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Rose-Hulman Mathematics Program Catalogue
2012-13 - frozen June 2012

This webpage collects together the mathematics components of the official 2012-13 institute bulletin. This "math catalogue" applies to students entering Rose-Hulman 1 Sep 12 or later. Students who entered before 1 Sep 12 but graduate after this date may elect to graduate under the catalogue in which they entered or a subsequent catalogue (provided courses exist). Any matters of interpretation among the various editions of the catalogue will be resolved by the Head of the Mathematics Department. The various versions of recent math catalogues may be found at these links:

The date of revision and posting of this page is automatically generated and displayed at the bottom of this page.

CONTENTS

  1. Faculty
  2. Program Overview
  3. Program Goals and Objectives
  4. Degree Requirements
  5. Suggested Schedule
  6. Area Minor in Mathematics
  7. Area Minor in Statistics
  8. Area Minor in Computational Science
  9. Special Programs - Fast Track Calculus
  10. Course Descriptions
  11. Faculty Educational Credentials

FACULTY

Professors Broughton, Bryan, Butske, Carlisle, Eichholz, Evans, Finn, Graves, Green, Goulet, Grimaldi, Holden, A. Holder, L. Holder, Inlow, Isaia, Langley, Leader, McSweeney, Rader, Reyes, Rickert, Sanborn, Selby, and Shibberu. For faculty educational credentials please see the educational credentials section.

PROGRAM OVERVIEW

MATHEMATICS
Why study mathematics? Many of the new wonders that we take for granted in our modern technological society have mathematical ideas and applications as their basis, though this role is often hidden from view. Complex economic and planning decisions, scientific discoveries that improve our lives, and new technologies and products are often possible only after mathematical or statistical analysis, or a computer visualization, simulation, design and implementation based on mathematics. Therefore, mathematicians, as well as mathematically educated scientists, engineers and economists, make important daily contributions in the understanding and advancement of science, the improvement and discovery of new technology, and decision-making and planning in business, industry and government. Students interested in using their mathematical skills in solving real world problems are well-prepared, by majoring or minoring in mathematics, for careers such as in the insurance industry, software design, data and systems analysis, scientific computing, combustion research, the animated movie industry, and cryptanalysis to name a few, or a graduate degree in a related technical field. Those students with a very strong interest in mathematics itself can pursue graduate study in mathematics in preparation for careers as university or college mathematics teachers and in the development of new mathematical and statistical concepts and methods as researchers in academia, government and industry.

The curriculum of the program in the Department of Mathematics is designed to provide a broad education in both theoretical and applied mathematics. It also develops the scientific knowledge and the problem solving, computing, and communications skills that are critical to a successful mathematically based career. This preparation is greatly enhanced by taking advantage of the wide variety of science and engineering courses available to students and developing good communications skills, both through technical courses and the strong humanities program. The program offers a solid grounding in the foundational areas of calculus, differential equations, linear algebra, discrete and combinatorial algebra, and probability and statistics. These basic courses are complemented by a varied selection of upper division courses for further elective study in areas such as numerical analysis, operations research, advanced statistics, mathematical modeling, optimization, and other advanced topics in mathematics. Students are encouraged to develop a strong background in an area of science or engineering through election of courses leading to a minor or double major. By appropriate course selection students may complete a double major in mathematics and another field such as computer science, physics, chemistry, applied biology, or economics.

PROGRAM GOALS AND OBJECTIVES
To provide a foundation for further learning as well as contributing to the general education of students, the programs at Rose-Hulman all have a heavy investment in mathematics and science in the first two years. The freshman and sophomore mathematics curriculum is designed to contribute to this foundation by ensuring that students are familiar with basic mathematical and statistical concepts, and mathematical and statistical reasoning and modeling. Students will also understand the use of mathematics in other disciplines as well as developing an appreciation of mathematics as a discipline in its own right. In addition, students will learn to be competent users of mathematics, especially in problem solving, and be able to effectively communicate mathematically. The curriculum makes strong use of computer methods to develop students' mathematical understanding and to enhance their ability to use the computer in modeling, computation and problem solving.

