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Rose-Hulman Mathematics Program Catalogue
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| MA 111, 112, 113 Calculus I, II, III | (15 hrs.) | |
| MA 221, 222 Differential Equations and Matrix Algebra I, II | (8 hrs.) | |
| MA 371 Linear Algebra I | (4 hrs.) | |
| MA 275 Discrete and Combinatorial Algebra I | (4 hrs.) | |
| MA 366 Functions of a Real Variable | (4 hrs.) | |
| MA 381 Introduction to Probability with Applications to Statistics | (4 hrs.) |
Mathematics Concentration Core (12 hrs.) Three courses selected as follows:
| MA 367 Functions of a Complex Variable | (4 hrs.) | |
| MA 376 Abstract Algebra | (4 hrs.) | |
| One of the following | (4 hrs.) | |
| MA 433 Numerical Analysis | ||
| MA 436 Introduction to Partial Differential Equations | ||
| MA 446 Combinatorial Optimization | ||
| MA 481 Introduction to Mathematical Statistics |
Continuous Applied Mathematics Concentration Core (12 hrs.) Three courses selected per the list below. Students completing the Continuous Applied Mathematics Concentration are strongly urged to complete mathematics coursework in statistics, as elective coursework.
| MA 330 Vector Calculus | (4 hrs.) | |
| MA 336 Boundary Value Problems | (4 hrs.) | |
| MA 433 Numerical Analysis | (4 hrs.) |
Discrete Applied Mathematics Concentration Core (12 hrs.) Three courses selected per the list below. Students completing the Discrete Applied Mathematics Concentration are strongly urged to complete mathematics coursework in statistics as elective coursework.
| MA 375 Discrete and Combinatorial Algebra II | (4 hrs.) | |
| MA 444 Deterministic Models in Operations Research | (4 hrs.) | |
| One of the following | (4 hrs.) | |
| MA 376 Abstract Algebra | ||
| MA 475 Topics in Discrete Mathematics | ||
| MA 476 Algebraic Codes | ||
| MA 477 Graph Theory |
Statistics and Operations Research Concentration Core (12 hrs.) Five courses selected per the list below. Students completing the Statistics and Operations Research Concentration are strongly urged to complete mathematics coursework in applied mathematics as elective coursework.
| MA 382 Introduction to Statistics with Probability | (4 hrs.) | |
| MA 444 Deterministic Models in Operations Research | (4 hrs.) | |
| One of the following | (4 hrs.) | |
| MA 445 Stochastic Models in Operations Research | ||
| MA 446 Combinatorial Optimization | ||
| MA 481 Introduction to Mathematical Statistics | ||
| MA 485 Applied Regression Analysis and Introduction to Time Series | ||
| MA 487 Design of Experiments |
It is strongly suggested that the student take as many of the above courses as possible.
Free Mathematics Electives (12 hrs.) Additional mathematics coursework in courses numbered 300 or above (MA351-MA356, MA450 excepted).
MA 190 – Contemporary Mathematical Problems (2 hrs.) A student taking a degree program in which mathematics is the primary major must also take MA190. A student whose second major is mathematics is not required to take MA 190, but is strongly encouraged to do so.
Senior Project or Thesis (8 hrs.) A student must complete either a Senior Project, equivalent to the 8 credit hours of MA 491 – 494, or a Senior Thesis, equivalent to the 8 credit hours of MA 496 – 498. The project and thesis are each important capstone experiences for the mathematics major, representing sustained efforts to solve a complex problem from industry or mathematical research.
Senior Project Option: Students seeking to do a senior project must complete a written project involving effort equivalent to the 8 credit hours of MA491 – 494. Specifically,
- MA 493 and MA 494 must be taken in separate terms.
- The requirement of MA 491-492 may be fulfilled through some project experience (such as an internship) and another 300-level or above mathematics course (4 hours), as approved by the project advisor. The course substitution procedure must be used.
- The project must involve work done by the student(s) to solve a problem presented by an external sponsor. The written project submission must be signed by the student's project advisor (who must be a member of the mathematics department) and two additional members (who are approved by the project advisor), and must be presented in the departmental seminar. The additional members of the committee may include representatives of the sponsor.
