# Mathematics

**FACULTY** Professors McAsey, Mou, Nanyes, Timm, Xue; Associate Professors Bedenikovic (chair), Carty, Goldman, Lang, Yolcu; Assistant Professor Ahanda; Lecturer and Director of the Math Success Center Davis.

A student considering mathematics, statistics, or related areas as a career should realize that emphasis in mathematics and statistics courses will change as the individual progresses through his or her academic program. The initial concern for solving problems is later dominated by the more important objectives of formulating problems in mathematical and statistical language and dealing with mathematical structures and abstract ideas. It should be stressed that an effective mathematician or statistician should be a well-educated person, possessing not only the technical background of mathematics or statistics but also knowledge and skills developed through a selection of courses from other disciplines.

The Department of Mathematics recognizes that students considering a major in a mathematical discipline will have diverse career interests and goals. In fact, flexibility is one of the defining attributes of the departmental offerings. With proper selection of a program and elective course within the program, programs may be designed for students who wish to do graduate study in mathematics or statistics, teach at the high school level, or for students with career interests in the application of mathematics and statistics to, for example, actuarial science, business, computer science, economics or the physical sciences. By selecting appropriate courses, students majoring in one of the programs offered by the Mathematics Department can complete a minor in one of these applied areas. All of the majors offered by the Department are built around core competencies obtained during the student’s freshman and sophomore years and more advanced study based on the student’s interests. The Mathematics Department Core requirements are:

- MTH 121, 122, 223 Calculus I, II, III
- MTH 207 Elementary Linear Algebra with Applications
- MTH 325 Probability and Statistics I
- CS 100 Introduction to Programming Concepts and Languages or CS 101 Introduction to Programming

All students enrolled in one of the majors offered by the Department must also satisfy depth and breadth requirements as appropriate to their major. The breadth requirements are specified within the descriptions of each major below. Students may meet additional depth requirements for their major by selecting courses from the following:

**Depth Groupings**

- Analysis/Topology/Geometry: MTH305 Modern Geometry, MTH345 Differential Equations, MTH403 Complex Variables, MTH406 Elementary Topology, MTH414/514 Partial Differential Equations, MTH420 Real Analysis, MTH421 Advanced Calculus.
- Algebra/Number Theory/Discrete Mathematics: MTH301 Combinatorics, MTH302 Graph Theory, MTH307 Linear Algebra, MTH310 Number Theory, MTH404/405 Abstract Algebra I/II.
- Statistics and Applied Mathematics: MTH325/326 Probability and Statistics I/II, MTH335 Topics in Actuarial Science, MTH345 Differential Equations, MTH414/514 Partial Differential Equations, MTH427 Applied Statistical Methods, MTH428 Topics in Applied Statistics, MTH435 Stochastic Processes, MTH410/411-MTH510/511 Numerical Analysis I/II, MTH501/502 Topics in Applied Mathematics I/II.

MTH495 may be included in any of the groups subject to the approval of the Department Chair.

The Department offers the following majors:

- Mathematics Major
- Applied Mathematics Track
- Traditional Mathematics Track

- Mathematics Education Major (9-12)
- Actuarial Science—Mathematics Major
- Statistics Major

The Department also offers a:

**Advanced Placement in Mathematics**

Students scoring a 5, 4 or 3 on the Advanced Placement (AP) program mathematics examination administered by the College Entrance Examination Board may receive up to eight semester hours of credit for MTH 121 Calculus I and MTH 122 Calculus II.

**Recommended Course of Study for Freshman Year**

Unless the requirements of a course have been met through some other means such as testing or transfer credit, all entering mathematics majors are advised to begin their academic program with the following course of study.

- MTH 121, 122 Calculus I, II - 8 hrs.
- ENG 101 English Composition - 3 hrs.
- COM 103 Oral Communication Process - 3 hrs.
- CS 100 Introduction to Programming Concepts and Languages or CS 101 Introduction to Programming - 3 or 4 hrs.
- Electives - 15 hrs.
- Recommended total Freshman year hours, 32 or 33.

## The Mathematics Major

Students obtaining a Mathematics Major must meet the following departmental requirements:

- The Mathematics Core - 21 or 22 hours
- MTH 120, 224, or an additional course ≥301 - 3 hours
- MTH420 Introduction to Analysis - 3 hours
- Students obtaining a Mathematics Major must choose a track.
- APPLIED MATHEMATICS TRACK (15 credits)
- MTH 224 or 345 - 3 hours
- MTH 414/514 - 3 hours
- 1 of MTH427, MTH428, MTH410/510 - 3 hours
- 1 additional course from Group III - 3 hours
- 1 additional course from Group I or II - 3 hours

2 upper division courses from outside the Mathematics Department,

chosen in consultation with an advisor and approved by the Department Chair, may be substituted for the additional courses.