For students seeking a major in mathematics, the curriculum prepares them for a mathematically based career after graduation or further graduate study. The major builds upon the goals and objectives of the freshman and sophomore curriculum. In addition to a deeper and broader study of mathematics, majors will further develop their ability to formulate and solve problems from a mathematical perspective, become familiar with the use of mathematics in other fields, and develop competence at the application of mathematics to at least one other field. Graduates will also be able to use technology effectively in mathematics and the application of mathematics. To complement these technical skills graduates will learn the professional skills of effective communication with both technical and non-technical audiences and the ability to work cooperatively with others. Students will complete a capstone senior project or senior thesis.

DEGREE REQUIREMENTS

Major Concentrations: Mathematics majors choose to complete their program in one of four concentrations: Mathematics, Continuous Applied Mathematics, Discrete Applied Mathematics, or Statistics and Operations Research. The Mathematics concentration provides the foundational mathematical depth of a traditional mathematics major and is intended for students planning on graduate study in an area of mathematics. In applied mathematics there are two areas: the Continuous Applied Mathematics concentration and the Discrete Applied Mathematics concentration. Students selecting these concentrations may tailor their programs to interface with another major or to enhance industrial employment or graduate school opportunities. The Statistics and Operations Research concentration is recommended for students pursuing careers in actuarial science, graduate study in statistics, or employment in government or industry in a statistical capacity. It is strongly recommended that students considering graduate education in mathematics include MA 376 Abstract Algebra among their elective mathematics courses. Upon graduation a student may request the Head of the Mathematics Department to issue a letter attesting to the fact that the requirements in the chosen concentration have been completed.

Mathematics Coursework Requirements: All mathematics majors must complete a common core consisting of 39 credit hours of mathematics coursework which provides breadth across the main areas of mathematics. A mathematics major must also complete an additional 12 credit hours of mathematics coursework specified for the selected major concentration plus an additional 12 credit hours earned in free elective mathematics courses. In addition, a mathematics major must complete 8 credit hours of either a senior thesis or project, meant as a capstone experience to the major. A total of 71 credit hours of mathematics courses is required for the major. None of the credits in the 71 hours above may be taken from the courses MA 190, MA 351-MA 356, MA 450 or MA 223 (unless approved by the department head). These courses (except MA 190) may be taken as free electives. In addition, 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.

Common Required Core (39 hrs.)

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.)

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 (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,

  • 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), must be presented publicly to the department. 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 - MA 498. Specifically,

  • MA 497 and MA 498 must be taken in separate terms.
  • The requirement of MA 496 may be fulfilled through some undergraduate research experience and an additional 300-level or above mathematics course (4 hours), as approved by the thesis advisor. The course substitution procedure must be used.
  • The thesis must involve creative work done by the student and a significant portion of this work must have been done by the student individually (not as part of a team). The written submission must be signed by the student's thesis advisor (who must be a member of the mathematics department) and two additional faculty members (who are approved by the thesis advisor), and must be presented publicly to the department.

Summary of Requirements

  Mathematics Coursework - core, concentration and electives
(MA 351-MA 356, MA 450 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, one course must be RH330) (36 hrs.)
  Technical Electives*** (24 hrs.)
  Free Electives (28 hrs.)
  Miscellaneous**** (2 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
(4 hrs.)
  AB 101 -- Essential Biology (or higher level AB course) (4 hrs.)
  4 additional credit hours in Physical or Life Sciences (4 hrs.)
 
** CS 120 -- Introduction to Software Development (4 hrs.)
CS 220 -- Object-Oriented Software Development (4 hrs.)
  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.

(24 hrs.)
 
**** CLSK 100 -- College and Life Skills (1 hr.)
  MA 200 Career Preparation (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 science schedule of six science courses starts with PH 111. If CHEM 111 is required in the fall quarter because of a double major or minor, then the alternate science sequence may be completed by taking the second science course in each place where a choice is given. Two science courses are to be taken in the winter quarter of freshman year.

