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Mathematics Course Descriptions
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- Math 099: Intermediate Algebra (4)
- (remedial) A study of the algebraic operations, polynomials, and
other functions,, first- and second-degree 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) or for Math 214
(Calculus for business). 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 102: The Nature of Mathematics (3)
- The underlying theme is that mathematics is a vibrant,
evolutionary discipline. This evoluationary nature will be observed
in detail in the development of the natural and real number systems,
Euclidean and non-Euclidean geometries, and probability and
statistics. Prerequisites: two years of high school algebra.
Satisfies general education requirement in
mathematics.
- Math 103: College Algebra (3)
- A study of the real number system, equations and inequalities, exponential
and logarithmic functions, complex numbers, matrices, and discrete algebra.
The emphasis of this course will be on logical implications and the basic
concepts rather than on symbol manipulations. Prerequisites: two years of
high school algebra and appropriate SAT or ACT math score.
- Math 104: Trigonometry (2)
- Trigonometric functions, functional relations, solution of right and
oblique triangles with applications, identities, inverse functions, equations,
and vectors. Prerequisite: Math 103 or concurrent
enrollment or appropriate score on college algebra placement exam.
- Math 110: 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 210: Calculus I (4)
- Differential and integral calculus of certain elementary functions with
associated function theory. Functions, parametric curves, and associated
analytic geometry. Fundamental Theorem of Calculus. Applications of
differentiation and integration.
Weekly computer lab. Prerequisite: Math 104
or equivalent (SAT Math of 600 or higher). Satisfies general education
requirement in mathematics. Note that 4 hours does not include computer
lab.
- Math 211: Calculus II (4)
- Methods of integration, infinite series, polar coordinates, parametric
equations, and applications. Weekly computer lab. Prerequisite:
Math 210 or equivalent (AP Calc. AB). Note that
4 hours does not include computer lab.
- Math 212: Calculus III (4)
- Vectors, solid analytic geometry, partial derivatives, and multiple
integration. Vector fields, gradient, divergence, curl, Green's theorem,
Divergence Theorem, Stokes' theorem. Weekly computer lab. Prerequisite:
Math 211 or equivalent (AP Calc. BC). Note that
4 hours does not include computer lab.
- Math 214: Calculus for Business (3)
- Study of functions (linear, exponential, polynomial, logarithmic),
limits, derivatives, and integrals. Optimization and other applications
of derivatives. Fundamental theorem of calculus. Business and economics
applilcations stressed. Prerequisite: two years of high school algebra
and appropriate score on math placement exam, or Math
099. Satisfies general education requirement in mathematics. Note
that class meets 4 hours a week.
- Math 215: Probability and Linear Algebra (3)
- A study of matrices, systems of linear equations, discrete probability
theory, partial derivatives and functions of several variables. Optimization
for functions of several variables. Business and economics applications
are stressed. Prerequisite: Math 214 or
Math 210 or equivalent (AP Calculus AB or BC). Note
that class meets 4 hours a week.
- 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. Applicatoin 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 360.
- Math 270: Foundations of Elementary Mathematics I
(4)
- Designed for elementary school teachers. Taught from a problem-solving
perspective, the course content for the first semester 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)
- Designed for elementary school teachers. Continuation of
Math 270. Taught from a problem-solving perspective,
the course content for the second semester is probability, statistics,
geometry, and algebra.
- Math 292: Special topics (1-4)
- Varies.
- Math 299: Special topics (1-4)
- Varies. Consent of divisional chairperson is required.
- Math 316: Statistical Research Methods (3)
- The role of statistics in scientific research. Descriptive statistics
for univariate and joint distributions; correlation and regression.
Statistical inference: sampling distributions, t test, and analysis of
variance. Computer analysis of data. Three hours of lecture and two hours
of discipline-specific laboratory per week. Prerequisite:
Math 103.
- Math 317: Statistical Research Methods Laboratory
(1)
- Discipline-specific laboratory for Math 316.
