|
||||
Rose-Hulman Mathematics Program Catalogue
|
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 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 MA 491 – 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 MA 496 – 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 201 -- Engineering Chemistry I or CHEM 111 -- Chemistry I |
(4 hrs.) | |
| AB 101 -- Essential Biology (or higher) | (4 hrs.) | |
| 4 additional credit hours in Physical or Life Sciences | (4 hrs.) | |
| ** | CS 120 -- Fundamentals of Software Development I | (4 hrs.) |
| CS 220 -- Fundamentals of Software Development II | (4 hrs.) | |
| *** | 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. |
(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 201 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 201 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 Fund of Soft Dev I | 4 | CHEM 201 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 Fund of Soft Dev II | 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 eletives are specific to the Mathetmics
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: MA 111, MA 112, MA 113, MA 221, MA 222
- Basic Probability and Statistics or Basic Statistics: one of MA 223 or MA 381
- sixteen additional credit hours of "upper division" courses:
- Courses selected from MA 275, 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 area minor advisor (Math Department Head) and the student's advisor. The department has a form for the planning and approval of an minor.
Notes 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.
- No student can take both MA 371 and MA 373 for credit.
- No student can take both MA223 and MA382 for credit
- If MA 381 is being counted towards the four additional courses then, MA 223 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.
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 215 see MA275
MA 221 Differential Equations and Matrix Algebra
I 4R-0L-4C F,W,S Pre: MA 113 or permission of mathematics department head
Basic matrix algebra with emphasis on understanding systems of linear equations
from algebraic and geometric viewpoints, including the least squares process
and eigenvalues and eigenvectors. First order differential equations including
basic solution techniques and numerical methods. Second order linear, constant
coefficient differential equations, including both the homogeneous and non-homogeneous
cases. Introduction to complex arithmetic, as needed. Applications to problems
in science and engineering.
MA 222 Differential Equations and Matrix Algebra
II 4R-0L-4C F,W,S Pre: MA 221
Solution of systems of first order linear differential equations by eigensystems
and investigation of their solution structure determined by eigensystems. Phase
portrait analysis and classification and stability of critical points for linear
and nonlinear systems. Laplace transforms. Solving small systems of first order
linear differential equations by Laplace transforms. Series solutions. Fourier
series. Applications to problems in science and engineering.
MA 223 Engineering Statistics I 4R-0L-4C F,W,S Pre:
MA 112
This is an introductory course in statistical data analysis. Topics covered
include descriptive statistics, introduction to simple probability concepts,
and random variables (including their linear combinations and expectations).
The Central Limit Theorem will be presented. Hypothesis testing and confidence
intervals for one mean, one proportion, and one standard deviation/variance
will be covered as well as hypothesis testing and confidence intervals for
the difference of two means. An introduction to one factor analysis of variance
and simple linear regression will be presented. A computer package will be
used for statistical analysis and simulation. Experimental data from a variety
of fields of interest to the science and engineering majors enrolled will also
be used to illustrate statistical concepts and facilitate the development of
the student's statistical thinking. A student cannot take both MA 223 and MA
382 for credit.
MA 275 (formerly MA215) Discrete
and Combinatorial Algebra I 4R-0L-4C F,W
An introduction to enumeration and discrete structures. Permutations, combinations
and the pigeonhole principle. Elementary mathematical logic and proof techniques,
including mathematical induction. Properties of the integers. Set theory. Introduction
to functions.
MA 302 see MA 336
MA 305 see MA 330
MA 306 see MA 366
MA 310 see MA 367
MA 315 see MA 375
MA 323 Geometric Modeling 4R-0L-4C W (even years)
Pre: MA113
Covers some of the mathematical methods for describing physical or virtual
objects in computer aided geometric design (CAGD) and computer graphics. Emphasizes
methods for curve and surface modeling, and discusses both the underlying geometric
concepts and the practical aspects of constructing geometric models of objects.
Topics covered include Bezier curves, Hermite curves, B-splines, Bezier patches,
subdivision surfaces. In discussing these, ideas from analytic geometry, differential
geometry, affine geometry, combinatorial geometry, and projective geometry
will be introduced.
MA 325 Fractals and Chaotic Dynamical Systems 4R-0L-4C
S Pre: CSSE 220 and MA 222
Emphasis on the mathematical and computer graphics foundations behind fractal
images and the relationship between chaotic dynamics and fractal geometry.
Self-similar fractals, random fractals with Brownian motion, and fractals generated
from dynamical systems. Fractal dimensions. Iterated Function Systems. Chaos
in one-dimensional maps. Controlling chaos. Mandelbrot and Julia sets. Computer
graphics. Same as CSSE 325.
MA 327 Low Dimensional Topology
4R-0L-4C W (2005-06 alternate years) Pre: MA 113 or consent
of instructor
An introduction to the topology of one-, two-, and three-dimensional manifolds
and its application to other areas of mathematics and science. Topics may include,
but are not restricted to, classification of curves and surfaces, Euler characteristic,
tiling and coloring theorems, graph embeddings, vector fields, knots and links,
and elementary algebraic topology. Intended for science and engineering majors
as well as mathematics majors.
