Major in Mathematics

Major Requirements

Mathematics is a broad discipline that contains a range of areas of specialization within it. The required courses in Part I provide fundamental background for Mathematics in general. The options in Part II allow the student to broaden this background or begin to specialize. (Also see the sections on majors in Actuarial Science, Mathematics and Computer Science, Statistics, and the curriculum for the Teaching of Mathematics.)

An entering student in Mathematics should have academic preparation to enroll in Math 220 during the first semester. Admission to Math 220 requires a passing grade on the Mathematics placement test. A student should attain grades of B in calculus in order to complete the advanced courses successfully.

Details of program requirements for a mathematics major or minor can also be found on the campus Programs of Study web page.

Minimum required major and supporting course work normally equates to 52-61 hours including 27 hours beyond calculus, 11-12 hours of calculus, and 3 hours of computer science.

General education: The LAS General Education requirements are set up so students automatically complete the Campus General Education requirements.

Minimum hours required for graduation: 120 hours

Departmental distinction: Distinction will be awarded on the basis of selection of 400-level courses in mathematics and the grade point average. Graduation with High Distinction or Highest Distinction in Mathematics requires participation in the Program for Distinction in Mathematics.

Hours Requirements

11-12 Calculus through one of the following:

MATH 241—Calculus III

3 MATH 347—Fundamental Mathematics or MATH 348- Fundamental Mathematics-ACP

3 Select one of the following:

MATH 415—Applied Linear Algebra

MATH 416—Abstract Linear Algebra

MATH 418—Intro to Abstract Algebra II

3 Select one of the following:

MATH 424—Honors Real Analysis

MATH 444—Elementary Real Analysis

MATH 447—Real Variables

3-4 Select one of the following:

MATH 461—Probability Theory

MATH 463—Statistics and Probability I

3 Select one of the following:

CS 101—Intro to Computing, Eng & Sci

CS 125— Intro to Computer Science

12 Approved supporting course work or any minor

Part II: Options

Each student must fulfill the requirements of PART I and one of the following options:

Mathematics Option

Hours	Requirements
3	Select one of the following:
	MATH 417—Intro to Abstract Algebra
	MATH 427—Honors Abstract Algebra
	MATH 453—Elementary Theory of Numbers
3	Select at least one from:
	MATH 402—Non Euclidean Geometry
	MATH 403—Euclidean Geometry
	MATH 423—Differential Geometry
	MATH 428—Honors Geometric Analysis
	MATH 481—Vector and Tensor Analysis
9	Three additional mathematics courses that are 400- or 500-level.

Graduate Preparatory Option

Hours	Requirements
3	Select one of the following:
	MATH 417—Intro to Abstract Algebra
	MATH 427—Honors Abstract Algebra
3	MATH 418—Intro to Abstract Algebra II
3	Select one of the following:
	MATH 425—Honors Advanced Analysis
	MATH 447—Real Variables
3	Select one of the following:
	MATH 423—Differential Geometry
	MATH 428—Honors Geometric Analysis
	MATH 432—Set Theory and Topology
3	Select one of the following:
	MATH 446—Applied Complex Variables
	MATH 448—Complex Variables
6	Two additional mathematics courses that are 400- or 500-level.

Applied Mathematics Option

Hours	Requirements
3	MATH 441—Differential Equations
3	Select one of the following:
	MATH 446—Applied Complex Variables
	MATH 448—Complex Variables
3	Select one of the following:
	MATH 257—Numerical Methods
	MATH 442—Intro Partial Diff Equations
	MATH 489—Differential Equations II
3	Select one of the following:
	MATH 412—Graph Theory
	MATH 413—Intro to Combinatorics
	MATH 417—Intro to Abstract Algebra
	MATH 427—Honors Abstract Algebra
	MATH 453—Elementary Theory of Numbers
3	One additional mathematics course that is 400- or 500-level1

Operations Research Option

Hours	Requirements
3	MATH 257—Numerical Methods
3	Select one of the following: MATH 412—Graph Theory MATH 413—Intro to Combinatorics
4	MATH 463—Statistics and Probability I
3	Select one of the following: MATH 464—Statistics and Probability II MATH 469—Methods of Applied Statistics
3	MATH 482—Linear Programming
3	MATH 484—Nonlinear Programming

Mathematics Teaching Option

In order to remain in good standing in this program and be recommended for certification, candidates are required to maintain UIUC, cumulative, content area, and professional education, grade-point averages of 2.5 (A= 4.0). Candidates should consult their adviser or the Council on Teacher Education for the list of courses used to compute these grade-point averages.

General education: Students must fulfill the LAS general education requirements. In addition, students must take a speech performance course chosen from the following list: SPCM 101, 113, 120, 321, and 323, THEA 210 or by satisfying the Comp I requirement with SPCM 111-112.

Prerequisites to transfer to the Teaching Option: EPSY 201, EPS 201 or 202, MATH 220 or 221, 231, 241, and three advanced mathematics courses must be completed prior to transfer into the teaching option.

