Professors
Bhatt, Broughton, Bryan, Butske, Carlson, Evans,
Finn, Galinaitis, Graves, Grimaldi, Holden, Inlow,
Lautzenheiser, Leader, Martensen, McMurdy, Naibo, Rader,
Rickert, Sherman, and Shibberu.
MAFTC Calculus I, Calculus II, Calculus III - Fast Track Calculus 15R-0L-15C Pre: At least one year of high school Calculus, at least a 700
Math Score or 680 math/700 verbal or better on the SAT test (31 Math or 30 Math/31 Verbal ACT score), and approval by the Fast Track Selection Committee.
A 5-week fast paced course equivalent to Calculus I, II and III. Taught in the summer only
to incoming freshmen. Review of differential calculus. Introduction to integration and the
Fundamental Theorem of Calculus. Techniques of integration, numerical integration, applications
of integration. L’Hopital’s rule (and improper integrals). Separable first order differential
equations, applications of separable first order differential equation. Series of constants,
power series, Taylor polynomials, Taylor and McLaurin series. Vectors and parametric equations
in three dimensions. 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. This course may be taken as Pass/Fail only.
MA 101 Introductory Calculus 5R-0L-2C F (5 weeks)
Covers approximately the first half of MA 111, including analytic geometry 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
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. Algebraic and transcendental functions. Limits
and continuity. Differentiation, geometric and physical interpretations of the derivative,
Newton’s method. 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. L’Hopital’s rule and improper integrals.
Separable first order differential equations, applications
of separable first order differential equations. Series of
constants, power series, Taylor polynomials, Taylor and McLaurin series.
MA 113 Calculus III 5R-0L-5C
F,W,S Pre: MA 112
Vectors and parametric equations in three dimensions. 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.
MA 190 Contemporary Mathematical Problems 2R-0L-2C S
co-requisite: MA 113
A seminar-style course consisting of an overview of selected
contemporary problems and areas in the mathematical
sciences. Problems to be discussed will be selected from
recent publications in research and applications, famous
problems, and outstanding problems of great significance.
MA 221 Differential
Equations and Matrix Algebra I 4R-0L-4C F, W, S Pre: MA 113
or permission of mathematics department head
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.
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
Solution of systems of first order linear differential equations by
eigensystems and investigation of their solution structure
determined by eigensystems. Phase portrait analysis and
classification and stability of critical points for linear
and nonlinear systems. Laplace transforms. Solving small
systems of first order linear differential equations by
Laplace transforms. Series solutions. 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. A student cannot take both MA 223 and
MA 382 for credit.
MA 275 Discrete and Combinatorial Algebra I 4R-0L-4C F,W
An introduction to enumeration and discrete structures.
Permutations, combinations and the pigeonhole principle. Elementary mathematical
logic and proof techniques, including mathematical induction. Properties of the integers.
Set theory. Introduction to functions.
MA 323 Geometric Modeling 4R-0L-4C W (even years) 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: CSSE 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.
Same as CSSE 325.
MA 327 Low Dimensional Topology 4R-0L-4C W Pre: MA 113 or
consent of instructor
An introduction to the topology of one-, two-, and
three-dimensional manifolds and its application to other
areas of mathematics and science. Topics may include, but
are not restricted to, classification of curves and
surfaces, Euler characteristic, tiling and coloring
theorems, graph embeddings, vector fields, knots and links,
and elementary algebraic topology. Intended for science and
engineering majors as well as mathematics majors.
MA 330 Vector Calculus 4R-0L-4C F Pre: MA 113
Calculus of vector- valued functions of one and several
variables. Topics include differentiation (divergence,
gradient and curl of a vector field) and integration (line
integrals and surface integrals). Applications of Green’s
theorem, Stokes’ theorem and the divergence theorem to
potential theory and/or fluid mechanics will be provided.
MA 336 Boundary Value
Problems 4R-0L-4C S Pre: MA 222
Introduction to boundary value problems and partial
differential equations. Emphasis on boundary values problems
that arise from the wave equation, diffusion equation, and
Laplace’s equation in one, two and three dimensions.
Solutions to such boundary value problems will be discussed
using Fourier series, numerical techniques, and integral
transforms.
MA 341 Topics in Mathematical Modeling 4R-0L-4C W Pre: MA 222 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 (even years) 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 instructor
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. Cannot count toward mathematics
major core hours or the math minor.
MA 366 Functions of a Real Variable 4R-0L-4C W Pre: MA 275
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 367 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 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,S 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 375 Discrete and Combinatorial Algebra II 4R-0L-4C W,S Pre: MA 275
A continuation of MA 275. Relations. An introduction to finite state machines.
More advanced enumeration techniques including recurrence relations, generating functions
and the principle of inclusion and exclusion.
MA 376 Abstract Algebra 4R-0L-4C S Pre: MA 275
An introduction to modern abstract algebra and algebraic structures. Topics
include congruence and modular arithmetic; rings, ideals, and quotient rings; fields,
finite fields, and subfields; groups and subgroups; homomorphisms and isomorphisms.
Other topics may also be introduced according to time and student interest.
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 Applications to Statistics 4R-0L-4C F, W, S
Pre: MA 113
Introduction to probability theory; axioms of probability, sample spaces,
and probability laws (including conditional probabilities).
