Professors Broughton, Bryan, Carlson, Evans, Finn, Graves,
Grimaldi, Holden, Inlow, Langley, Lautzenheiser, Leader,
Leise, Lopez, Muir, Rader, Rickert, Sherman, and Shibberu.
MA 101 Introductory Calculus 5R-0L-2C F (5 weeks)
Covers approximately the first half of MA 111, including
analytic geometry in the plane, vectors in the plane,
algebraic and transcendental functions, limits and
continuity, and an introduction to differentiation. Entering
first-year students will enroll in MA 111 and transfer to MA
101 if continuation of MA 111 is not appropriate.
MA 102 Differential Calculus 5R-0L-3C W Pre: MA 101
Covers approximately the second half of MA 111, including
continuity, the derivative, geometrical and physical
applications of differentiation, and an introduction to
integration and Fundamental Theorem of Calculus. Students
who do not transfer to MA 101 in the fall quarter, but do
not satisfactorily complete all of MA 111, may use their
midterm grade in MA 111 for credit and grade in MA 101 and
enter MA 102 at the beginning of the winter quarter.
MA 111 Calculus I 5R-0L-5C F
Calculus and analytic geometry in the plane, including
vectors. Algebraic and transcendental functions.
Differentiation, geometric and physical interpretations of
the derivative. Introduction to integration and the
Fundamental Theorem of Calculus.
MA 112 Calculus II 5R-0L-5C F, W, S Pre: MA 111 or 102
Techniques of integration, numerical integration,
applications of integration. Taylor polynomials and Newton’s
method. First order differential equations, applications of
first order differential equations.
MA 113 Calculus III 5R-0L-5C F, W, S Pre: MA 112
Functions of several variables, partial derivatives, maxima
and minima of functions of several variables, multiple
integrals, and other coordinate systems. Applications of
partial derivatives and multiple integrals. Vectors and
parametric equations in three dimensions, line integrals.
MA 215 Discrete and Combinatorial Algebra I 4R-0L-4C F
An introduction to enumeration and discrete structures.
Elementary mathematical logic. Permutations, combinations
and related concepts. Set theory, relations and functions on
finite state machines. Mathematical induction.
MA 221 Differential Equations and Matrix Algebra I 4R-0L-4C
F, W, S Pre: MA 113
Basic matrix algebra with emphasis on understanding systems
of linear equations from algebraic and geometric viewpoints,
including the least squares process and eigenvalues and
eigenvectors. Review of first order differential equations
including basic solution techniques and numerical methods.
Second order linear, constant coefficient differential
equations, including both the homogeneous and
non-homogeneous cases. Introduction to complex arithmetic,
as needed. Applications to problems in science and
engineering.
MA 222 Differential Equations and Matrix Algebra II 4R-0L-4C
F, W, S Pre: MA 221
Laplace transforms. Solving systems of first order linear
differential equations by Laplace transforms and
investigation of their solution structure determined by
eigensystems. Phase portrait analysis and classification and
stability of critical points for linear and non-linear
systems. Approximation of functions including Taylor series
and Fourier series. Applications to problems in science and
engineering.
MA 223 Engineering Statistics I 4R-0L-4C F, W, S Pre: MA 112
This is an introductory course in statistical data analysis.
Topics covered include descriptive statistics, introduction
to simple probability concepts, and random variables
(including their linear combinations and expectations). The
Central Limit Theorem will be presented. Hypothesis testing
and confidence intervals for one mean, one proportion, and
one standard deviation/variance will be covered as well as
hypothesis testing and confidence intervals for the
difference of two means. An introduction to one factor
analysis of variance and simple linear regression will be
presented. A computer package will be used for statistical
analysis and simulation. Experimental data from a variety of
fields of interest to the science and engineering majors
enrolled will also be used to illustrate statistical
concepts and facilitate the development of the student’s
statistical thinking.
MA 302 Boundary Value Problems 4R-0L-4C S Pre: MA 222
Boundary value problems posed by partial differential
equations. Extensions to three-dimensional problems,
irregular regions, and non-rectangular coordinate systems.