Fall Winter Spring
 
Freshman Year
MA 111 Calculus I 5 MA 112 Calculus II 5 MA 113 Calculus III 5

PH 111 Physics I  
or
CHEM 111 - General Chem I

4 PH 112 Physics II
or
PH 111 Physics I
4 PH 113 Physics III
or
PH 112 Physics II
4
CSSE 120 Introduction to Software Development 4 CHEM 111 - General Chem I
or
AB101 Essential Biology (or higher)
4 MA 190 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
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)
or
PH113 Physics III
4 Science Elective 4    
*CSSE 220 Object-Oriented Software Development 4 Technical Elective 4 Technical Elective 4
    HSS Elective 4 HSS Elective 4
    **MA 200 Career Preparation      
  __
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
or
RH330 Technical Communications
4 RH330 Technical Communications
or
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 MA 493 Senior Project II
or
MA 497 Senior Thesis II
2 MA 494 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 195

* 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
** MA200 Career preparation may be taken in either the winter or spring quarter of the sophomore year


Notes and Definitions

  • The suggested four year plan is a guideline.
  • Close consultation with the advisor on electives is required, especially for electives after the freshman year, or if a double major or minor is planned.
  • The following definitions of electives are specific to the Mathematics Department.
    • Math Elective: A course either required by the concentration or a true math elective.
    • Science Elective: Any Physical or Life Sciences elective (not Computer Science) at any level.
    • Technical Elective: Non-mathematics courses numbered 200 or above in Engineering, Science or Economics.
    • Free Elective: Any course.

AREA MINOR IN MATHEMATICS

A student, not pursuing a major 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 211, MA 212
    • Basic Probability and Statistics or Basic Statistics: one of MA 223, MA 381, or MA 382
  • sixteen additional credit hours of "upper division" courses:
    • Courses selected from MA 275, all MA courses numbered 300 or higher (except MA 351-356 and MA 450), or other MA course approved by the area minor advisor for mathematics.

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.

Notes and limitations on requirements

  • Almost all students are required to take six foundational courses as a requirement for their major, therefore only four "extra courses" are required for most students.
  • Only MA 111, MA 112, MA 113, MA 212 and one of MA 223, MA 381, or MA 382 can be counted towards both a statistics minor and a mathematics minor.
  • No student can take both MA 371 and MA 373 for credit.
  • No student can take both MA 223 and MA 382 for credit
  • Except as noted above, 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.

AREA MINOR IN STATISTICS

A student, not pursuing a major or second major in mathematics may obtain an area minor in statistics by taking ten or more mathematics courses including the following: 

  • Globally required mathematics courses
    • MA 111 Calculus I
    • MA 112 Calculus II
    • MA 113 Calculus III
    • MA 212 Matrix Algebra and Systems of Differential Equations
  • Required Introductory Statistics/Probability Courses
    • MA 381 Introduction to Probability with Applications to Statistics,
    • one of MA 223 Engineering Statistics I or MA 382 Introduction to Statistics with Probability. If MA 381 is taken before MA 223/MA 382 the student will be strongly recommended to take MA 382.
  • Required Second Statistics Course
    • one of MA 383 Engineering Statistics II; or MA 482 Bioengineering Statistics
  • Electives 3 courses (12 credits) selected from the following list, at least two of which must be starred. Statistics courses not on this list may count towards the minor if approved by statistics area minor advisor.
    • MA 385* Quality Methods
    • MA 371  Linear Algebra  or MA 373 Applied Linear Algebra for Engineers
    • MA 386* Statistical Programming
    • MA 387* Statistical Methods in Six Sigma
    • MA 445  Stochastic Models in Operations Research
    • MA 481* Mathematical Statistics
    • MA 485* Regression and Time Series Analysis
    • MA 487* Design of Experiments
    • MA 480* Topics in Probability and Statistics

All area minors in Statistics must be approved by the statistics area minor advisor the student's advisor. The department has a form for the planning and approval of a statistics minor.

