IUPUI Campus Bulletin 2010-2012

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Departments & Centers

Department of Mathematical Sciences

Degree Requirements

Major Requirements

Pure Mathematics Option

With this option, students will be well prepared for graduate work in pure mathematics. However, students with undergraduate degrees in pure mathematics have also been successful with graduate studies in business administration, computer science, economics, educational research, engineering, law, medicine, operations research, physics, psychology, and statistics. Persons with advanced degrees in pure mathematics find careers primarily in college teaching, but careers in business, industry, or government service are also possible.

Courses taken to satisfy the Area IIIC requirements must include PHYS 15200 (or a more advanced physics course).

The Area IV major requirements are as follows:

1. Core curriculum: MATH 16500, MATH 16600, MATH 17100, MATH 26100, MATH 26600, and MATH 35100 (or MATH 51100)
2. MATH 45300 Beginning Abstract Algebra
3. MATH 46200 Elementary Differential Geometry
4. Two of the three: MATH 44400, MATH 42500, MATH 32101
5. Twelve (12) additional credit hours selected from MATH 27600 and mathematics and statistics courses at the 300 level or above. Courses in computer science or courses in other departments of the School of Science that have appropriate mathematical content may be selected with the approval of the advisor. Normally, no more than 6 credit hours will be approved outside of mathematics and statistics.
6. The 45 credit hours required above must include at least 6 credit hours by completing two of the course sequences listed below.
7. Minimum two (2) credit hours of MATH 49200 Capstone Experience

Course Sequences

Two course sequences (each course 3 credit hours) are required. There must be at least one * sequence. No overlaps are allowed.

• *Foundations of Analysis: MATH 44400 and MATH 44500
• *Complex Analysis and Differential Equations: MATH 42500 and MATH 52000
• *Abstract Algebra: MATH 45300 and MATH 45400
• *Algebra and Number Theory: MATH 45600 and MATH 45300
• *Linear Algebra: MATH 35100 and MATH 35300
• *Differential Geometry: MATH 46200 and MATH 56200
• *Topology: MATH 32101 and MATH 57100
• Probability and Statistics: Two statistical-type courses at the STAT 35000 level or higher, with advisor's approval
• Modeling: MATH 41700 and MATH 42600
• Numerical Analysis: MATH 41400 and CSCI 51500
• Scientific computing: CSCI 47500 and 47600¹
• Theoretical computer science: CSCI 34000 and 47000¹

¹ Students are generally allowed to select only one of these two course sequences.

Pure Mathematics Option Sample Program (124 credits required)

Freshman Year

Sophomore Year

Junior Year

Senior Year

Applied Mathematics Option

Graduates with training in applied mathematics are employed in business, industry, and government. They would probably work as part of a team and would often need to communicate mathematical ideas to persons trained in other subjects. In many instances, they would need to formulate problems for solution on a computer and interpret the answers. Thus, besides a fundamental knowledge of mathematics, a knowledge of what computers can do is essential. This option is also good preparation for graduate study in applied mathematics, computer science, statistics, and engineering.

Courses taken to satisfy the Area IIIC requirements must include PHYS 15200 and PHYS 25100 (or more advanced physics courses).

The Area IV major requirements are as follows:

1. Core curriculum: MATH 16500, MATH 16600, MATH 17100, MATH 26100, MATH 26600, and MATH 35100 (or MATH 51100)
2. MATH 41400 Numerical Methods or CSCI 47500 and CSCI 47600 Scientific Computing (6 cr.)
3. MATH 51000 Vector Calculus or MATH 46200 Elementary Differential Geometry
4. Mathematical modeling: MATH 42600 Introduction to Applied Mathematics or MATH 41700 Modeling and Game Theory
5. MATH 44400 Foundations of Analysis I
6. Twelve (12) additional credit hours selected from MATH 27600 and mathematics and statistics courses at the 300 level or above. Courses in computer science or courses in other departments of the School of Science that have appropriate mathematical content may be selected with the approval of the advisor. Normally, no more than 6 credit hours outside of mathematics and statistics will be approved.
7. The 45 credit hours of courses required above must include at least 6 credit hours in each of two of the course sequences listed below. Students planning on attending graduate school in mathematics are advised to take MATH 44500.
8. Minimum two (2) credit hours of MATH 49200 Capstone Experience

Course Sequences

Two course sequences (each course 3 credit hours) are required. No overlaps are allowed.

• Differential Equations: MATH 52000 and MATH 52200
• Foundations of Analysis: MATH 44400 and MATH 44500
• Complex Analysis and Differential Equations: MATH 42500 and MATH 52000
• Abstract Algebra: MATH 45300 and MATH 45400
• Algebra and Number Theory: MATH 45600 and MATH 45300
• Linear Algebra: MATH 35100 and MATH 35300
• Differential Geometry: MATH 46200 and MATH 56200
• Probability and Statistics: Two statistical-type courses at the STAT 35000 level or higher, with advisor's approval
• Modeling: MATH 41700 and MATH 42600
• Numerical Analysis: MATH 41400 and CSCI 51500
• Scientific computing: CSCI 47500 and 47600²
• Theoretical computer science: CSCI 34000 and 47000²

²Students are generally allowed to select only one of these two course sequences.

Applied Mathematics Option Sample Program  (124 credits required)

Freshman Year

Sophomore Year

Junior Year

Senior Year

Actuarial Science Option

The Actuarial Science Option for mathematics majors will provide students with the strong background in mathematics, statistics, and economics necessary to analyze financial risks. This concentration aims to prepare students for the first three actuarial examinations administered by the professional actuarial organizations. The secondary area of concentration for students in this option is fulfilled by required courses in business and economics.

Actuarial science deals with the analysis of financial consequences of risk. Actuaries are highly trained professionals, well versed in mathematical, statistical, and economic techniques that enable them to evaluate financial risk of uncertain future events, especially those pertaining to health care, insurance, and pension plans. Actuaries answer risk-related questions by developing, implementing, and interpreting sophisticated mathematical models.

The Area IV major requirements are as follows:

1. Core Curriculum: MATH 16500, MATH 16600, MATH 17100, MATH 26100, MATH 26600, and MATH 35100 (or MATH 51100)
2. ECON-S201, ECON-E202 or ECON-S202, ECON-E305, ECON-E321, ECON-E322
3. BUS-A200, BUS-F300, BUS-F305
4. MATH 37300 Mathematical Finance
5. Mathematical Modeling: MATH 42600 Introduction to Applied Mathematics or MATH 41700 Modeling and Game Theory
6. STAT 41600 Probability and STAT 41700 Statistical Theory
7. Actuarial Models: STAT 47200 / STAT 47300
8. Two (2)-credit hour or 3-credit hour STAT elective at the 300 level or above (not STAT 30100, 30200, or 31100) Suggested course: STAT 37100 (Prep for Actuarial Exam 1)
9. Three (3) credit hour MATH or STAT course selected from MATH 27600 and mathematics and statistics courses at the 300 level or above (not STAT 30100, 30200, or 31100). Suggested course: STAT 35000 Introduction to Statistics
10. Two (2) or three (3) credit hours of MATH 49200 Capstone Experience

Actuarial Science Option Sample Program (124 credits required)

Freshman Year

 Sophomore Year