MA 330 (formerly MA 305)
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 331 see MA 341
MA 336 (formerly MA 302)
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 (formerly MA331)
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 (formerly MA 306)
Functions of a Real Variable 4R-0L-4C W Pre: MA 275
Calculus of functions of a single variable. A more careful development
of the basic concepts of analysis, including sequences, limits, continuity,
differentiability, integration, infinite series, power series, Taylor's Theorem,
and uniform convergence.
MA 367 (formerly MA 310)
Functions of a Complex Variable 4R-0L-4C S Pre: MA 113
Elementary properties of analytic functions including Cauchy's theorem and
its consequences, Laurent series, the Residue Theorem, and mapping properties
of analytic functions.
MA 371 Linear Algebra I 4R-0L-4C F,S Pre: MA 221
or consent of instructor
Systems of linear equations, Gaussian elimination, and the LU decomposition
of a matrix. Projections, least squares approximations, and the Gram-Schmidt
process. Eigenvalues and eigenvectors of a matrix. The diagonalization theorem.
The singular value decomposition of a matrix. Introduction to vector spaces.
A student cannot take both MA 371 and MA 373 for credit.
MA 373 Applied Linear Algebra for Engineers 4R-0L-4C
F,S Pre: MA 221 or consent of instructor
Similar to MA 371, with more emphasis on applications. Systems of linear equations,
Gaussian elimination, and the LU decomposition of a matrix. Projections, least
squares approximations, and the Gram-Schmidt process. Eigenvalues and eigenvectors
of a matrix. The diagonalization theorem. The singular value decomposition
of a matrix. A student cannot take both MA 371 and MA 373 for credit.
MA 375 (formerly MA 315)
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 W Pre:
MA 223 or MA 382
Hypothesis testing, confidence intervals, sample size determination, and power
calculations for means and proportions; two factor analysis of variance (with
and without interactions); analysis of several proportions; confidence
and prediction intervals for estimated values using simple linear regression;
Pearson (linear) correlation coefficient; introduction to multiple regression
to include polynomial regression; review of fundamental prerequisite statistics
will be included as necessary.
MA 385 Quality Methods 4R-0L-4C S Pre: MA 223, or
MA 381 and consent of instructor
Introduction to various aspects of statistical quality control and statistical
process control to include the following topics: importance of variance reduction
and probability concepts influencing product quality and reliability; development
and application of control charts (P-charts, NP-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 415 see MA 475
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 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: 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 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 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 (formerly MA 315)
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 (formerly MA 315)
Students study mathematical models by which to answer three questions: What
is a computer? What limits exist on what problems computers can solve? What
does it mean for a problem to be hard? Topics include models of computation
(including Turing machines), undecidability (including the Halting Problem)
and computational complexity (including NP-completeness). Same as CSSE 474.
MA 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 (formerly MA 416)
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 481 Mathematical Statistics 4R-0L-4C W (even
years) Pre: MA 382, or MA 381 and consent of instructor
An introduction to mathematical statistics. Review of distributions
of functions of random variables. Moment generating functions. Limiting distributions.
Point estimation and sufficient statistics. Fisher information and Rao-Cramer
inequality. Theory of statistical tests.
MA 482 Bioengineering Statistics 4R-0L-4C S Pre:
MA 223 or MA 382
Hypothesis testing and confidence intervals for two means, two proportions,
and two variances. Introduction to analysis of variance to include one factor
and two factors (with interaction) designs. Presentation of simple linear and
multiple linear regression modeling; development of analysis of contingency
table to include logistic regression. Presentation of Log odds ratio as well
as several non-parametric techniques of hypothesis testing and construction
of non-parametric confidence intervals and correlation coefficients. Review
of fundamental prerequisite statistics will be included as necessary. Same
as BE 482.
MA 485 Applied Regression Analysis and Introduction
to Time Series 4R-0L-4C F (odd years) Pre: MA 223 or MA
382.
Review of simple linear regression; confidence and prediction intervals for
estimated values using simple linear regression; introduction to such concepts
as model fit, 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 F (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
BHATT, Ghan Shyam, Visiting Assistant Professor of Mathematics. 2005 --
M.Sc., Tribhuvan University Kathmandu, Nepal, 1993; Ph.D., Iowa State University,
2004
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, Professor of Mathematics. 1993 --
A.B., Reed College, 1984; Ph.D., University of Washington, 1990.
BUTSKE, William, 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.
EVANS, Diane L., Assistant Professor of Mathematics. 2001 --
B.S., The Ohio State University; M.A., ibid., 1992; Ph.D., College
of William and Mary, 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., Assistant Professor of Mathematics. 2001 --
A.B., Harvard University, 1992; M.A., Brown University, 1994; Ph.D., ibid.,
1998.
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, Assistant Professor of
Mathematics. 2006 --
RNDr., Comenius University, Slovakia, 1988; Ph.D. University of Nebraska-Lincoln,
1997.
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.
McMURDY, Ken W., Assistant Professor of Mathematics. 2004 --
B.A., University of Rochester 1993; M.A., ibid., 1993; Ph.D., University
of California-Berkeley, 2001.
MILLS, Donald, Assistant Professor of Mathematics. 2006 --
B.S., Bob Jones University, 1993; M.S., Clemson University, 1995; Ph.D., ibid.,
1999.
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.
Questions and Comments to: mathwebmaster@rose-hulman.edu