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Programs of Study

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.

SUGGESTED SCHEDULE
The schedule below is a suggested schedule only. Scheduling of courses may be altered, subject to approval of the advisor, in order to take advantage of advanced placement or to accommodate a second major, area minor or other special program. However, note that some courses are offered only at certain times during the year, and all prerequisites must be met. In the schedule an MA elective is either a concentration elective or free math elective, as described above, and a science elective is a physical or life science elective as defined on this page.

Alternate Science Schedule: The recommended basic chemistry course is CHEM 105 unless a student is taking a second major or minor requiring CHEM 111 or credit for CHEM 111 has already been received. If CHEM 111 is taken instead of CHEM 105 then the order of the basic science electives in the freshman and sophomore is the second science course listed. Two science courses are to be taken in the winter quarter of freshman year

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 Elective College and Life Skills Introduction to Software Development 5 4     4 1 4       18 Winter Term Credit MA PH PH CHEM   AB   HSS RH 112 112 111 111    101   131 Calculus II Physics II or Physics I General Chemistry I or Essential Biology (or higher level AB course) 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 Elective 5 4  2 4       15

Sophomore Year Fall Term Credit MA MA AB PH *CSSE 211 275 101 113 220 Differential Equations Disc. & Comb. Algebra I Essential Biology (or higher level AB course) or Physics III Object-Oriented Software Development 4 4 4   4       16 Winter Term Credit MA     HSS **MA 212       200 Matrix Algebra and Systems of Differential Equations Science Elective Technical Elective Elective Career Preparation 4 4 4 4 1     17 Spring Term Credit MA MA   HSS 381 371 Introduction to Probability Linear Algebra I Technical Elective Elective 4 4 4 4       16

Junior Year Fall Term Credit MA   Elective Technical Elective Technical Elective 4 4 4 HSS   Elective   or  4 RH 330 Technical and Professional Communication 16 Winter Term Credit MA MA   HSS 366 Functions of a Real Variable Elective Technical Elective Elective or 4 4 4 4 RH 330 Technical and Professional Communication       16 Spring Term Credit MA MA       Elective Elective Technical Elective 4 4 4 HSS   Elective   or 4 RH 330 Technical and Professional Communication       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 4 4 4 4       16 Winter Term Credit MA MA MA 493 497 Senior Project II (2 hours)   or Senior Thesis II (2 hours) 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) Elective Free Elective Free Elective 2 4 4 4       14             Total credits required:  195

Notes: *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 **MA 200 - 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.

Computational Science Major (CPLS) (Second Major Only)

Computational methods are widely employed in science and engineering for simulation, experimentation, analysis, and design. In many areas the use of high-performance computing is essential. The Computational Science major provides Rose-Hulman students with the opportunity to add to their primary major a second major that increases their knowledge and skill in applied scientific and engineering computation.

Requirements for a second major in Computational Science (71 credit hours)

The second major in Computational Science is open to all students. It requires 71 credit hours, including a 55 credit hour core and a 16 credit hour specialization. The courses used to satisfy the requirements in the Advanced Core may not be counted toward any other major or minor. All Computational Science programs of study are subject to approval by the Chair of the Computational Science Steering Committee

I. Computational Science Core (55 credit hours)

Fundamentals (35 credit hours)

• MA 111, 112, 113 Calculus I, II, III
• MA 211 Differential Equations
• MA 212 Matrix Algebra and Systems of Differential Equations
• CSSE 120 (1) Introduction to Software Development, or any of BE 100, CE 110, CHE 110 (plus 2 cr.), ME 123
• CSSE 132 or ECE130 Introduction to Computer Systems, Introduction to Logic Design
• MA 332 (2) Introduction to Computational Science, or any of CE 310 (plus 2 cr.) CHE 310, ME 323(plus 2 Credits)


Advanced (20 credit hours; these courses may not be counted toward any other major or minor)
• CSSE/MA 335 Introduction to Parallel Computing
• MA 336 Boundary Value Problems
• MA 342 Computational Modeling
• MA 435 or ME 422 Finite Difference Methods, Finite Element Methods for Engineering Applications
• Any upper-level computational science course (see list below)

List of Advanced Electives
• BE 510 Biomedical Signal and Image Processing
• CHE 521 Advanced Chemical Engineering Computation
• CSSE 304 Programming Language Concepts
• ECE 480/PH 437 Introduction to Image Processing
• ECE 483 DSP System Design
• ECE 582/PH 537 Advanced Image Processing
• EMGT 526 Technology Forecasting
• EMGT 534/MA 534 Management Science
• MA 323 Geometric Modeling
• MA 348 Continuous Optimization
• MA 433 Numerical Analysis
• MA 434 Topics in Numerical Analysis
• MA 435 Finite Difference Methods
• MA 439 Mathematical Methods of Image Processing
• MA 444 Deterministic Models in Operations Research
• MA 446 Combinatorial Optimization
• MA 490 Mathematical Biology
• ME 422 Finite Element Methods for Engineering Applications
• ME 427 Introduction to Computational Fluid Dynamics
• ME 522 Advanced Finite Elements Analysis
• Other courses may be counted as advanced electives upon approval by the Chair of Computational Science.