- Math 330: Linear Algebra (4)
- Systems of linear equations, matrices, determinants, rank, eigenvalues,
eigenvectors, linear independence, vector spaces and subspaces, bases,
dimensions, inner products, norms, linear transformations, applications to
geometry. Suggested prerequisite: Math 212 or
concurrent enrollment.
- Math 340: Differential Equations (3)
- A study of ordinary differential equations, including separable, exact,
and linear first order differential equations, linear second order
constant coefficient and n-th order constant coefficient differential
equations. Systems of equations, Power series and Laplace transform methods.
Also introduces nonlinear differential equations and partial differential
equations. Prerequisite: Math 212 or concurrent
enrollment.
- Math 360: Transition to Abstract Mathematics (4)
- Proof-writing, the logical structure of theorems, predicate calculus,
problem-solving, mathematical induction, set theory, function theory,
foundations of the number system. Topics may include some group theory or
analysis. Prerequisite: Math 211 or
Math 214.
- Math 420: Foundations of mathematics (4)
- The nature of mathematical thought, essentials of logical reasoning,
postulational concepts and methods, Euclidean and non-Euclidean geometries,
elementary number-theoretic concepts are studied. All of these topics are
taught from a historical perspective. Prerequisite: Math
212.
- Math 430: Algebraic structures I (4)
- The fundamental properties of groups and subgroups, homomorphisms
and isomorphisms. Examples such as permutation groups and geometric
groups. Normal subgroups and classification of finitely-generated
abelian groups. Applications to number theory. Ring theory, ideals,
ring homomorphisms, polynomial rings, unique factorization, principal ideal
domains. Fields, including field extensions, finite fields, and vector
spaces. Prerequisites: Math 330,
and either Math 360 or Math
221.
- Math 431: Algebraic structures II (4)
- More in-depth study of groups and classification issues. Field
extensions, algebraic closure, algebraic and transcendental extensions,
Galois theory. Advanced linear algebra (Jordan canonical form, diagonalization
of symmetric operators). Prerequisite: Math 430.
- Math 460: 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 360.
- Math 510: Probability (4)
- Studies the theory of probability, conditional probability,
random variables, discrete and continuous distributions,
expectation value and variance, covariance, moment generating functions,
and applications. Law of large numbers and Central limit theorems.
Prerequisites: Math 212 and either
Math 360 or Math 221.
- Math 511: Statistics (4)
- Sampling, analysis of variance, point and interval estimation,
large sampling methods, parametric and nonparametric hypothesis testing,
regression and correlation. Prerequisite: Math 510.
- Math 530: Real analysis (4)
- A study of properties of real numbers and functions of a real variable,
metric spaces (completeness, compactness, connectedness), spaces of continuous
functions, convergence in function spaces, Riemann and other types of
integration. Prerequisites: Math 212 and either
Math 360 or Math 221.
- Math 531: Complex analysis (4)
- Analytic functions and the theory of power series, contour integration
and Cauchy's integral formula, conformal mapping and fractional linear
transformations, the maximum principle, and the calculus of
residues. Prerequisite: Math 530.
- Math 540: Applied mathematics (4)
- A study of chaotic dynamical systems as exhibited in nonlinear iterative
systems and nonlinear ordinary differential equations. Includes coverage
of fixed and periodic points, period doubling and bifurcation, attractors,
transitivity, conjugacy, sensitivity, almost linearity, capacity and
Lyapunov dimensions, and fractals. Case studies focus on the Henon and
horseshoe maps, Julia and Mandelbrot sets, and the Lorenz system.
Sarkovsky's theorem. Prerequisite: Math 330.
- Math 590: 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.
- Math 592: Selected Topics (1-4)
- Varies.
- Math 599: Directed Studies (1-4)
- One-on-one reading course on topic agreed by student and instructor.
Consent of instructor and divisional chairperson required.
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