Notes and limitations on requirements

  • Almost all students are required to take the four globally required mathematics courses  plus one probability or statistics course as a requirements for their major, therefore only five "extra courses" are required for most students.
  • Only MA 111, MA 112, MA 113, MA 212 and one of  M223, MA 381, or MA 382 can be counted towards both a statistics minor and a mathematics minor.
  • No student can take both MA 371 and MA 373 for credit.
  • No student can take both MA 223 and MA 382 for credit.

AREA MINOR IN COMPUTATIONAL SCIENCE

      Any student may obtain an area minor in Computational Science by taking the following courses:

  • Five courses in foundational mathematics: MA 111, MA 112, MA 113, MA 211,  MA 212
  • Basic computing course: CSSE 120 or departmental equivalent of at least 4 credit hours
  • Introductory Computational Science courses:
    • MA 332 Introduction  to Computational Science
    • MA 342 Computational Modeling
  • Four credit hours of applied Computational Science course from list A
  • Four credit hours of additional Computational Science course from list B

List A: Applied Computational Science courses

  • MA 323 -Geometric Modeling
  • MA 439 - Mathematical Methods of Image Processing
  • MA 444 - Deterministic Models in Operations Research
  • CSSE 351 - Computer Graphics
  • CSSE 451 -  Advanced Computer Graphics
  • CSSE 413 - Artificial Intelligence
  • CSSE 453 - Topics in Artificial Intelligence
  • CSSE 461 - Computer Vision
  • CSSE 463 -  Image Recognition
  • CE522 - Advanced Finite Element Analysis
  • ME 422- Finite Elements for Engineering Applications
  • ME 427 -  Introduction to Computational Fluid Dynamics
  • ME 511 - Numerical Methods for Dynamic Systems Analysis
  • ME 522 - Advanced Finite Elements Analysis
  • 4XX - Introduction to MEMS:Fabrication and Applications
  • 5XX - Advanced Topics in MEMS
  • CHE 521 - Advanced  Chemical  Engineering Computation
  • BE510 - Biomedical Signal and Image Processing
  • EMGT 526 - Technology Forecasting
  • MA 534/EMGT 534 - Management. Science
  • ECE 420 - Nonlinear Control Systems
  • ECE 480//PH 437 - Introduction to Image Processing
  • ECE 582/PH 537 - Advanced Image Processing
  • ECE 483 - DSP System Design

List B: Additional Computational Science courses

  • MA/CSSE 335 - Introduction to Parallel Computing
  • MA 433 - Numerical Analysis
  • MA 434 - Topics in Numerical Analysis
  • MA 348 - Continuous Optimization
  • MA 446 - Combinatorial Optimization
  • CSSE 304 - Programming Language Concepts
  • CSSE 371 - Software Requirements and Specification

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.

Notes and limitations on requirements

  • Almost all students are required to take the five foundational courses as a requirement for their major
  • Most majors should be able to apply the basic computing requirement and/or one of the elective courses towards their major.
  • Math majors or double majors are not allowed to count MA 332 and MA 342 for both the minor and the major.
  • A student may not apply the four upper-division courses toward both this minor and a math or statistics minor.

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 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: 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 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.

MA 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 of instructor
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 MA 382
Hypothesis testing, confidence intervals, sample size determination, and power calculations for means and proportions; two factor analysis of variance (with and without interactions); analysis of several proportions;  confidence and prediction intervals for estimated values using simple linear regression; Pearson (linear) correlation coefficient; introduction to multiple regression to include polynomial regression; review of fundamental prerequisite statistics will be included as necessary.

MA 385 Quality Methods 4R-0L-4C S Pre: MA 223 or MA 382
Introduction to various aspects of statistical quality control and statistical process control to include the following topics: importance of variance reduction and probability concepts influencing product quality and reliability; development and application of control charts (P-charts, NP-chart, C-charts, U-charts, Individuals Charts, moving range charts, X-bar and R as well as X-bar and S charts); process capability indices (their use and misuse); introduction to acceptance sampling. Other topics to be included as time allows: 6 sigma thinking, gauge reproducibility and repeatability, and total quality management with the philosophies of Deming, Juran, and Crosby. Review of fundamental prerequisite statistics will be included as necessary.