In addition to the requirements listed below, students must complete the Teacher Education Minor in Secondary School Teaching (36 hours). Conferral of the degree of Bachelor of Science in Liberal Arts and Sciences prior to completion of the minor requires approval by petition to the LAS Student Affairs Office. While it is possible to complete this program in eight semesters, many students may require an extra semester or two.

Students must complete the requirements for the Teaching Option as well as Part I requirements in the Sciences and Letters Curriculum.

Hours	Requirements
3	MATH 402—Non Euclidean Geometry
3	Select one of the following: MATH 417—Intro to Abstract Algebra MATH 453—Elementary Theory of Numbers
9	Three additional mathematics courses that are 400- or 500-level.

For All Options

Twelve hours of 300- and 400-level courses in the major must be taken on this campus.

All foreign language requirements must be satisfied.

A Major Plan of Study Form must be completed and submitted to the LAS Student Affairs Office before the end of the fifth semester (60-75 hours). Please see your adviser.

1. In the Applied Mathematics and Operations Research options MATH/CS 257 will be accepted as a substitute for an advanced course in this major.

Honors Sequence and Departmental Distinction

Honors Sequence:: Honors Sequence courses are aimed at highly motivated and mathematically talented freshmen and sophomores interested in mathematics, engineering, and other sciences. See the Honors Sequence webpage for complete details.

Departmental Distinction:: Graduation with distinction will be awarded on the basis of selection of 400-level courses in mathematics and the grade-point average. See the graduation with distinction webpage for complete details.

Suggested Schedule of Mathematics Courses

Every student's situation is different, so you should consult an adviser rather than follow this schedule blindly. Math 347 is intended to prepare students for more abstract work in later courses and hence should be taken as soon as possible after completing Math 231 but probably not in the first semester of the Freshman year.

Below two different sample programs are presented for two different students. One is for a typical student in the general Mathematics option and the other is for a student in the graduate preparatory option.

For a typical student in the general Mathematics Option

Experience shows that many students have difficulty with the more abstract courses such as Math 417 and Math 444/447. You should prepare yourself for these courses by previously taking Math 347 and several other advanced courses such as 415 (Applied Linear Algebra), 463 (Statistics), or 402 (Non Euclidean Geometry). Students choosing between 444 and 447 might use the following guideline: If you get A's in your preceding math courses, take Math 447!

First Year
- Fall Semester
  - Math 220 or 221
- Spring Semester
  - Math 231
Second Year
- Fall Semester
  - Math 241
  - Math 347
- Spring Semester
  - Math 402(403) or Math Elective
  - Math 415 or 463(461) or CS
Third Year
- Fall Semester
  - Math 402(403) or Math Elective
  - Math 415 or 463(461) or CS
- Spring Semester
  - Math 415 or 463(461) or CS
  - Math 417 or 453
Fourth Year
- Fall Semester
  - Math 444(447)
  - Math Elective
- Spring Semester
  - Math Elective

For a student in the Graduate Preparatory Option

Let us assume that the student arrives with Advanced Placement Credit in Math 221 and Math 231. Notice that the suggested program has the student taking only one Mathematics course in each of the last five semesters. It is recommended that this be filled out with quality 400 level Mathematics electives, or additional computer science courses.

Students who intend to do graduate work in Mathematics need to take as extensive and challenging a program as possible. Extremely talented students will find ways to telescope this program so as to allow room for some 500 level work before completing the Bachelor's degree.

First Year
- Fall Semester
  - Math 241
  - Math 347
- Spring Semester
  - Math 416
  - CS 125
Second Year
- Fall Semester
  - Math 417
  - Math 461
- Spring Semester
  - Math 418
  - Math 441
Third Year
- Fall Semester
  - Math 447
- Spring Semester
  - Math 448 or 446
Fourth Year
- Fall Semester
  - Math 423 or 432
- Spring Semester
  - 400-level Math Elective

Advising

The chief adviser for the Mathematics program is

Joseph Miles
joe@math.uiuc.edu
313 Altgeld Hall
(217) 333-1108

The transition and math minor adviser is

Ms. Alison Champion
abc@math.uiuc.edu
313 Altgeld Hall
(217) 333-9199

The freshman adviser is

Ms. Dianna Armstrong
armstron@math.uiuc.edu
313 Altgeld Hall
(217) 333-3353

Students are assigned permanent faculty advisers in the semester they are completing the calculus. If you do not know your adviser consult

Mrs. Kay Daly
daly@math.uiuc.edu
313 Altgeld Hall
(217) 244-9383

Department of Mathematics
273 Altgeld Hall, MC-382
1409 W. Green Street, Urbana, IL 61801 USA
Telephone: (217) 333-3350 Fax: (217) 333-9576 Email: office@math.uiuc.edu

College of Liberal Arts and Sciences
University of Illinois at Urbana-Champaign

Last modified May 2, 2008