Senior Thesis Option: Students seeking to do a senior thesis must complete a written thesis involving effort equivalent to the 8 credit hours of MA496 – MA 498. Specifically,
- MA 497 and MA 498 must be taken in separate terms.
- The requirement of MA 496 may be fulfilled through some undergraduate research experience and an additional 300-level or above mathematics course (4 hours), as approved by the thesis advisor. The course substitution procedure must be used.
- The thesis must involve creative work done by the student and a significant portion of this work must have been done by the student individually (not as part of a team). The written submission must be signed by the student's thesis advisor (who must be a member of the mathematics department) and two additional faculty members (who are approved by the thesis advisor), and must be presented in the departmental seminar.
| Mathematics Coursework - core, concentration and electives (MA351-MA356, MA450 not allowed) |
(63 hrs.) | |
| Mathematics Senior Project/Thesis | (8 hrs.) | |
| MA 190 – Contemporary Mathematical Problems (primary major only) | (2 hrs.) | |
| Physical and Life Sciences* | (24 hrs.) | |
| Computer Science** | (8 hrs.) | |
| Humanities and Social Science (standard requirement) | (36 hrs.) | |
| Technical Electives*** | (24 hrs.) | |
| Free Electives (MS and AS not permitted) | (28 hrs.) | |
| Miscellaneous**** | (1 hr.) | |
| ________ | ||
| Total hours required for graduation | (194 hrs.) | |
| * | PH 111, 112, and 113 -- Physics I, II, and III | (12 hrs.) |
| CHEM 105 -- Engineering Chemistry I or CHEM 111 -- Chemistry I |
(4 hrs.) | |
| AB 101 -- Essential Biology (or higher level AB course) | (4 hrs.) | |
| 4 additional credit hours in Physical or Life Sciences | (4 hrs.) | |
| ** | CS 120 -- Introduction to Software Development | (4 hrs.) |
| CS 220 -- Object-Oriented Software Development | (4 hrs.) | |
| *** |
200 level or above non-mathematics coursework, approved by the major advisor, |
(24 hrs.) |
| **** | CLSK 100 -- College and Life Skills | (1 hr.) |
SUGGESTED SCHEDULE
The schedule below is a suggested schedule only. Scheduling of courses may be altered, subject to approval of the advisor, in order to take advantage of advanced placement, or to accommodate a second major, area minor or other special program. However, note that some courses are offered only at certain times during the year, and all prerequisites must be met. In the schedule an MA elective is either a concentration elective or free math elective, as described above, and a science elective is a physical or life science elective as defined on this page.
Alternate Science Schedule: The recommended basic chemistry course is CHEM 105 unless a student is taking a second major or minor requiring CHEM 111 or credit for CHEM 111 has already been received. If CHEM 111 is taken instead of CHEM 105 then the order of the basic science electives in the freshman and sophomore is the second science course listed. Two science courses are to be taken in the winter quarter of freshman year
| Fall | Winter | Spring | |||
| Freshman Year | |||||
| MA111 Calculus I | 5 | MA112 Calculus II | 5 | MA113 Calculus III | 5 |
|
PH111 Physics I |
4 | PH112 Physics II or PH111 Physics I |
4 | PH113 Physics III or PH112 Physics II |
4 |
| CSSE 120 Introduction to Software Development | 4 | CHEM 105 Engineering Chemistry I or AB101 Essential Biology (or higher) |
4 | MA190 Contemporary Mathematics Problems | 2 |
| RH131 Rhetoric and Comp or HSS Elective |
4 | HSS Elective or RH131 Rhetoric and Comp |
4 | HSS Elective | 4 |
| CLSK100 College & Life Skills | 1 | ||||
| __ 18 |
__ 17 |
__ 15 |
|||
| Sophomore Year | |||||
| MA221 Diff Eq & Matrix Alg I | 4 | MA222 Diff Eq & Matrix Alg II | 4 | MA381 Intro to Probability | 4 |
