4)
 An introduction to the theory and applications of complex numbers
and complexvalued functions. Topics include the complex number system,
CauchyRiemann conditions, analytic functions and their properties, complex
integration, CauchyÕs 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.
 MATH 365: Automata Theory (3)
 Theoretical models of computation. Finite automata: regular expressions,
Kleene's theorem, regular and nonregular languages. Pushdown automata:
contextfree grammars, Chomsky normal form, parsing. Turing machines: the
halting problem. NPcomplete problems. Prerequisite: MATH 221 or MATH 320.
 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.
 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.
 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;
SturmLiouville problems; numerical techniques such as finite differences,
forward Euler, backward Euler and CrankNicholson. Linear and nonlinear
discrete and continuous dynamical systems; bifuraction theory. Prerequisite:
MATH 340.
 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 leastsquares 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
nonlinear regression, tests for normality, graphical aspects of data presentation,
and nonparametric methods. Prerequisite: MATH 350.
 MATH 470: Real Analysis II (4)
 Convergence and other properties of series of realvalued 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.
 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 rulerand
compass constructions, advanced linear algebra, Burnsides's theorem.)
Prerequisite: MATH 380.
 MATH 490. Research in Mathematics (14)

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.
 MATH 492. Selected Topics (14)
 Varies.
 MATH 499. Directed Studies (14)
 Oneonone reading course on topic agreed by student and instructor.
Consent of instructor and divisional chairperson required.