Integral transforms, Fourier series, numerical techniques.
MA 305 Advanced Calculus 4R-0L-4C F Pre: MA 113
Calculus of functions of several variables. Topics include
differentiation (divergence, gradient, curl) and integration
(line and surface integrals). Green’s theorem, Stokes’s
theorem, and the divergence theorem are also covered.
MA 306 Functions of a Real Variable 4R-0L-4C W Pre: MA 113
Calculus of functions of a single variable. A more careful
development of the basic concepts of analysis, including
sequences, limits, continuity, differentiability,
integration, infinite series, power series, Taylor’s Theorem,
and uniform convergence.
MA 307 Introduction to Topology 4R-0L-4C F Pre: MA 222 or
consent of instructor
An introduction to some of the important ideas, problems,
and applications of topology from an intuitive point of
view. Topics may include, but are not restricted to, classification
of surfaces, orientability, the Euler Characteristic,
patterns and complexes, coloring theorems, graph embeddings,
vector fields, and the fundamental group. Intended for
non-majors as well as mathematics majors.
MA 310 Functions of a Complex Variable 4R-0L-4C S Pre: MA
113
Elementary properties of analytic functions including
Cauchy’s theorem and its consequences, Laurent series, the
Residue Theorem, and mapping properties of analytic
functions.
MA 315 Discrete and Combinatorial Algebra II 4R-0L-4C W Pre:
MA 215
A continuation of MA 215. More advanced enumeration
techniques including recurrence relations, generating
functions and the principle of inclusion and exclusion.
Boolean functions with application to circuit design. An
introduction to group theory and its application to error
correcting codes.
MA 323 Geometric Modeling 4R-0L-4C W Pre: MA113
Covers some of the mathematical methods for describing
physical or virtual objects in computer aided geometric
design (CAGD) and computer graphics. Emphasizes methods for
curve and surface modeling, and discusses both the
underlying geometric concepts and the practical aspects of
constructing geometric models of objects. Topics covered
include Bezier curves, Hermite curves, B-splines, Bezier
patches, subdivision surfaces. In discussing these, ideas
from analytic geometry, differential geometry, affine
geometry, combinatorial geometry, and projective geometry
will be introduced.
MA 325 Fractals and Chaotic Dynamical Systems 4R-0L-4C S
Pre: CS 220 and MA 222
Emphasis on the mathematical and computer graphics
foundations behind fractal images and the relationship
between chaotic dynamics and fractal geometry. Self-similar
fractals, random fractals with Brownian motion, and fractals
generated from dynamical systems. Fractal dimensions.
Iterated function systems. Chaos in one-dimensional maps.
Controlling chaos. Mandelbrot and Julia sets. Computer
graphics.
MA 331 Mathematical Modeling 4R-0L-4C W Pre: MA 221 or
consent of instructor
An introduction to techniques of mathematical modeling
involved in the analysis of meaningful and practical
problems arising in many disciplines including mathematical
sciences, operations research, engineering, and the
management and life sciences. Topics include creative and
empirical model construction, model fitting, models requiring
optimization, and modeling dynamic behavior. Student
participation in significant individual and group projects
will be emphasized.
MA 348 Continuous Optimization 4R-0L-4C S (2004) Pre: MA 222
Optimization of nonlinear functions of real variables:
algorithms for univariate optimization; Golden section,
parabolic interpolation, hybrid methods; Newton’s Method and
variations for multivariate functions; conjugate gradients
and quasi-Newton methods; line search strategies; penalty
functions for constrained optimization; modeling and
applications of optimization.
MA 351-6 Problem Solving Seminar 1R-0L-1C F, W, S Pre:
Consent of department head
An exposure to mathematical problems varying widely in both
difficulty and content. Students will be expected to
participate actively, not only in the solution process
itself but also in the presentation of finished work, both
orally and in writing. A student may earn a maximum of six
credits in MA 351-6.