Univariate random variables (discrete and continuous) and
their expectations including these distributions: binomial,
Poisson, geometric, uniform, exponential, and normal.
Introduction to moment generating functions. Introduction to
jointly distributed random variables. Univariate and joint
transformations of random variables. The distribution of
linear combinations of random variables and an introduction
to the Central Limit Theorem. Applications of probability to
statistics.
MA 382 Introduction to Statistics
with Probability 4R-0L-4C (F) Pre: MA 381
This is an introductory course in statistical data analysis and
mathematical statistics.
Topics covered include descriptive statistics, Sampling
distributions (including the entral Limit Theorem), point estimation, Hypothesis testing
and confidence
intervals for both one and two populations, linear
regression, and analysis of
variance. Emphasis will be placed on both data analysis and
mathematical
derivations of statistical techniques. A computer package
will be used for statistical
analysis and simulation. Experimental data from a variety of
fields of interest will
also be used to illustrate statistical concepts and
facilitate the development of the
student's statistical thinking. A student cannot take both
MA 223 and MA 382 for
credit.
MA 383 Engineering Statistics II 4R-0L-4C W Pre: MA 223 or
MA 382
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
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. Same as CHE 385.
MA 423 Topics in Geometry 4R-0L-4C S (odd years) 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 (arranged) Pre: MA 330
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 W 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 (arranged) 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 F (even years) Pre: MA 330
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
F (odd years) 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
(even years)
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 (even years) Pre: MA
375
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 (arranged) Pre: MA 366 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
(arranged) Pre: MA
366
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 S (even years) 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 473 Design and Analysis of
Algorithms 4R-0L-4C F Pre: CSSE 230 and MA 375
Students study techniques for designing algorithms and for
analyzing the time and space efficiency of algorithms. The
algorithm design techniques include divide-and-conquer, greedy
algorithms, dynamic programming, randomized algorithms and
parallel algorithms. The algorithm analysis includes
computational models, best/average/worst case analysis, and
computational complexity (including lower bounds and
NP-completeness). Same as CSSE 473.
MA 474 Theory of Computation 4R-0L-4C W Pre: CSSE 230 and MA 375
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 475 Topics in Discrete Mathematics 4R-0L-4C S Pre: MA 375
An extension of the material presented in MA 275 and 375. Topics may include
combinatorial design, Fibonacci numbers, or the Probabilistic Method, among others.
MA 476 Algebraic Codes 4R-0L-4C S (odd years) Pre: MA 375 or consent of instructor
Construction and theory of linear and nonlinear 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 477 Graph Theory 4R-0L-4C S
(even years) Pre: MA 375 or consent of instructor
An introduction to the theory and applications of directed
and undirected graphs. Possible topics include the
following: Connectivity, subgraphs, graph isomorphism, Euler
trails and circuits, planarity and the theorems of
Kuratowski and Euler, Hamilton paths and cycles, graph
coloring and chromatic polynomials, matchings, trees with
applications to searching and coding, and algorithms dealing
with minimal spanning trees, articulation points, and
transport networks
MA 479 Cryptography 4R-0L-4C S Pre: CSSE 220 and MA 275
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 Mathematical
Statistics 4R-0L-4C W (even years) Pre: MA 382, or MA 381 and consent
of instructor
An introduction to mathematical statistics. Review of distributions of
functions of random variables. Moment generating functions.
Limiting distributions. Point estimation and sufficient
statistics. Fisher information and Rao-Cramer inequality.
Theory of statistical tests.
MA 482 Bioengineering Statistics 4R-0L-4C S Pre: MA 223 or
MA 382
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. Same as BE 482.
MA 485 Applied Regression Analysis and Introduction to Time
Series 4R-0L-4C F (odd years) Pre: MA 223 or MA 382
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 F (even years) Pre: MA 223 or MA 382
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 491 Introduction to
Mathematical Modeling 2C F Pre: Senior Standing or
permission of the instructor
An introduction to the
process of mathematically modeling a problem, including data
collection, defining the appropriate mathematical model and
interpreting the results of the proposed model. Emphasis
placed on the modeling process, using examples from both
continuous and discrete mathematics.
MA 492 Senior Project I 2C F
Pre: Senior Standing or permission of the instructor
MA 493 Senior Project II 2C F, W Pre: MA 492 or permission
of the instructor
MA 494 Senior Project III 2C W, S Pre: MA 493
Participation in sponsored projects
or problems with a substantial mathematical and/or
computational content. Students typically work in teams of
at most 3, with appropriate
faculty supervision. Problems vary considerably, depending
upon student interest, but normally require computer
implementation and documentation. All work required for
completion of Senior Project must be completed in a form
acceptable to the sponsor and the advisor.
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.
MA 496 Senior Thesis I 4C F
Pre: Senior Standing or permission of the instructor
MA 497 Senior Thesis II 2C F, W Pre: MA 496 or permission
of instructor
MA 498 Senior Thesis III 2C W, S Pre: MA 497
Individual study and research of a topic in mathematics. Topic is
expected to be at an advanced level. Research paper and
presentation to department seminar are required.
Graduate Level Courses