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 instructor
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 330
Euler-Lagrange and Hamiltonian equations, with possible applications in mechanics, electrostatics, optics, quantum mechanics and elasticity theory. An introduction to "direct methods." Applications will be chosen in accordance with the interest of the students. Both classical and numerical methods have their place in this course.

MA 433 Numerical Analysis 4R-0L-4C W Pre: MA 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: MA 433
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 instructor
Student must attend at least 10 mathematics seminars or colloquia. The student must present at one of the seminars, based on material mutually agreed upon by the instructor and the student. A successful presentation is required for a passing grade. As seminars may not be offered every week during the quarter a student may extend the course over more than one quarter, but it must be completed with in a single academic year. A student may take this course a maximum of four times. Cannot count toward mathematics major core hours or the math minor.

MA 460 Topics in Analysis 4R-0L-4C (arranged) Pre: instructor permission
  An advanced topics course in analysis. Topic of the course could be advanced topics in real analysis, advanced topics in complex analysis, analysis on manifolds, measure theory or an advanced course in applied analysis (differential equations). May be taken more than once provided topics are different.

MA 461 Topics in Topology 4R-0L-4C (arranged) Pre: MA 366 or consent of instructor
Introduction to selected topics from point-set topology or algebraic topology from a rigorous point of view. Possible topics include metric spaces, general topological spaces, compactness, connectedness, separation axioms, compactification and metrization theorems, homotopy and homology, and covering spaces. Intended for mathematics majors planning to pursue graduate studies in mathematics.

MA 466 Introduction to Functional Analysis 4R-0L-4C (arranged) Pre: MA 366
An introduction to the theory of Banach spaces emphasizing properties of Hilbert spaces and linear operators. Special attention will be given to compact operators and integral equations.

MA 470 Topics in Algebra 4R-0L-4C (arranged) Pre: instructor permission
An advanced topics course in algebra.  Topic of the course could be commutative algebra, Galois theory, algebraic geometry, Lie groups and algebras, or other advanced topics in algebra.  May be taken more than once provided topics are different.

MA 471 Linear Algebra II 4R-0L-4C S (even years) Pre: MA 371 or MA 373
Continuation of Linear Algebra I. Properties of Hermitian and positive definite matrices and factorization theorems (LU, QR, spectral theorem, SVD). Linear transformations and vector spaces.

MA 473 Design and Analysis of Algorithms 4R-0L-4C Pre: CSSE 230 and MA 375
Students study techniques for designing algorithms and for analyzing the time and space efficiency of algorithms. The algorithm design techniques include divide-and-conquer, greedy algorithms, dynamic programming, randomized algorithms and parallel algorithms. The algorithm analysis includes computational models, best/average/worst case analysis, and computational complexity (including lower bounds and NP-completeness). Same as CSSE 473.

MA 474 Theory of Computation 4R-0L-4C W Pre: CSSE 230 and MA 375
Students study mathematical models by which to answer three questions: What is a computer? What limits exist on what problems computers can solve? What does it mean for a problem to be hard? Topics include models of computation (including Turing machines), undecidability (including the Halting Problem) and computational complexity (including NP-completeness). Same as CSSE 474.

MA 475 Topics in Discrete Mathematics 4R-0L-4C (arranged) Pre: MA 375
An extension of the material presented in 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 MA 382
Hypothesis testing and confidence intervals for two means, two proportions, and two variances. Introduction to analysis of variance to include one factor and two factors (with interaction) designs. Presentation of simple linear and multiple linear regression modeling; development of analysis of contingency table to include logistic regression. Presentation of Log odds ratio as well as several non-parametric techniques of hypothesis testing and construction of non-parametric confidence intervals and correlation coefficients. Review of fundamental prerequisite statistics will be included as necessary. Same as BE 482.

MA 485 Applied Regression Analysis and Introduction to Time Series 4R-0L-4C W (odd years) Pre: MA 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 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. 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.

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

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.

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