| MA275 Disc & Comb Alg I | 4 | MA371 Linear Algebra I | 4 | ||
| AB101 Essential Biology (or higher) or PH113 Physics III |
4 | Science Elective | 4 | ||
| CSSE220 Object-Oriented Software Development | 4 | Technical Elective | 4 | Technical Elective | 4 |
| HSS Elective | 4 | HSS Elective | 4 | ||
| __ 16 |
__ 16 |
__ 16 |
|||
| Junior Year | |||||
|
MA Elective |
4 | MA 366 Functions of a Real Variable | 4 | MA Elective |
4 |
| Technical Elective | 4 | MA Elective | 4 | MA Elective | 4 |
| Technical Elective | 4 | Technical Elective | 4 | Technical Elective | 4 |
| HSS Elective | 4 | HSS Elective | 4 | HSS Elective | 4 |
| __ 16 |
__ 16 |
__ 16 |
|||
| Senior Year | |||||
| MA 491 Intro to Math Modeling (2 hrs) and MA 492 - Senior Project I (2 hrs) or MA 496 Senior Thesis I (4 hrs) |
4 | MA493 Senior Project II or MA 497 Senior Thesis II |
2 | MA494 Senior Project III or MA 498 Senior Thesis III |
2 |
| HSS Elective | 4 | MA Elective | 4 | MA Elective |
4 |
| Free Elective | 4 | Free Elective | 4 | Free Elective | 4 |
| Free Elective | 4 | Free Elective | 4 | Free Elective | 4 |
| Free Elective | 4 | ||||
| __ 16 |
__ 18 |
__ 14 |
|||
| Total Hours | 194 | ||||
Notes and Definitions
- The suggested four year plan is a guideline.
- Close consultation with the advisor on electives is required, especially for electives after the freshman year, or if a double major or minor is planned.
- The following definitions of electives are specific to the Mathematics Department.
- Math Elective: A course either required by the concentration or a true math elective.
- Science Elective: Any Physical or Life Sciences elective (not Computer Science) at any level.
- Technical Elective: Non-mathematics courses numbered 200 or above in Engineering, Science or Economics.
- Free Elective: Any course except Military Science or Aerospace Studies.
AREA MINOR IN MATHEMATICS
A student, not pursuing a major in mathematics, computer science, economics, or a second major in mathematics may obtain an area minor in mathematics by taking 10 or more mathematics courses as follows:- six courses in foundational mathematics
- Calculus, Differential Equations and Matrix Algebra: MA111, MA112, MA113, MA221, MA222
- Basic Probability and Statistics or Basic Statistics: one of MA223, MA381, or MA382
- sixteen additional credit hours of "upper division" courses:
- Courses selected from MA275, all MA courses numbered 300 or higher (except MA351-356 and MA450), or other MA course approved by the area minor advisor for mathematics.
All area minors must be approved by the Mathtmatics area minor advisor and the student's advisor. The department has a form for the planning and approval of an minor.
Notes and limitations on requirements
- Almost all students are required to take six foundational courses as a requirement for their major, therefore only four "extra courses" are required for most students.
- Only MA111, MA112, MA113, MA221 and one of MA223, MA381, or MA382 can be counted towards both a statistics minor and a mathematics minor.
- No student can take both MA371 and MA373 for credit.
- No student can take both MA223 and MA382 for credit
- Except as noted above, if MA381 is being counted towards the four additional courses then, MA223 may taken and counted towards the Basic Probability and Statistics.
- Science and engineering, especially the most recent "high tech" developments, have sophisticated mathematical and statistical concepts and methodologies as their foundation. Thus a well chosen set of courses for a mathematics minor (or a second major in mathematics) will greatly enhance a student's analytical and computational skills. Students thinking of going on to graduate school should especially give consideration to this option.
