Rose-Hulman Mathematics Program Catalogue
|MA 111, 112, 113 Calculus I, II, III||(15 hrs.)|
|MA 211 , 212 Differential Equations, and Matrix Algebra and Systems of Differential Equations||(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.)|
|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 (MA 351-MA 356, MA 450 excepted).
MA 190 - Contemporary Mathematical Problems (2 hrs.) A student taking a degree program in which mathematics is the primary major must also take MA 190. 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 MA 491 - 494. Specifically,
Senior Thesis Option: Students seeking to do a senior thesis must complete a written thesis involving effort equivalent to the 8 credit hours of MA 496 - MA 498. Specifically,
|Mathematics Coursework - core, concentration and electives
(MA 351-MA 356, MA 450 not allowed)
|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, one course must be RH330)||(36 hrs.)|
|Technical Electives***||(24 hrs.)|
|Free Electives||(28 hrs.)|
|Total hours required for graduation||(195 hrs.)|
|*||PH 111, 112, and 113 -- Physics I, II, and III||(12 hrs.)|
|CHEM 105 -- Engineering Chemistry I
or CHEM 111 -- Chemistry I
|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.)|
|MA 332 - Introduction to Computational Science - may be taken instead of CSSE 220 but then MA 332 cannot be counted towards the 63 hours of mathematics coursework|
200 level or above non-mathematics coursework, approved by the major advisor, in areas of science, engineering, or economics in which 12 credit hours constitute a coherent set of three courses representing a specific area of technical depth and 12 credit hours represent technical breadth.
|****||CLSK 100 -- College and Life Skills||(1 hr.)|
|MA 200 Career Preparation||(1 hr.)|
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
|MA 111 Calculus I||5||MA 112 Calculus II||5||MA 113 Calculus III||5|
PH 111 Physics I
|4||PH 112 Physics II
PH 111 Physics I
|4||PH 113 Physics III
PH 112 Physics II
|CSSE 120 Introduction to Software Development||4||CHEM 105 Engineering Chemistry I
AB101 Essential Biology (or higher)
|4||MA 190 Contemporary Mathematics Problems||2|
|RH131 Rhetoric and Comp
RH131 Rhetoric and Comp
|CLSK100 College & Life Skills||1|
|MA 211 Differential Equations||4||MA 212 Matrix Algebra and Systems of Differential Equations||4||MA 381 Intro to Probability||4|
|MA 275 Disc & Comb Alg I||4||MA 371 Linear Algebra I||4|
|AB 101 Essential Biology (or higher)
PH113 Physics III
|*CSSE 220 Object-Oriented Software Development||4||Technical Elective||4||Technical Elective||4|
|HSS Elective||4||HSS Elective||4|
|**MA 200 Career Preparation|
|4||MA 366 Functions of a Real Variable||4||MA Elective
|Technical Elective||4||MA Elective||4||MA Elective||4|
|Technical Elective||4||Technical Elective||4||Technical Elective||4|
|HSS Elective||4||HSS Elective
RH330 Technical Communications
|4||RH330 Technical Communications
|MA 491 Intro to Math Modeling (2 hrs)
and MA 492 - Senior Project I (2 hrs)
MA 496 Senior Thesis I (4 hrs)
|4||MA 493 Senior Project II
MA 497 Senior Thesis II
|2|| MA 494 Senior Project III
MA 498 Senior Thesis III
|HSS Elective||4||MA Elective||4||MA Elective
|Free Elective||4||Free Elective||4||Free Elective||4|
|Free Elective||4||Free Elective||4||Free Elective||4|
All area minors must be approved by the Mathematics area minor advisor and the student's advisor. The department has a form for the planning and approval of an minor.
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:
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.
Any student may obtain an area minor in Computational Science by taking the following courses:
List A: Applied Computational Science courses
List B: Additional Computational Science courses
Electives not on list A or B may be substituted with other courses with the approval of the area minor advisor. All area minors must be approved by the area minor advisor for Computational Sciences and the student's advisor. The department has a form for the planning and approval of a minor.
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.
MAFTC Calculus I, Calculus II, Calculus III - Fast Track
Pre: At least one year of high school Calculus, at least a 700 Math Score or 680 math / 700 critical reading or better on the SAT (31 Math or 30 Math /31 English 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:
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 200 Career Preparation 1R -0L-1C W,S
This course is for mathematics majors to be taken in the second year. The course addresses career choices, summer opportunities, employment and graduate school preparation, and curriculum vitae and resumes preparation. This course is cross-listed with CHEM 200, PH 200 and SV 200.
MA 211 Differential Equations 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. Laplace transforms, Introduction to complex arithmetic, as needed. Applications to problems in science and engineering.
MA 212 Matrix Algebra and Systems of Differential Equations 4R-0L-4C
F,W,S Pre: MA 113
Basic matrix algebra with emphasis on understanding systems of linear equations from algebraic and geometric viewpoints, and eigenvalues and eigenvectors. 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. Fourier series. Introduction to complex arithmetic, as needed. 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: MA 113
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 212
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 332 Introduction to Computational Science 4R-0L-4C F Pre: MA212
An introduction to Computational Science using Matlab. Floating point arithmetic, Matlab programming, solution of nonlinear equations, interpolation, least squares problems, numerical differentiation and integration, solution of linear systems.
MA 335 Introduction to Parallel Computing 4R-0L-4C S (odd
years) Pre: MA 212 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. Same as CSSE 335.
MA 336 Boundary
Value Problems 4R-0L-4C S Pre: MA 211, MA 212
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.
