Descriptions of Mathematics

Prerequisites: MATH 220, MATH 330.
Metric spaces, continuous functions, homeomorphisms, separation, and
covering axioms, connectedness. (005563)

Prerequisites: MATH 342. as a Mathematics Department intern.
Corequisites: Assignment
Supervised internship in teaching mathematics with accompanying
seminar. Guidance in facilitation of mathematical learning. Topics include
contemporary mathematics curriculum topics, mathematical learning
theories, communication, and assessment. 3.0 hours seminar, 3.0 hours
supervision. You may take this course more than once for a maximum of
8.0 units. Credit/no credit grading only. (005546)

Prerequisites: MATH 220, MATH 235, MATH 330.
Introduction to basic algebraic structures such as groups, ring, and fields.
The fundamental concepts of homomorphism, subgroup, normal subgroup
and factor group of a group as well as subring, ideal and factor ring of a
ring; permutation groups and matrix groups. (005582)

Prerequisites: MATH 220, MATH 330, MATH 351.
A rigorous theoretical treatment of the following topics: transformations of
random variables, estimation, Neyman-Pearson hypothesis testing, likelihood
ratio tests, and Bayesian statistics. (005562)

Prerequisites: MATH 315.
Advanced topics in applied statistics including multiple regression,
multivariate methods, nonparametrics, analysis of covariance, bootstrap
methods and others as appropriate. Statistical computer packages are
introduced and used. Appropriate for biology, agriculture, nutrition, business,
psychology, social science and other majors. (005570)

Prerequisites: One course chosen from MATH 105, MATH 305, MATH 350, or
MATH 315.
The theory and application of survey sampling techniques. Topics include
simple random sampling, stratified sampling, systematic sampling, and
cluster sampling. Appropriate for mathematics, computer science, psychology,
social science, agriculture, biology, and other majors. (005573)

Prerequisites: MATH 220, MATH 235, completion of the computer literacy requirement.
Error analysis; numerical solution of algebraic and transcendental equations;
systems of linear and non-linear equations; matrix inversion; matrix
eigenvalues and eigenvectors. (005583)

Prerequisites: MATH 235, MATH 260 (may be taken concurrently), completion of the
computer literacy requirement. MATH 460 is not a prerequisite for MATH 461.
Approximation; numerical integration; numerical solution of ordinary and
partial differential equations; interpolation and extrapolation. (005584)

Prerequisites: MATH 220.
Algebra of Complex Numbers, Cauchy-Riemann Equations, the exponential,
trigonometric, and logarithmic functions, complex integration and
Cauchy integral formula, Taylor and Laurent series, the residue theorem,
conformal mapping, and applications. (005577)

Prerequisites: MATH 220. MATH 260 (or concurrent enrollment) is recommended.
Cartan’s exterior calculus in n-dimensional space. Applications to
Maxwell’s equations, thermodynamics, potential theory, the heat equations,
and flux transport. Suitable for engineering, physics, chemistry and
mathematics majors. (005536)

Prerequisites: MATH 260; MATH 235 and MATH 360 are recommended.
An introduction to the study of non-linear dynamical systems. Both
discrete and continuous systems will be studied using classical analysis
combined with geometric techniques and computer simulation. Areas
of application include fractal geometry, coding theory, fluid turbulence,
population fluctuation, and chaotic vibrations of structures and circuits.
(005588)

Prerequisites: MATH 260.
The Fourier transform and its properties. Inversion, convolution, correlation,
Parseval’s theorem, band-limited functions, sampling theorem, and
uncertainty principles. The discrete Fourier transform using the FFT. Application
to rapid convolution, the estimation of Fourier series coefficients,
power spectra, and frequency response. (005589)

Prerequisites: MATH 260; MATH 235 is recommended.
Introduction to mathematical models of competition, conflict, and decision-
making. Games involving risk and uncertainty will be analyzed using
the Minimax Theorem and linear programming. Multi-state games and
continuous games will be studied using difference equations and differential
forms. (005558)

Prerequisites: MATH 260; MATH 361 is recommended.
Classical problems in the calculus of variations. Euler-Lagrange equations.
Isoperimetric problems, Fermat’s principle. Lagrangian and Hamiltonian
mechanics of particles. Two independent variables. Applications to physics
and engineering. (005590)

Prerequisites: MATH 235, MATH 260.
The translation of real world phenomena into mathematical language.
Possible applications include population and competing species models,
mathematical theories of war, traffic flow, river pollution, water waves and
tidal dynamics, probabilistic and simulation models. (005592)

Prerequisites: Admission to the Department Honors Program, completion of MATH
420 with a grade of B or higher.
Directed reading in an advanced topic under the guidance of an Honors
thesis supervisor. The course exceeds the usual level of difficulty associated
with undergraduate work. It provides the background necessary to
write an Honors thesis. (005595)

Prerequisites: At least one 300- or 400-level mathematics course appropriate to the
subject, faculty permission.
This course is for special topics offered for 1.0-3.0 units. Typically the
topic is offered on a one-time-only basis and may vary from term to term
and be different for different sections. See the Class Schedule for the specific
topic being offered. (005593)

Prerequisites: Completion of MATH 495H with a grade of B or higher, and approval
by the department Honors advisor and thesis supervisor of the proposed thesis topic.
Preparation of written thesis in mathematics under supervision of Honors
thesis advisor. The thesis, based on studies begun in MATH 495H, will require
original work beyond that normally required in undergraduate work.
Completed written thesis must be approved by the thesis supervisor and
Honors advisor. A summary of the thesis will be presented by the student
in public lecture. Successful completion of MATH 495H and MATH 499H
is one of the requirements for being designated as an Honors graduate in
mathematics. (005596)

Prerequisites: Admission to the master’s program in mathematics education or
instructor permission.
Through an array of pedagogical strategies, secondary mathematics teachers
explore analysis topics appropriate for the secondary school curriculum.
These topics and strategies provide a basis for reflective analysis and
deepening knowledge of analysis. You may take this course more than
once for a maximum of 6.0 units. (005599)

Prerequisites: MATH 105, MATH 350, MATH 315, or MATH 305 (only one is
required).
Introduction to common procedures used to analyze data. Single and
two-sample inference, analysis of variance, multiple regression, analysis
of co-variance, experimental design, repeated measures, nonparametric
procedures, and categorical data analysis. Examples will be drawn
from Biology and related disciplines. Statistical computer packages will
be introduced. Appropriate for biology, agriculture, nutrition, psychology,
social science, and other majors. Special fee required; see the Class
Schedule. (005597)

Prerequisites: Admission to the master’s program in mathematics education or
instructor permission.
Through an array of pedagogical strategies, secondary mathematics teachers
explore geometry appropriate for the secondary school curriculum.
These topics and strategies provide a basis for reflective analysis and
deepening knowledge of geometry. You may take this course more than
once for a maximum of 6.0 units. (005602)