AREA MINOR IN STATISTICS
A student, not pursuing a major or second major in mathematics may obtain an area minor in statistics by taking ten or more mathematics courses including the following:
- Globally required mathematics courses
- MA111 Calculus I
- MA112 Calculus II
- MA113 Calculus III
- MA221 Differential Equations and Matrix Algebra I
- Required Introductory Statistics/Probability Courses
- Required Second Statistics Course
- Electives 3 courses (12 credits) selected from the following list, at least
two of which must be starred. Statistics courses not on this list may count towards the minor if
approved by statistics area minor advisor.
- MA385* Quality Methods
- MA371 Linear Algebra or MA373 Applied Linear Algebra for Engineers
- MA386* Statistical Programming
- MA387* Statistical Methods in Six Sigma
- MA445 Stochastic Models in Operations Research
- MA481* Mathematical Statistics
- MA485* Regression and Time Series Analysis
- MA487* Design of Experiments
- MA480* Topics in Probability and Statistics
All area minors in Statistics must be approved by the statistics area minor advisor the student's advisor. The department has a form for the planning and approval of a statistics minor.
Notes and limitations on requirements
- Almost all students are required to take the four globally required mathematics courses plus one probability or statistics course as a requirements for their major, therefore only five "extra courses" are required for most students.
- Only MA111, MA112, MA113, MA221 and one of M223, MA381, or MA382 can be counted towards both a statistics minor and a mathematics minor.
- No student can take both MA371 and MA373 for credit.
- No student can take both MA223 and MA382 for credit.
FAST TRACK CALCULUS
Differential, integral and multivariable calculus, is offered during the summer (late July through late August) for selected members of our entering freshman class who have demonstrated outstanding ability in mathematics and studied a year of calculus during high school. Participants are expected to have scored at least 700 on the mathematics portion of the SAT or 31 on the mathematics portion of the ACT. Students, who have a 680 mathematics score and at least a 700 verbal score on the SAT, or a 30 mathematics score and at least a 31 verbal score on the ACT have also been admitted to the program. Participants who successfully complete Fast Track Calculus (graded on a pass/fail basis) satisfy Rose-Hulman's freshman Calculus requirement, are awarded 15 quarter hours of credit toward graduation , and begin their college careers as "mathematical sophomores."
Admission to Fast Track Calculus is competitive. Interested students should contact the Head of the Mathematics Department or Director of Fast Track Calculus.
Fast Track Calculus is graded on a pass/fail basis. For course details, see the MAFTC course in the section on mathematics course descriptions. For information on the program and application procedures see the Fast Track Calculus site.
COURSE DESCRIPTIONS
MAFTC Calculus I, Calculus II, Calculus III - Fast Track
Calculus 15L-0R-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
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. Basic matrix algebra with emphasis on understanding systems of linear
equations from algebraic and geometric viewpoints, and eigenvalues and eigenvectors. 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
of the nature of the 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 Pre: MA 112
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 (odd 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 333 Introduction to Parallel Computing 4R-0L-4C S (odd
years) Pre: MA221 and programming experience
Principles of scientific computation on parallel computers. Algorithms for the solution of linear
systems and other scientific computing problems on parallel machines. Course includes a major project
on RHIT's parallel cluster.
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 113 and 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 221
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
Similar to MA373, but with an emphasis on the theory behind matrices and vector spaces. 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.
Some proof writing will be required. Those interested in applications of matrices and vector spaces
should take MA373. 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 of matrices and vector spaces. 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. Those interested in the theory behind matrices
and vector spaces should take MA 371. 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 Central 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 F 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 382
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-chart,
C-charts, U-charts, Individuals 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 386 Statistical Programming 4R-0L-4C Pre: previous
programming course and either MA 223 or MA 382
Database management and statistical analysis using SAS and possibly, R/S+. Topics will
include database management (including SQL), data step programming, macro programming, standard data
analysis methods (from MA223 or higher level courses), and coding of advanced and/or computationally
intense modern algorithms, e.g., bootstrapping and Monte Carlo methods.
MA 387 Statistical Methods in Six Sigma 4R-0L-4C Pre: MA223
or MA382
A course on statistical methods used in the Six Sigma /DMAIC (Define, Measure, Analyze, Improve,
Control) paradigm. Topics will include, but are not limited to, gauge repeatability and reproducibility,
control charts, regression, design of experiments, and response surface optimization.
