# Descriptions of Mathematics

MATH 437 |
Topology |
3.0 EvnSp |

Prerequisites: MATH 220, MATH 330.

Metric spaces, continuous functions, homeomorphisms, separation, and

covering axioms, connectedness. (005563)

MATH 441 |
Math Topics for the Credential |
4.0 Fa/Spr |

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)

MATH 449 |
Modern Algebra |
3.0 Spring |

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)

MATH 450 |
Mathematical Statistics |
3.0 Fall |

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)

MATH 456 |
Applied Statistical Methods II |
3.0 EvnSp |

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)

MATH 458 |
Sampling Methods |
3.0 OddSp |

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)

MATH 460 |
Numerical Analysis |
3.0 Inquire |

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)

MATH 461 |
Numerical Analysis |
3.0 Spring |

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)

MATH 465 |
Introduction to Complex Variables |
3.0 Fall |

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)

MATH 470 |
Differential Forms |
3.0 Inquire |

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)

MATH 472 |
Introduction to Chaotic Dynamical Systems |
3.0 OddFa |

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)

MATH 473 |
Fourier Transforms and the FFT |
3.0 Inquire |

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)

MATH 474 |
Game Theory |
3.0 Inquire |

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)

MATH 475 |
Calculus of Variations |
3.0 EvnFa |

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)

MATH 480 |
Mathematical Modeling |
3.0 Spring |

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)

MATH 495H |
Honors Reading Course |
3.0 Fa/Spr |

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)

MATH 498 |
Advanced Topics in Mathematics |
1.0–3.0 Fa/Spr |

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)

MATH 499H |
Honors Thesis |
3.0 Fa/Spr |

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)

MATH 610 |
Topics in Mathematics for Secondary Teachers:
Analysis |
3.0 Inquire |

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)

MATH 615 |
Statistical Methods for Graduate Research |
3.0 Fall |

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)

MATH 620 |
Topics in Mathematics for Secondary Teachers:
Geometry |
3.0 Inquire |

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)