2003-2005
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Timothy Prickel
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(812) 877- 8438

 

Programs - 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.

DEGREE REQUIREMENTS
   Major Concentrations: Mathematics majors choose to complete their program in one of three concentrations: Mathematics, Applied Mathematics, or Statistics. 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. The Applied Mathematics concentration may be completed in one of two areas: continuous applied mathematics or discrete applied mathematics. Students selecting this concentration may tailor their programs to interface with another major or to enhance industrial employment or graduate school opportunities. The Statistics concentration is recommended for students pursuing careers in actuarial science, graduate study in statistics, or employment in government or industry in a statistical capacity. 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 20 credit hours of mathematics coursework specified for the selected major concentration plus an additional 8 credit hours earned in free elective mathematics courses. A total of 67 credit hours of mathematics courses is required for the major.

Common Required Core

(39 hrs.)

MA 111, 112, 113 Calculus I, II, III
MA 221, 222 Differential Equations and Matrix Algebra I, II
MA 371 Linear Algebra I
MA 215 Discrete and Combinatorial Algebra I
MA 306 Functions of a Real Variable
MA 381 Introduction to Probability with Statistical Applications
     

(15 hrs.)
 (8 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)

Mathematics Concentration Core

(20 hrs.)

Five courses selected from the following and including all courses marked with *.

(A student may take an appropriate MA 490 course in place of either of the two courses not marked with * upon obtaining permission from the students’s advisor and the Mathematics Departmment Head.)
     

 
 
*
*
 
 
 
 
 
 
*
MA 305
MA 307
MA 310
MA 315
MA 321
MA 325
MA 378
MA 415
MA 416
MA 431
MA 433
MA 436
MA 471
MA 481
MA 580
 
Advanced Calculus
Introduction to Topology
Functions of a Complex Variable
Discrete and Combinatorial Algebra II
Topics in Geometry
Fractals and Chaotic Dynamical Systems
Number Theory
Discrete and Combinatorial Algebra III
Algebraic Codes
Calculus of Variations
Numerical Analysis
Introduction to Partial Differential Equations
Linear Algebra II
Introduction to Mathematical Statistics
Topics in Advanced Probability Theory and Its
     Applications

(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)

       
       
Applied Mathematics Concentration Core

(20 hrs.)

Five courses selected from the following and including either all courses marked with * or all courses marked with **. (* corresponds to continuous applied mathematics; ** corresponds to discrete applied mathematics.) Students completing the Applied Mathematics Concentration are strongly urged to complete mathematics coursework in statistics, either as a part of this core requirement or as elective coursework.

(A student may take an appropriate MA 490 course in place of either of the two courses not marked with * or ** upon obtaining permission from the student’s advisor and the Mathematics Department Head.)

 
*
*
 
**
 
 
 
 
**
 
  
*
 
**




 
MA 223
MA 302
MA 305
MA 310
MA 315
MA 323
MA 325
MA 331
MA 383
MA 415
MA 416
MA 431
MA 433
MA 436
MA 444
MA 445
MA 471
MA 481
MA 580
Engineering Statistics I
Boundary Value Problems
Advanced Calculus
Functions of a Complex Variable
Discrete and Combinatorial Algebra II
Geometric Modeling
Fractals and Chaotic Dynamical Systems
Mathematical Modeling
Engineering Statistics II
Discrete and Combinatorial Algebra III
Algebraic Codes
Calculus of Variations
Numerical Analysis
Introduction to Partial Differential Equations
Deterministic Models in Operations Research
Stochastic Models in Operations Research
Linear Algebra II
Introduction to Mathematical Statistics
Topics in Advanced Probability Theory and Its
     Applications

(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)

    
             
Statistics Concentration Core

(20 hrs.)

Five courses selected from the following and including all courses marked with * and at least one marked with **.

(A student may take an appropriate MA 490 course in place of either of the two courses not marked with * or ** upon obtaining permission from the student’s advisor and the Mathematics Department Head.)
     

 
 
 
 
*
**
 
 
 
 
*
**
 
**
 
MA 223 MA 305 MA 310 MA 315
MA 383
MA 385
MA 415
MA 444
MA 445
MA 471
MA 481
MA 485

MA 487
MA 580
 
Engineering Statistics I
Advanced Calculus
Functions of a Complex Variable
Discrete and Combinatorial Algebra II
Engineering Statistics II
Quality Methods
Discrete and Combinatorial Algebra III
Deterministic Models in Operations Research
Stochastic Models in Operations Research
Linear Algebra II
Introduction to Mathematical Statistics
Applied Regression Analysis and Introduction to
     Time Series
Design of Experiments
Topics in Advanced Probability Theory and Its    
     Applications

(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)
(4 hrs.)

       
Free Mathematics Electives

 (8 hrs.)