341 Topics in Mathematical Modeling 4R-0L-4C W Pre: MA 211, MA 212
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 342 Computational Modeling 4R-0L-4C S Pre: MA 212 and one of CHE 310, CE
310, MA 332 or ME 323
Computational modeling and simulation of scientific problems using Matlab. Students will create and utilize computer-based models to solve practical problems. Monte Carlo methods, linear systems, solution of ODEs.
MA 348 Continuous Optimization 4R-0L-4C S (even years) Pre: MA 212
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 212
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 212 or consent
Similar to MA 373, 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 MA 373. A student cannot take both MA 371 and MA 373 for credit.
MA 373 Applied Linear Algebra for Engineers 4R-0L-4C W
Pre: MA 212 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
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.
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 MA 223 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: MA 223
or MA 382
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 390 Topics in the Mathematics of Engineering, 1-2C (arranged) Pre: consent of
A succinct mathematical study that is supportive of the engineering curricula. Topics could be chosen from signal processing, fluid dynamics, thermodynamics, as well as others. A student may take the course for credit more than once provided the topics are different.
MA 421 Tensor Calculus and Riemannian Geometry 4R-0L-4C (arranged) Pre: MA 330
An introduction to the calculus of tensor fields and the local geometry of manifolds.Topics covered include: manifolds, tangent space, cotangent spaces, vector fields, differential forms, tensor fields, Riemannian metrics, covariant derivative and connections, parallel transport and geodesics, Ricci tensor, Riemannian curvature tensor. Applications will be given in physics (general relativity, mechanics, string theory) and engineering (continuum mechanics).
MA 423 Topics in Geometry 4R-0L-4C (arranged) Pre: MA 371
or MA 373 or consent of instructor
An advanced geometry course with topics possibly chosen from the areas of projective geometry, computational geometry, differential 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 430 Topics in Applied Mathematics 4R-0L-4C (arranged) Pre: instructor permission
A topics course in the general area of continuous applied mathematics. Topics may include mathematical physics, mathematical biology, mathematical finance, mathematics of vision, PDEs, image processing methods, continuum mechanics, dynamical systems, and mathematical modeling. 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
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 212
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:
An extension of the material presented in MA 433. 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 435 Finite Difference Methods 4R-0L-4C W Pre: MA 332 or MA 371 or MA 373 or MA 433
An introduction to finite difference methods for linear parabolic, hyperbolic, and elliptic partial differential equations. Consistency, stability, convergence, and the Lax Equivalence Theorem. Solution techniques for the resulting linear systems.
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-Louiville theory, Green's function.
MA 439 Mathematical Methods
of Image Processing 4R-0L-4C F Pre: MA 212
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 212
and one of MA371 or MA373
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
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
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
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
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 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
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 212 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 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. 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 public presentation to the department are required.
MA 534 Management Science 4R-OL-4C Pre: Senior or graduate
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.
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., Associate Professor of Mathematics. 2005 --
B.S., Wayne State University, 1996; M.S., ibid., 1997, Ph.D., Purdue University, 2005.
CARLISLE, Sylvia, Visiting Assistant Professor of Mathematics. 2012 --
B.A., Carleton College, 2002; Ph.D., University of Illinois at Urbana-Champaign, 2009.
EICHHOLZ, Joseph A., Assistant Professor of Mathematics. 2011 --
B.S., Western Illinois University, 2005; Ph.D., University of Iowa, 2011.
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.
GOULET, David M., Assistant Professor of Mathematics. 2011 --
B.S.. California Institute of Technology, 1999; M.S., Courant Institute of Mathematical Sciences, 2001; Ph.D. California Institute of Technology, 2006.
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.
GREEN, William, Assistant Professor of Mathematics. 2012 --
B.A., Albion College, 2005,;M.Sc., University of Illinois at Urbana-Champaign, 2006 Ph.D., ibid, 2010
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., Associate Professor of Mathematics. 2003 --
A.B., DePauw University, 1981; M.S., San Diego State University, 1993; Ph.D., Texas A&M University, 2001.
ISAIA, Vincenzo M., Assistant Professor of Mathematics. 2010 --
B.S., Civil Eng. Rensselaer Polytechnic Institute, 1992; M.S., Civil Eng. Manhattan College, 1994; M.S., Applied Mathematics, University of Wyoming, 1998; Ph.D., Applied Mathematics, University of Wyoming, 2002.
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.
LEADER, Jeffery J., Professor of Mathematics. 1999 --
B.S. & B.S.E.E., Syracuse University, 1985; M.S., Brown University, 1987; Ph.D., ibid., 1989.
MCSWEENEY, John K., Assistant Professor of Mathematics. 2012 --
B.Sc., McGill University, 2005; M.Sc., The Ohio State University, 2004; Ph.D., ibid, 2009
RADER, David J., Professor of Mathematics. 1997 --
B.S., University of Richmond, 1991; Ph.D., Rutgers University, 1997.
REYES, Eric M. Assistant Professor of Mathematics. 2012 --
B.Sc., Rose-Hulman Institute of Technology, 2006: M.Stat.: North Carolina State University, 2008; Ph.D., ibid, 2011.
RICKERT, John H., Associate Professor of Mathematics. 1990 --
B.S., University of Wisconsin, 1984; Ph.D., University of Michigan, 1990.
SANBORN, Barbara, Visiting Assistant Professor of Mathematics. 2012 --
B.A., Reed College, 1980; B.Sc., University of Washington, 1986; Ph.D., (Physics) State University of New York at Stony Brook, 1992; Ph.D., (Mathematics) Arizona State University, 2011.
SELBY, Christina, Assistant Professor of Mathematics. 2012 --
B.A., Western Kentucky University, 2001; M.Sc., Purdue University, 2003; Ph.D., ibid, 2006.
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.