II. Area of Concentration (16 credit hours): Each student must complete 16 credit hours in an area of concentration within Computational Science. Courses used to satisfy the core requirements may not be used to satisfy the area of concentration requirements.

Computational Methods
• MA 371 or MA 373 Linear Algebra I, Applied Linear Algebra for Engineers
• MA 433 Numerical Analysis
• Eight credit hours chosen from CSSE 304, CSSE/MA 473, MA 348, MA 386, MA 434, MA 435, MA439, MA 444, MA 446, MA 485, ME 422

Computational Mechanics

• MA 435 or ME 422 Finite Difference Methods, Finite Element Methods for Engineering Applications
• ME 401 Foundations of Fluid Mechanics
• ME 427 Introduction to Computational Fluid Dynamics
• ME 522 Advanced Finite Element Analysis

Computational Signals and Image Processing

• ECE 380 Discrete-Time Signals and Systems
• ECE 480/PH 437 Introduction to Image Processing
• ECE 483 DSP System Design
• MA 439 Mathematical Methods of Image Processing

Computational Physics and Chemistry

• CHEM 361 Physical Chemistry I
• CHEM 362 Physical Chemistry II
• CHEM 363 Quantum Chemistry & Molecular Specroscopy
• OE 570 Nanomedicine
• PH 540 Computer Physics

Computational Biomedics

• BE 482/MA 482 Bioengineering Statistics
• BE 535/OE 535 Biomedical Optics
• BE 541/ECE 597 Medical Imaging
• MA 490-01 Mathematical Biology 1
• MA 490-02 Mathematical Biology 2

AREA MINOR IN MATHEMATICS
A student, not pursuing a major or 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 MA382
  
• 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 courses approved by the area minor advisor for mathematics.

Approval and Math Minor Form
All area minors must be approved by the area minor advisor and the student’s advisor. The department has a form for the planning and approval of a mathematics minor.

Notes and Limitations on Requirements:

• Almost all students are required to take six foundational courses as a requirement for their major; therefore only four "extra courses" are required for most students.
• Only MA111, MA112, MA113, MA211 and one of MA223, MA381, or MA382 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 MA223 and MA382 for credit
• Except as noted above, if MA 381 is being counted towards the four additional courses then, MA 223 may be 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 COMPUTATIONAL SCIENCE
Any student may obtain an area minor in Computational Science by taking the following courses:

• Five courses in foundational mathematics: MA111, MA112, MA113, MA211,  MA212
• Basic computing course: CSSE 120 or departmental equivalent of at least 4 credit hours
• Introductory Computational Science courses:
  • MA332 Introduction  to Computational Science
  • MA342 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

• MA323 – Geometric Modeling

• MA439 – Mathematical Methods of Image Processing

• MA444 – Deterministic Models in Operations Research

• CSSE351 – Computer Graphics

• CSSE451 - Advanced Computer Graphics

• CSSE413 – Artificial Intelligence

• CSSE453 – Topics in Artificial Intelligence

• CSSE461 – Computer Vision

• CSSE463 - Image Recognition

• CE522 - Advanced Finite Element Analysis

• ME422 – Finite Elements for Engineering Applications

• ME427 - Introduction to Computational Fluid Dynamics

• ME511 - Numerical Methods for Dynamic Systems Analysis

• ME522 - Advanced Finite Elements Analysis

• 4XX – Introduction to MEMS:Fabrication and Applications

• 5XX – Advanced Topics in MEMS

• CHE521 – Advanced Chemical Engineering Computation

• BE510 – Biomedical Signal and Image Processing

• EMGT526 - Technology Forecasting

• MA534/EMGT534 - Management. Science

• ECE420 - Nonlinear Control Systems

• ECE480//PH437 – Introduction to Image Processing

• ECE582/PH537 – Advanced Image Processing

• ECE483 - DSP System Design

List B: Additional Computational Science courses

• MA/CSSE335 - Introduction to Parallel Computing

• MA433 - Numerical Analysis

• MA434 – Topics in Numerical Analysis

• MA348 - Continuous Optimization

• MA446 - Combinatorial Optimization

• CSSE304 - Programming Language Concepts

• CSSE371 - 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. 

The minor must be approved by the area minor advisor for Computational Science 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 MA332 and MA342 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.

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 (40 credit hours) including the following:

• Globally required mathematics courses
  MA 111 Calculus I
  MA 112 Calculus II
  MA 113 Calculus III
  MA 212 Differential Equations
• Required Introductory Statistics/Probability Courses:
  MA 381 Introduction to Probability with Applications to Statistics,
  One of MA223 Engineering Statistics I or MA382 Introduction to Statistics with Probability. If MA 381 is taken before MA223/MA382 the student will be strongly recommended to take MA382.
• Required Second Statistics Course
  One of MA383 Engineering Statistics II or MA482 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 386* Statistical Programming
  MA 387* Statistical Methods in Six Sigma
  MA 371 Linear Algebra or MA373 Applied Linear Algebra for Engineers
  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 and the student's advisor. The department has a form for the planning and approval of a statistics minor.

Notes and Limitations on Requirements

• Almost all students are required to take the four globally required mathematics courses plus one probability or statistics course as a requirements for their major, therefore only five "extra courses” are required for most students
• Only MA111, MA112, MA113, MA212 and one of M223, MA381, or MA382 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 MA223 and MA382 for credit.