MA 423 Topics in Geometry 4R-0L-4C (arranged) Pre: MA371
or MA373 or consent of instructor
An advanced geometry course with topics possibly chosen from the areas of projective geometry, computational
geometry, differential geometry, Riemannian geometry, algebraic geometry, Euclidean geometry or 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: MA222
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 366
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-Louiville 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
Student must attend at least 10 mathematics seminars or colloquia. The student must 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 with
in a single academic year. A student may take this course a maximum of four times. Cannot count toward
mathematics major core hours or the math minor.
MA 460 Topics in Analysis 4R-0L-4C (arranged) Pre: instructor
permission
An advanced topics course in analysis. Topic of the course could be advanced topics in real
analysis, advanced topics in complex analysis, analysis on manifolds, measure theory or an advanced
course in applied analysis (differential equations). May be taken more than once provided topics
are different.
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 studies 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 470 Topics in Algebra 4R-0L-4C (arranged) Pre: instructor
permission
An advanced topics course in algebra. Topic of the course could be commutative algebra, Galois
theory, algebraic geometry, Lie groups and algebras, or other advanced topics in algebra. May
be taken more than once provided topics are different.
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 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 MA275 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: MA378
or MA375 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 480 Topics in Probability or Statistics 4R-0L-4C (arranged)
Pre: instructor permission
An advanced course in probability or statistics. Possible topics include (but are not restricted
to) reliability, discrete event simulation, multivariate statistics, Bayesian statistics, actuarial
science, nonparametric statistics, categorical data analysis, and time series analysis. May
be taken more than once provided topics are different.
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 W (odd years) Pre: MA 221 and either 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, miss specification, 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; auto-correlation; moving averages
and exponential smoothing.
MA 487 Design of Experiments 4R-0L-4C W (even years) 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 491 Introduction to Mathematical Modeling 2C F Pre: Senior
Standing or consent 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
consent of the instructor
MA 493 Senior Project II 2C F,W Pre: MA 492 or consent 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
consent of the instructor
MA 497 Senior Thesis II 2C F,W Pre: MA 496 or consent 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
MA 534 Management Science 4R-OL-4C Pre: Senior or graduate
standing
A study of the development and analysis of various mathematical models useful in managerial decision-making.
This includes discussions of what models are, how to create them, how they are used, and what insights
they provide. Spreadsheets will be used to do much of the computational work. Topics considered include
linear, integer, and nonlinear programming, network models, inventory management, project management,
and simulation models. Examples from all areas of business and industry will be investigated. We
will also investigate how companies are using these techniques to solve current problems. Same as
EMGT 534.
MA 580 Topics in Advanced Probability Theory and Its Applications
(arranged) 4R-0L-4C Pre: MA 381
Advanced topics in probability theory as well as applications that are not offered in the listed
courses.
MA 581 Topics in Advanced Statistics 4R-0L-4C Pre: (arranged)
MA 223 or MA 381 and consent of instructor
This course will cover advanced topics in mathematical statistics as well as applied statistics that
are not offered in the listed courses.
MA 590 Graduate Topics in Mathematics, variable credit, Pre:
consent of instructor
This course will cover graduate level topics in mathematics not offered in listed courses.
FACULTY EDUCATIONAL CREDENTIALS
BROOKS, Cara D., Assistant Professor of Mathematics. 2007 --
B.S., Eastern Michigan University, 1999; M.S. Michigan State University; Ph.D., ibid., 2007.
BROUGHTON, S. Allen, Professor and Head of Mathematics. 1994 --
B.S., University of Windsor, 1975; M.S., Queen's University, 1978; Ph.D., ibid., 1982.
BRYAN, Kurt M., Professor of Mathematics. 1993 --
A.B., Reed College, 1984; Ph.D., University of Washington, 1990.
BUTSKE, William D., Assistant Professor of Mathematics. 2005- -
B.S., Wayne State University, 1996; M.S., ibid., 1997, Ph.D., Purdue University, 2005.