MA 371 Linear Algebra I 4R-0L-4C F, S Pre: MA 221 or consent
of instructor
Systems of linear equations, Gaussian elimination, and the
LU decomposition of a matrix. Projections, least squares
approximations, and the Gram-Schmidt process. Eigenvalues
and eigenvectors of a matrix. The diagonalization theorem.
The singular value decomposition of a matrix. Introduction
to vector spaces. A student cannot take both MA 371 and MA
373 for credit.
MA 373 Applied Linear Algebra for Engineers 4R-0L-4C F Pre:
MA 221 or consent of instructor
Similar to MA 371, with more emphasis on applications.
Systems of linear equations, Gaussian elimination, and the
LU decomposition of a matrix. Projections, least squares
approximations, and the Gram-Schmidt process. Eigenvalues
and eigenvectors of a matrix. The diagonalization theorem.
The singular value decomposition of a matrix. A student
cannot take both MA 371 and MA 373 for credit.
MA 378 Number Theory 4R-0L-4C S Pre: Consent of instructor
Divisibility, congruences, prime numbers, factorization
algorithms, RSA encryption, solutions of equations in
integers, quadratic residues, reciprocity, generating
functions, multiplicative and other important functions of
elementary number theory. Mathematical conjecture and proof,
mathematical induction.
MA 381 Introduction to Probability with Statistical
Applications 4R-0L-4C F, S Pre: MA 113
Standard probability concepts and laws; standard statistical
distributions (both discrete and continuous) to include
binomial, geometric, Poisson, normal, and exponential;
introduction to sums of random variables and the central
limit theorem; introduction to statistical estimators.
MA 383 Engineering Statistics II 4R-0L-4C W Pre: MA 223 or
MA 381 and permission of instructor
Hypothesis testing, confidence intervals, sample size
determination, and power calculations for means and
proportions; two factor analysis of variance (with and
without interactions); analysis of several proportions; confidence
and prediction intervals for estimated values using simple
linear regression; Pearson (linear) correlation coefficient;
introduction to multiple regression to include polynomial
regression; review of fundamental prerequisite statistics
will be included as necessary.
MA 385 Quality Methods 4R-0L-4C S Pre: MA 223 or MA 381 and
consent of instructor (May be taken as CHE 385.)
Introduction to various aspects of statistical quality
control and statistical process control to include the
following topics: importance of variance reduction and
probability concepts influencing product quality and
reliability; development and application of control charts
(P-charts, NP-charts, C-charts, U-charts, individual’s
charts, moving range charts, X-bar and R as well as X-bar
and S charts); process capability indices (their use and
misuse); introduction to acceptance sampling. Other topics
to be included as time allows: 6 sigma thinking, gauge
reproducibility and repeatability, and total quality
management with the philosophies of Deming, Juran, and
Crosby. Review of fundamental prerequisite statistics will
be included as necessary.
MA 415 Discrete and Combinatorial Algebra III 4R-0L-4C S
Pre: MA 315
Permutation groups and Polya’s theory of enumeration. An
introduction to graph theory. Applications in chemistry,
electrical networks, and computer science.
MA 416 Algebraic Codes 4R-0L-4C S Pre: MA 315 or consent of
instructor
Construction and theory of linear and non-linear error
correcting codes. Generator matrices, parity check matrices,
and the dual code. Cyclic codes, quadratic residue codes,
BCH codes, Reed-Solomon codes, and derived codes. Weight
enumeration and information rate of optimum codes.
MA 423 Topics in Geometry 4R-0L-4C S (2005) Pre: MA371 or
MA373 or consent of instructor
An advanced course in geometry. Topics could include from
projective geometry, computational geometry, differential
geometry, Riemannian geometry, algebraic geometry, Euclidean
geometry and non-Euclidean geometry.