- TRADITIONAL MATHEMATICS TRACK (12 credits)
- MTH 404 - 3 hours
- MTH 495 - 3 hours
- 1 additional course from Group I - 3 hours
- 1 additional course from Group II - 3 hours

- APPLIED MATHEMATICS TRACK (15 credits)
- Upper Division Requirement - Students must have at least 24 hours in mathematics courses numbered 301 or greater
- A Mathematics Major with either track requires a minimum of 42 hours.

Students considering further study of mathematics at the graduate level should select courses such as:

- MTH 307 Linear Algebra
- MTH 345 Differential Equations
- MTH 403 Complex Variables
- MTH 405 Modern Algebra II
- MTH 406 Elementary Topology
- MTH 421 Advanced Calculus

In addition, a year of physics (PHY 110 and 201), MTH 120, and a foreign language may prove beneficial.

## The Mathematics Education Major (9-12)

This course of study is designed to provide graduates with the education and training to teach mathematics at the secondary school level (grades 9-12). The mathematics requirements for this degree program consist of a core of required classes and a collection of upper division courses which provide additional mathematical breadth and depth to the major. In addition, students who select this major must also complete all the education requirements as mandated by the Illinois State Board of Education, which includes 44 hours of course work in the Teacher Education - High School Education program.

Students obtaining a Mathematics Education Major (9-12) must meet the following departmental requirements.

- The Mathematics Core - 21 or 22 hours
- MTH 404 Modern Algebra I - 3 hours
- MTH 420 Introduction to Analysis I - 3 hours
- Upper Division requirements: Students must complete 5 additional courses at the >= 301 level not all from the same Depth Grouping. - 15 credits
- A Mathematics Education Major (9-12) requires a minimum of 42 hours.
- The state currently requires that students be introduced to various topics in order to meet the Mathematics subject area licensure requirements. Most of the mathematical topics required for endorsement are covered in the Mathematics Core in number 1 above. Currently, there are additional requirements in graph theory, geometry, and history of mathematics. State licensure requirements change frequently. It is the student’s responsibility to see that the current state requirements are satisfied.
- Completion of the Teacher Education - High School Education program. For more information, see Teacher Education - High School Education program in the College of Education and Health Sciences section of this catalog.

## The Actuarial Science - Mathematics Major

Actuaries use analytical skills to evaluate the likelihood of future events, manage risk, and advise clients with decisions requiring statistical expertise. Actuaries work across industry; including the insurance industry and for finance and health care institutions.

Students obtaining an Actuarial Science-Mathematics Major must meet the following departmental requirements.

- The Mathematics Core - 21 or 22 hours
- MTH 326 Probability and Statistics II - 3 hours
- MTH 335 Topics in Actuarial Science (two different topics) - 6 hours
- MTH 427 Applied Statistical Methods - 3 hours
- Two additional mathematics courses from courses numbered MTH 301 or above - 6 hours

Students obtaining an Actuarial Science-Mathematics major must meet the following additional requirements.

- ATG 157 Accounting Principles - Financial - 3 hours
- ECO 221, 222 Microeconomics, Macroeconomics - 6 hours
- IME 313, 314 Operations Research I, II - 6 hours
- FIN 322 Business Finance - 3 hours
- FIN 325 Investment Analysis (or another finance course with departmental approval) - 3 hours

Total: 60-61 hours

For an Actuarial Science-Mathematics major a maximum of 25 percent of the total undergraduate program credit hours including required courses may consist of courses from the Foster College of Business. For example, in a 124-credit-hour program a maximum of 31 credit hours of business courses may be taken.

Students wishing to take business or programming courses in addition to those required courses listed above should consider choosing from among the following, subject to the restriction noted above: ATG 158, BLW 342, BUS 100, CS 102, FIN 425, and ML 250.

## The Statistics Major

Statisticians are in high demand across industry. In addition to the general mathematics emphasis on logical reasoning and creative problem solving, the statistics major focuses on analyzing data. The study of statistics includes theory, applications of probability, and facility with computing tools.

Students obtaining a Statistics Major must meet the following departmental requirements.

- The Mathematics Core - 21 or 22 hours
- MTH 326 Probability and Statistics II - 3 hours
- MTH 420 Real Analysis - 3 hours
- MTH 427 Applied Statistical Methods - 3 hours
- Two courses selected from: MTH 428 Topics in Applied Statistics (may be repeated) and MTH 435 Stochastic Processes - 6 hours
- MTH 494, 495 Senior Project I, II 3 hours
- A mathematics elective numbered MTH 301 or above 3 hours

Total: 42-43 hours

Optional supporting courses include MTH 224 or MTH 345, IME 313, and CS 102.

## The Mathematics Minor

Students obtaining a Mathematics Minor must meet the following departmental requirements.

- MTH 121, 122 - 8 hours
- MTH 120 or 223 - 3 or 4 hours
- Students obtaining a Mathematics Minor have two options.

Option A: MTH 207 or 224 AND 3 courses ≥301‡ - 12 hours

Option B: 4 courses ≥301‡ -12 hours - A Mathematics Minor requires a minimum of 23 hours.

‡ MTH 494/495 may not be used to fulfill requirements for a minor.