CARLSON, Stephan C., Professor of Mathematics. 1989 --
A.B., University of Kansas, 1969; M.A., ibid., 1975; Ph.D., ibid., 1978.
DeVASHER, Michael S., Visiting Assistant Professor of Mathematics. 2007 --
B.S., University of Alabama, 2001; M.S., ibid., 2003; Ph.D., ibid., 2008.
EVANS, Diane L., Associate Professor of Mathematics. 2001 --
B.S., The Ohio State University; 1990; M.A., ibid., 1992; M.S. College of William and Mary,
1998;. Ph.D., ibid., 2001.
FINN, David L., Associate Professor of Mathematics. 1999 --
B.S., Stevens Institute of Technology, 1989; M.S., Northeastern University, 1992; Ph.D., ibid., 1995.
GALINAITIS, William S., Assistant Professor of Mathematics. 2004 --
B.S., American University 1982; M.A., Central Connecticut State University, 1993; Ph.D., Virginia
Polytechnic Institute and State University 1999.
GRAVES, G. Elton, Associate Professor of Mathematics. 1981 --
A.B., Willamette University, 1969; M.S., University of Minnesota, 1971;
D.A., Idaho State University, 1981.
GRIMALDI, Ralph P., Professor of Mathematics. 1974 --
B.S., State University of New York, 1964; M.S., ibid., 1965; Ph.D., New Mexico State University,
1972.
HOLDEN, Joshua B., Associate Professor of Mathematics. 2001 --
A.B., Harvard University, 1992; M.A., Brown University, 1994; Ph.D., ibid., 1998.
HOLDER, Allen, Associate Professor of Mathematics. 2008 --
B.S. University of Southern Mississippi,1990; M.S. ibid., 1993; Ph.D., University
of Colorado at Denver 1998.
HOLDER, Leanne D., Assistant Professor of Mathematics. 2008 --
B.S. University of Southern Mississippi,1994; M.S. University of Colorado at Denver, 1997: Ph.D., ibid.,
2001.
INLOW, Mark H., Assistant Professor of Mathematics. 2003 --
A.B., DePauw University, 1981; M.S., San Diego State University, 1993; Ph.D., Texas A&M University,
2001.
JAJCAYOVA, Tatiana B, Assistant Professor of Mathematics. 2006 --
RNDr., Comenius University, Slovakia, 1988; Ph.D. University of Nebraska-Lincoln, 1997.
LANGLEY, Thomas L, Associate Professor of Mathematics. 2001-2005 and 2008 --
B.S.E.E., Rice University, 1989; M.S.E.E University of Southern of California,1991; M.A. San Diego
State University, (1996); Ph.D., University of California - San Diego, 2001.
LAUTZENHEISER, Roger G., Professor of Mathematics. 1975 --
A.B., Indiana University, 1968; M.A., ibid., 1969; Ph.D., ibid., 1973.
LEADER, Jeffery J., Associate Professor of Mathematics. 1999 --
B.S. & B.S.E.E., Syracuse University, 1985; M.S., Brown University, 1987; Ph.D., ibid., 1989.
MASSMAN, John, Visiting Assistant Professor of Mathematics. 2007 --
B.A., Whitman College, 1988, M.S., University of Illinois, 1991; Ph.D., University of Colorado at
Boulder, 2005.
MONTGOMERY, Kimberly, Visiting Assistant Professor of Mathematics. 2007 --
B.S., University of Iowa, 1998, M.S., Norhtwestern University, 2001; Ph.D., ibid., 2004.
RADER, David J., Associate Professor of Mathematics. 1997 --
B.S., University of Richmond, 1991; Ph.D., Rutgers University, 1997.
RICKERT, John H., Associate Professor of Mathematics. 1990 --
B.S., University of Wisconsin, 1984; Ph.D., University of Michigan, 1990.
SHIBBERU, Yosi, Associate Professor of Mathematics. 1992 --
B.S., Swarthmore College, 1983; M.S.E.E., Univ. of Texas at Arlington, 1986; M.S., ibid., 1990;
Ph.D. ibid., 1992.
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