MA 431 Calculus of Variations 4R-0L-4C Pre: MA 305
Euler-Lagrange and Hamiltonian equations, with possible
applications in mechanics, electrostatics, optics, quantum
mechanics and elasticity theory. An introduction to “direct
methods.” Applications will be chosen in accordance with the
interest of the students. Both classical and numerical
methods have their place in this course.
MA 433 Numerical Analysis 4R-0L-4C Pre: MA 222
Root-finding, computational matrix algebra, nonlinear
optimization, polynomial interpolation, splines, numerical
integration, numerical solution of ordinary differential
equations. Principles of error analysis and scientific
computation. Selection of appropriate algorithms based on
the numerical problem and on the software and hardware (such
as parallel machines) available.
MA 434 Topics in Numerical Analysis 4R-0L-4C Pre: MA 433
An extension of the material presented in MA 433. Topics
might include numerical eigenproblems, numerical solution of
partial differential equations (finite differences, finite
elements, spectral methods), sparse matrices, global
optimization, approximation theory.
MA 436 Introduction to Partial Differential Equations
4R-0L-4C Pre: MA 305
Partial differential equations, elliptic, hyperbolic, and
parabolic equations. Boundary and initial value problems.
Separation of variables, special functions. Eigenfunction
expansions. Existence and uniqueness of solutions. Sturm-Liouville
theory, Green’s function.
MA 439 Mathematical Methods of Image Processing 4R-0L-4C
Pre: MA222
Mathematical formulation and development of methods used in
image processing, especially compression. Vector space
models of signals and images, one- and two-dimensional
discrete Fourier transforms, the discrete cosine transform,
and block transforms. Frequency domain, basis waveforms, and
frequency domain representation of signals and images.
Convolution and filtering. Filter banks, wavelets and the
discrete wavelet transform. Application to Fourier based and
wavelet based compression such as the JPEG compression
standard. Compression concepts such as scalar quantization
and measures of performance.
MA 444 Deterministic Models in Operations Research 4R-0L-4C
W Pre: MA 221 or MA 371/373
Formulation of various deterministic problems as
mathematical optimization models and the derivation of
algorithms to solve them. Optimization models studied
include linear programs, integer programs, and various
network models. Emphasis on model formulation and algorithm
development “from the ground up.”
MA 445 Stochastic Models in Operations Research 4R-0L-4C S
Pre: MA 223 or MA 381
Introduction to stochastic mathematical models and
techniques that aid in the decision-making process. Topics
covered include a review of conditional probability,
discrete and continuous Markov chains, Poisson processes,
queueing theory (waiting line problems), and reliability.
MA 446 Combinatorial Optimization 4R-0L-4C S (2004) Pre: MA
315
An introduction to graph- and network-based optimization
models, including spanning trees, network flow, and matching
problems. Focus is on the development of both models for
real-world applications and algorithms for their solution.
MA 450 Mathematics Seminar 1R-0L-1C F, W, S Pre: Consent of
instructor
A student must attend at least 10 mathematics seminars or
colloquia and present at one of the seminars, based on
material mutually agreed upon by the instructor and the
student. A successful presentation is required for a passing
grade. As seminars may not be offered every week during the
quarter a student may extend the course over more than one
quarter, but it must be completed within two consecutive
quarters. A student may take this course a maximum of four
times.
MA 461 Topics in Topology 4R-0L-4C Pre: MA 307 or consent of
instructor
Introduction to selected topics from point-set topology or
algebraic topology from a rigorous point of view. Possible
topics include metric spaces, general topological spaces,
compactness, connectedness, separation axioms, compactification
and metrization theorems, homotopy and homology, and
covering spaces. Intended for mathematics majors planning to
pursue graduate study in mathematics.
MA 466 Introduction to Functional Analysis 4R-0L-4C Pre: MA
306
An introduction to the theory of Banach spaces emphasizing
properties of Hilbert spaces and linear operators. Special
attention will be given to compact operators and integral
equations.
MA 471 Linear Algebra II 4R-0L-4C W or S Pre: MA 371 or MA
373
Continuation of Linear Algebra I. Properties of Hermitian
and positive definite matrices and factorization theorems
(LU, QR, spectral theorem, SVD). Linear transformations and
vector spaces.