Additional mathematics coursework in courses numbered 300 or above, or MA 223.
        
Summary of Requirements  
Mathematics Coursework
Physical and Life Sciences*
Computer Science**
Humanities and Social Science (standard requirement)
Technical Electives***
Free Electives (MS and AS not permitted)
Miscellaneous****

(67 hrs.)
(24 hrs.)
(8 hrs.)
(36 hrs.)
(24 hrs.)
(32 hrs.)
(3 hrs.)

         

Total hours required for graduation

(194 hrs)

     
* PH 111, 112, and 113 — Physics I, II, and III
CHEM 111 — Chemistry I
CHEM 113 — Chemistry II or
CHEM 153 — Introduction to Organic Chemistry or
AB 101 — Essential Biology ( or higher)
one additional 4 credit hour course 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
EM 104 — Graphical Communications
(1 hr.)
(2 hrs.)

    
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 above.

MATHEMATICS
Freshman Year
Fall Term

Credit

MA
CHEM
RH
 
HSS
CLSK
EM
111
111
131


100
104
Calculus I ..............................
General Chemistry I..............
Rhetoric and Composition
   or
Elective..................................
College and Life Skills ........
Graphical Comm....................

5
4
 
 
4
1
2

     


16

       
Winter Term

Credit

MA
PH
CSSE
 
HSS
 
RH
112
111
120
 
 
 
131
Calculus II.............................
Physics I................................
Fundamentals of
   Software Dev I ..................
Elective
  or
Rhetoric & Composition .....

5
4
 
4


4

     


17

       
Spring Term

Credit

MA
PH
CHEM
 
CHEM
 
AB
HSS
113
112
113
 
153
 
101
Calculus III............................
Physics II...............................
General Chemistry II
  or
Intro To Organic Chemistry
  or
Essential Biology
(or higher).
Elective..................................

5
4
 
 


4
4

     


17

Sophomore Year
Fall Term

Credit

MA
PH
CSSE

HSS
221
113
220
 
Diff Eq & Matrix Alg I .........
Physics III .............................
Fundamentals of
   Software Dev II .................
Elective...................................

4
4
 
4
4

     


16

       
Winter Term

Credit

MA
 
 
HSS
222
 
 
 
Diff Eq & Matrix Alg II ........
Science Elective....................
Technical Elective ................
 Elective..................................

4
4
4
4

     


16

       
Spring Term

Credit

MA
MA
 
HSS
381
371
Intro to Probability ...............
Linear Algebra ......................
Technical Elective ................
Elective...................................

4
4
4
4

     


16

       
  
Junior Year
Fall Term

Credit

MA
MA
 
 HSS
215 Disc & Comb Alg I ..............
Elective ..................................
Technical Elective ................
Elective...................................

4
4
4
4

     


16

       
Winter Term

Credit

MA
MA
 
HSS
306 Functions of a Real Variable.
Elective..................................
Technical Elective ...............
Elective...................................

4
4
4
4

     


16

       
Spring Term

Credit

MA
MA
 

HSS
 
 
 

Elective...................................
Elective ..................................
Technical Elective ................
Elective..................................

4
4
4
4

     


16

Senior Year
Fall Term

Credit

MA
 
401 Elective ..................................
Technical Elective ...............
Free Elective .........................
Free Elective .........................

4
4
4
4

     


16

       
Winter Term

Credit

MA   Elective ..................................
Free Elective .........................
Free Elective .........................
Free Elective .........................

4
4
4
4

     


16

       
Spring Term

Credit

MA
 
 
Elective ..................................
Free Elective .........................
Free Elective .........................
Free Elective .........................

4
4
4
4

     


16

       
  

 

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

WITH THESIS OPTION
Students pursuing a major or second major in Mathematics may elect to complete a “thesis option” as follows: Students seeking a degree “with thesis” must complete

  • a written thesis or a project and project write-up involving effort equivalent to at least 8 credit hours of MA495;
  • at least 2 credit hours of MA495.

The thesis or project 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/project advisor and two additional mathematics faculty members, and must be presented in the departmental seminar. The student’s transcript would have the designation “with thesis”.
   

AREA MINOR IN MATHEMATICS
   A student, not pursuing a major in mathematics, computer science, or 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/Statistics: one of MA 223 or MA 381
         
  • Sixteen additional credit hours of “upper division” courses
    Courses selected from MA 215, all MA courses numbered 300 or higher (except MA 351-356), or other MA courses approved by the area minor advisor for mathematics.

   All area minors must be approved by the area minor advisor (Math Department Head) and the student’s advisor. The department has a form for the planning and approval of a minor. In addition, note that:

  • 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 MA371 and MA373 for credit.
  • If MA 381 is being counted towards the four additional courses, then MA223 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.