Department of Mathematics & Graduate Industrial and Systems Engineering

B.A. (Mathematics) + M.S. (Industrial and Systems Engineering) = Employment Opportunities

### WHAT IS INDUSTRIAL AND SYSTEMS ENGINEERING?

Industrial and systems engineering (ISE) is a profession concerned with the design, operation, analysis, and improvement of integrated systems of people, materials, technology, and information. It draws on specialized knowledge in the mathematical, physical, and social sciences. Industrial and systems engineers apply mathematical models, statistical analysis, economic analysis, and information technology to solve problems.

** Typical tasks for industrial and systems engineers include **

- Investigate new technologies (such as E-Z pass) and their impact on traffic flow
- Analyze marketing data for a financial services company
- Perform economic studies for companies purchasing health care plans
- Design supply chain support and logistics for an e-commerce bookseller
- Monitor a manufacturing process with sophisticated statistical analyses
- Optimize reliability for telecommunication networks by properly locating redundant and backup components
- Simulate port operations to maximize efficiency

The ISE program at Rutgers is a recognized leader in this field. It carries out research, often in collaboration with industry and other disciplines, to advance the state of knowledge and practice in ISE. The Department of ISE has 11 faculty members, 30 Ph.D. students and 60 M.S. students.

## Learning Industrial and Systems Engineering at Rutgers

An undergraduate major in mathematics is excellent preparation for graduate study in ISE, especially if it includes a good choice of electives. This brochure describes how to enter this rewarding field by studying at Rutgers.

The M.S. (Master of Science) degree in ISE addresses both theory and practice. Graduates with this degree enter careers in the private and public sectors - careers in which the methods of ISE are applied to solve important practical problems.

## Requirements

The M.S. degree requires either (1) 30 credits of coursework or (2) 24 credits of course work and 6 credits of thesis research. The requirements for the degree are the same for the two tracks.

** Find full information at http://coewww.rutgers.edu/ie/**

Additional advising is available:

Department of Mathematics (Hill Center)

Department of Industrial and Systems Engineering (CoRE)

### THE STANDARD B.A.-M.S. SEQUENCE

Some students apply to the M.S. program in their senior year of college. Others return for graduate work after a period of employment. In either case, students should use electives both inside and outside their major program to fulfill the ISE prerequisites for application. The M.S. degree can usually be completed in 3 or 4 semesters of full-time graduate study. Part-time study is also possible.

### THE FIVE-YEAR B.A.-M.S. SEQUENCE

Students in this sequence take two or three graduate courses in addition to all required undergraduate course work before graduating from college. These graduate courses cannot be counted toward the undergraduate degree, but will transfer to the masters program. Thus students in this track will take at least 126 or 129 credits before graduating from college. With careful advising and planning, students in this track can earn the M.S. in one year after graduating from college. This will be easier for students earning AP credits. Students should use electives to meet ISE admissions requirements and to strengthen their preparation for graduate work.

Application to the five year program is made to the graduate director in ISE during the student's sixth semester at Rutgers. Early admission to the M.S. program will be offered to qualified students contingent upon successful completion of specified coursework in the senior year. Final admission requires formal application to the Graduate School.

## Financial Aid

Financial support as a Teaching Assistant, Graduate Assistant, or Fellow is sometimes available to students with extremely competitive credentials. Some corporate employers provide tuition reimbursement for successful completion of M.S. courses in ISE which are relevant to the employee's duties.

## Using A Mathematics Major To Prepare For An M.S. In I.S.E.

### REQUIREMENTS for the MATHEMATICS MAJOR

- Calculus I (Math 151), Calculus II (Math 152), and Calculus III (Math 251)
- Introductory Linear Algebra (Math 250)
- Ordinary Differential Equations (Math 252 or 244)
- Introduction to Computer Science (C.S. 111)
- Advanced Calculus I (Math 311)
- Either Linear Algebra (Math 350) or Introduction to Abstract Algebra (Math 351)
- Six (6) additional 3- or 4-credit Math courses numbered 300 or above.

**Notes:**

Among the prerequisites for Math 311, Math 350, and Math 351 is "Math 300 or permission of the Department."

Math 350 is more relevant to ISE than Math 351.

### MINIMAL REQUIREMENTS for ADMISSION to M.S. program in I.S.E.

- Calculus I (Math 151), Calculus II (Math 152),Calculus III (Math)
- Differential Equations (Math 252 or 244)
- Engineering Economics (14:540:343) -- see catalog for prerequisites.
- Calculus-based probability (Math 477)
- Linear Programming (Math 354 or Math 453)
- Facility with a programing language like C++

**Notes:**

For students who do not major in engineering, I.S.E. sets a cumulative g.p.a. of 3.2 or better as one guideline for admissibility into the masters program.

Grades in mathematics courses and other technical courses are most important.