MA 474 Theory of Computation 4R-0L-4C F (2004) Pre: CSSE 230
and MA 315
Students study mathematical models by which to answer three
questions: What is a computer? What limits exist on what
problems computers can solve? What does it mean for a
problem to be hard? Topics include models of computation
(including Turing machines), undecidability (including the
Halting Problem) and computational complexity (including
NP-completeness). Same as CSSE 474.
MA 479 Cryptography 4R-0L-4C S Pre: CSSE220 and MA215
Introduction to basic ideas of modern cryptography with
emphasis on mathematical background and practical
implementation. Topics include: the history of cryptography
and cryptanalysis, public and private key cryptography,
digital signatures, and limitations of modern cryptography.
Touches upon some of the societal issues of cryptography
(same as CSSE 479)
MA 481 Introduction to Mathematical Statistics 4R-0L-4C W
Pre MA381
An introduction to the mathematics of statistics. Topics
include: central limit theorem, gamma, Weibull, Chi-squared
and bivariate normal probability distributions,
transformations of two or more random variables, estimation
of parameters by maximum likelihood and the method of
moments, hypothesis testing for means, proportions, and
variances, Neyman Pearson Lemma, Bayesian inference,
distribution of order statistics, and other topics as time
allows. Applications and derivation of Student’s t and F
distributions. Emphasis will be placed on computer
simulations to illustrate theoretical results.
MA 482 Bioengineering Statistics 4R-0L-4C Pre: MA 223 or MA
381 and consent of instructor (cross listed with BE422)
Hypothesis testing and confidence intervals for two means,
two proportions, and two variances. Introduction to analysis
of variance to include one factor and two factors (with
interaction) designs. Presentation of simple linear and
multiple linear regression modeling; development of analysis
of contingency table to include logistic regression.
Presentation of Log odds ratio as well as several
non-parametric techniques of hypothesis testing and
construction of non-parametric confidence intervals and
correlation coefficients. Review of fundamental prerequisite
statistics will be included as necessary.
MA 485 Applied Regression Analysis and Introduction to Time
Series 4R-0L-4C Pre: MA 223 or MA 381 and consent of
instructor
Review of simple linear regression; confidence and prediction
intervals for estimated values using simple linear
regression; introduction to such concepts as model fit,
misspecification, multi-collinearity, heterogeneous variances
and transformation of both independent and dependent
variables; introduction to multiple regression to include
polynomial regression; use of dummy variables and
diagnostics based on residuals; sequential variable
selection to include forward inclusion and backward
exclusion of variables; best subset regression; introduction
to time series; autocorrelation; moving averages and
exponential smoothing.
MA 487 Design of Experiments 4R-0L-4C Pre: MA 223 or MA 381
and consent of instructor
Review of one factor analysis of variance; tests for
homogeneity of variance and model assumptions; multiple
comparisons, post hoc comparisons, and orthogonal contrasts;
two factor analysis of variance (with and without
interactions); three factor and higher full factorial
designs; analysis of covariance and repeated measures
designs; screening designs to include 2 to the k and 3 to
the k design; fractional factorial designs; introduction to
General Linear Models. Other topics that may be included as
time allows: fixed, random, and mixed designs as well as
nested designs. Review of fundamental prerequisite
statistics will be included as necessary.
MA 490 Topics in Mathematics Variable credit Pre: consent of
instructor
This course will cover advanced topics in mathematics not
offered in listed courses.
MA 495 Research Project in Mathematics Variable credit Pre:
consent of instructor
An undergraduate research project in mathematics or the
application of mathematics to other areas. Students may work
independently or in teams as determined by the instructor.
Though the instructor will offer appropriate guidance in the
conduct of the research, students will be expected to
perform independent work and collaborative work if on a
team. A satisfactory written report and oral presentation
are required for a passing grade. The course may be taken
more than once provided that the research or project is
different.
