Professors Bhatt, Broughton, Bryan, Butske, Carlson, Evans,
Finn, Galinaitis, Graves, Grimaldi, Holden, Inlow, Jajcayova, Lautzenheiser,
Leader, McMurdy, Mills, Rader, Rickert, 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, (2005-2006 Alternate Years) 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 may 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 (arranged) 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. A student may take the
course for credit more than once provided the topics are
different.
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: MA433
An extension of the material presented in MA433. Topics may include
numerical problems, numerical solution of partial differential
equations (finite differences, finite elements, spectral
methods), sparse matrices, global optimization, approximation
theory. A student may take the course for credit more than once
provided the topics are different.
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
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 (arranged) 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. A student may
take the course for credit more than once provided the topics
are different.
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 478 Topics in Number Theory
4R-0L-4C (arranged) Pre: MA 378 or MA 375 or consent of the
instructor
Advanced topics in Number Theory. Topics may include elliptic curve
cryptography, the Fermat-Wiles Theorem, elliptic curves, modular
forms, p-adic numbers, Galois theory, diophantine
approximations, analytic number theory, algebraic number theory.
A student may take the course for credit more than once
provided the topics are different.
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
