Rose-Hulman Institute of Technology-Catalog

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.

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 MA190, MA351-MA356, MA450 or MA223 (unless approved by the department head). These courses (except MA190) may be taken as free electives. Finally, 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.

Common Required Core			(39 hrs.)
MA 111, 112, 113 Calculus I, II, III MA 221, 222 Differential Equations and Matrix Algebra I, II MA 275 Discrete and Combinatorial Algebra I MA 366 Functions of a Real Variable MA 371 Linear Algebra I MA 381 Introduction to Probability with Applications to Statistics			(15 hrs.) (8 hrs.) (4 hrs.) (4 hrs.) (4 hrs.) (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.)
Three 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
MA 444

Introduction to Statistics with Probability
Deterministic Models in Operations Research

(4 hrs.)
(4 hrs.)

One of the Following (4 hrs.)

MA 445
MA 446
MA 481
MA 485

MA 487

Stochastic Models in Operations Research
Combinatorial Optimization
Introduction to Mathematical Statistics
Applied Regression Analysis and Introduction to Time Series
Design of Experiments

It 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 MA491 – 494. Specifically,

MA 493 and MA 494 must be taken in separate terms.
The requirement of MA 491-492 may be fulfilled through some project experience (such as an internship) and another 300-level or above mathematics course (4 hours), as approved by the project advisor. The course substitution procedure must be used.
The project must involve work done by the student(s) to solve a problem presented by an external sponsor. The written project submission must be signed by the student's project advisor (who must be a member of the mathematics department) and two additional members (who are approved by the project advisor), and must be presented in the departmental seminar. The additional members of the committee may include representatives of the sponsor.

Senior Thesis Option: Students seeking to do a senior thesis must complete a written thesis involving effort equivalent to the 8 credit hours of MA496 – MA 498. Specifically,

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

Summary of Requirements

Mathematics Coursework - core, concentration and electives
(MA351-MA356, MA450 not allowed)
Mathematics Senior Project/Thesis
MA 190 - Contemporary Mathematical Problems
(primary major only)
Physical and Life Sciences*
Computer Science**
Humanities and Social Science (standard requirement)
Technical Electives***
Free Electives (MS and AS not permitted)
Miscellaneous****

(63 hrs.)
(8 hrs.)

(2 hrs.)
(24 hrs.)
(8 hrs.)
(36 hrs.)
(24 hrs.)
(28 hrs.)
(1 hr.)

Total hours required for graduation

(194 hrs.)

*	PH 111, 112, and 113 — Physics I, II, and III AB 101 — Essential Biology (or higher-level AB course) CHEM 201 - Engineering Chemistry I or CHEM 111 — General Chemistry I 4 additional credit hours in Physical or Life Sciences	(12 hrs.) (4 hrs.) (4 hrs.) (4 hrs.)

**	CSSE 120 — Fundamentals of Software Development I CSSE 220 — Fundamentals of Software Development II	(4 hrs.) (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

MATHEMATICS

Freshman Year
Fall Term		Credit
MA PH CHEM RH HSS CLSK CSSE	111 111 111 131 100 120	Calculus I .............................. Physics I or General Chemistry I ............. Rhetoric and Composition or HSS Elective........................... College and Life Skills ........ Fundamentals of Software Development I...................	5 4 4 1 4
			18

Winter Term		Credit
MA PH PH CHEM AB HSS RH	112 112 111 201 101 131	Calculus II............................. Physics II or Physics I................................ Engineering Chemistry I or Essential Biology (or higher level AB course)............... HSS Elective or Rhetoric & Composition .....	5 4 4 4
			17

Spring Term		Credit
MA PH PH MA HSS	113 113 112 190	Calculus III............................ Physics III or Physics II............................... Contemporary Mathematics Problems.............................. HSS Elective............................	5 4 2 4
			15

Sophomore Year
Fall Term		Credit
MA MA AB PH CSSE	221 275 101 113 220	Differential Equations I....... Disc. & Comb. Algebra I ... Essential Biology (or higher level AB course) or Physics III ............................. Fundamentals of Software Development II..	4 4 4 4
			16

Winter Term		Credit
MA HSS	222	Differential Equations II...... Science Elective ................... Technical Elective................ HSS Elective...........................	4 4 4 4
			16

Spring Term		Credit
MA MA HSS	381 371	Introduction to Probability.. Linear Algebra I .................... Technical Elective ................ HSS Elective...........................	4 4 4 4
			16

Junior Year
Fall Term		Credit
MA HSS		MA Elective........................... Technical Elective ................ Technical Elective ................ HSS Elective...........................	4 4 4 4
			16

Winter Term		Credit
MA MA HSS	366	Functions of a Real Variable MA Elective........................... Technical Elective ................ HSS Elective...........................	4 4 4 4
			16

Spring Term		Credit
MA MA HSS		MA Elective........................... MA Elective .......................... Technical Elective ................ HSS Elective...........................	4 4 4 4
			16

Senior Year
Fall Term		Credit
MA MA MA HSS	491 492 496	Intro to Math Modeling (2 hours) Senior Project I (2 hours) or Senior Thesis I (4 hours) Free Elective ......................... Free Elective ......................... HSS Elective .........................	4 4 4 4
			16

Winter Term		Credit
MA MA MA	493 497	Senior Project II (2 hours) or Senior Thesis II (2 hours) MA Elective ......................... Free Elective ......................... Free Elective ......................... Free Elective .........................	2 4 4 4 4
			18

Spring Term		Credit
MA MA MA	494 498	Senior Project III (2 hours) or Senior Thesis III (2 hours) MA Elective ......................... Free Elective ......................... Free Elective .........................	2 4 4 4
			14

Notes and Definitions

The suggested four year plan is a guideline.
Close consultation with the advisor on electives is required, especially for electives after the freshman year, or if a double major or minor is planned.

The following definitions of electives are specific to the Mathematics Department.

Math Elective: A course either required by the concentration or a true math elective.
Science Elective: Any Physical or Life Sciences elective (not Computer Science) at any level.
Technical Elective: Non-mathematics courses numbered 200 or above in Engineering, Science or Economics.
Free Elective: Any course except Military Science or Aerospace Studies.

AREA MINOR IN MATHEMATICS
A student, not pursuing a major in mathematics, computer science, economics, or a second major in mathematics may obtain an area minor in mathematics by taking 10 or more mathematics courses as follows:

Six courses in foundational mathematics
Calculus, Differential Equations and Matrix Algebra: 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:
selected from MA 275, all MA courses numbered 300 or higher (except MA 351-356 and MA 450).

Approval and Math Minor Form
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 a 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 MA 223 and MA 382 for credit.
If MA 381 is being counted towards the four additional courses, then MA 223 may be taken and counted towards the Basic Probability/Statistics requirement.
Science and engineering, especially the more recently developed “high tech” areas, have sophisticated mathematical and statistical concepts and methodologies in 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.