## Using A Mathematics Major To Prepare For An M.S. In I.S.E.

**Consult advisers in both departments** to insure that course selections are compatible with prerequisites, credit restrictions, and scheduling. Undergraduates need special permission to register for graduate courses; ask the graduate director for procedures.

Select at least some **math electives** from the following list:

- Math 477, Probability (required for entry to M.S. program in I.S.E)
- Math 354
**or**Math 453, Linear Optimization ( At least one is required for entry to M.S. program in I.S.E.; Math 453 is preferred.) - Math 321, Introduction to Applied Mathematics
- Math 424, Stochastic Models in Operations Research
- Math 428, Graph Theory
- Math 429, Case Studies in Industrial Mathematics
- Math 478, Probability II
- Math 481, Mathematical Statistics

Select at least some **general electives** from the following list:

- Computer Sciences, courses beyond C.S. 111
- Economics 406, Game Theory
- ISE 338, Probability Models in Operations Research (similar to Math 428)
- ISE 433, Quality Engineering and Statistics
- Statistics 382, Theory of Statistics
- Statistics 384, Intermediate Statistical Analysis
- Statistics 390, Introductory Computing for Statistics
- Statistics 401, Basic Statistics for Research
- Statistics 484, Basic Applied Statistics

**Use summers to advantage.** Seek opportunities during undergraduate years to explore your interest in this area. Possibilities include employment, internships, and research experiences for undergraduates.

### SAMPLE 5-YEAR B.A.-M.S. in I.S.E. (Actual programs will vary!)

**Year 1:** at least 30 credits including

- Calculus I and II (Math 151 and 152)
- Introduction to Computer Science (C.S. 111)
- Micro-Economics and Macro-Economics (Econ 102 and 103)

**Year 2:** at least 30 credits including

- Calculus III (Math 251)
- Introductory Linear Algebra (Math 250)
- Differential Equations (Math 252 OR 244)
- Linear Optimization (Math 354) [u1]
- Probability (Math 477) [u2]

**Summer after Year 2:** 6 credits

- Engineering Economics (ISE 343) and/or Intro. to Applied Math. (Math 321) [u3]

**Year 3: ** at least 30 credits including

- Intro. to Math Reasoning (Math 300) [u4]
- Linear Algebra (Math 350) 424 OR 478 [u5]
- Stochastic Models (Math 424) or Probability II (Math 478) [u6]
- Probability Models in Operations Research (ISE 338)

**Summer after Year 3:** 3 credits

- Case Studies in Industrial Mathematics (Math 429) [u7]
*or*a research internship*or*a research experience for undergraduates

** Year 4:** 30 credits including

- Advanced Calculus (Math 311) [u8]
- First Graduate Course [g1] Fall. one of
- ISE Deterministic Methods (14:540:510) Prerequisite: Math 354.
- ISE Reliability I (14:540:585) Prerequisite: Math 477

- Second graduate course [g2] Spring: Production Analysis I (14:540:560) Prerequisite: Math 354 and Math 477

** Summer after Year 4:**

After graduation, relevant summer internship or employment is suggested. Some students may prefer to use this time to complete undergraduate coursework.

** Masters year:**

- ISE 510 or 5 (whichever was not taken before) [g3]
- ISE 555 [g4]
- Six additional graduate courses chosen in consultation with the graduate director, [g5]-[g10]

**Notes:**

- Eight upper-level math major courses are noted [u1]...[u8]. Ten courses applicable to the M.S. program are noted [g1] ... [g10].
- Undergraduate need special permission to take graduate courses. See your undergraduate college and the ISE graduate director for advice.
- If the suggested summer courses are not included, then addition courses in Math must be taken during the academic year.
- Careful advising and planning is essential to ensure that courses are taken in an order that satisfies all undergraduate and graduate prerequisites, all scheduling constraints, and all general education and college requirements.

## Some M.Sc. Programs

- University of Arizona

Applied Mathematics

- University of British Columbia

Applied Mathematics

- Georgia Institute of Technology

4 Options

- University of Illinois at Chicago

Mathematical Information Sciences for Industry

- Marquette University

Computational Science

- Michigan State University

Industrial Mathematics (MSIM)

- University of Minnesota

Industrial and Applied Mathematics

- Purdue Universityâ€”Indianapolis

Applied Mathematics

- Rice University

Computational and Applied Mathematics

- Stanford

Mathematical and Computational Science

- University of Wisconsin/Milwaukee

Formerly, Center for Industrial Mathematics

(update needed)

- Worcester Polytechnic Institute

Industrial Mathematics

### Workshops

- The Pacific Institute for Mathematical Sciences

Industrial Mathematical Modelling for Graduates and Industrial Problem Solving Workshops

- Rensselaer Polytechnic Institute, (D. Schwendeman)

Mathematical Problems in Industry Workshops

### For more information:

- Society for Industrial and Applied Mathematics

Information for Students - Randall Pyke (What is Industrial Mathematics?)