Mathematics
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. Students must complete Part I and an option from Part II.
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.
The Department of Mathematics sponsors the Mathematics major and minor, the Mathematics teaching option, the Actuarial Science major, and a major in Mathematics and Computer Science in coordination with the Department of Computer Science.
Major in Sciences and Letters Curriculum
E-mail: office@math.uiuc.edu
Degree title: Bachelor of Science in Liberal Arts and Sciences
Minimum required major and supporting course work normally equates to 52-61 hours including 27 hours beyond calculus, 10-12 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 Mathematics Honor Program.
Part I
| Hours | Requirements |
|---|---|
| 10-12 | Calculus through one of the following: |
MATH 242—Calculus of Several Variables |
|
MATH 243—Calculus III Plus or equivalent |
|
| 3 | MATH 347—Fundamental Mathematics or MATH 348— Fundamental Mathematics-ACP |
| 3 | Select one of the following: |
MATH 415—Linear Algebra |
|
MATH 418—Advanced Linear Algebra |
|
MATH 426—Honors Linear Algebra |
|
| 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 I |
|
STAT 400—Statistics and Probability I |
|
| 3 | Select one of the following: |
CS 101—Intro to Computing, Eng & Sci1 |
|
CS 125— Intro to Computer Science |
|
| 12 | Approved supporting course work or any minor |
1. Students with 2 hours credit in CS 101 must take CS 110
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 300-, 400- or 500-level Math courses 2 |
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—Advanced Linear Algebra |
| 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 | MATH 448—Complex Variables |
| 6 | Two additional 300-, 400- or 500-level Math courses 2 |
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: |
CS 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 |
|
| 3 | One additional 300-, 400- or 500-level Math course 2 |
Operations Research Option
| Hours | Requirements |
|---|---|
| 3 | CS 257—Numerical Methods |
| 3 | Select one of the following: |
MATH 412—Graph Theory |
|
MATH 413—Intro to Combinatorics |
|
| 4 | STAT 400 —Statistics and Probability I |
| 3 | Select one of the following: |
STAT 410—Statistics and Probability II |
|
STAT 420—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 advisor 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. Departmental distinction: A subcommittee of the Mathematics Area Committee will select students for distinction based upon grades in the mathematics, overall grade point average, and evidence of accomplishment in the teaching portion of the program.
Prerequisites to transfer to the Teaching Option: EPSY 201, EPS 201, MATH 220, 230, 242 (or MATH 243), 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 (37 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 or MATH 403—Euclidean Geometry |
| 3 | Select one of the following: |
MATH 417—Intro to Abstract Algebra |
|
MATH 453—Elementary Theory of Numbers |
|
| 9 | Three additional advanced mathematics courses |
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. Students with 2 hours credit
in CS 101 must take CS 110.
2. In the Applied Mathematics and Operations
Research options MATH/CS 257 will be accepted as a substitute for
an advanced course in this major.
Minor in Mathematics
E-mail: office@math.uiuc.edu
Web address for department: http://www.math.uiuc.edu
| Hours | Requirements |
|---|---|
| 3-12 | Calculus through one of the following |
MATH 242—Calculus of Several Variables |
|
MATH 243—Calculus III Plus |
|
| 15 | Completed in one of two ways: |
| EITHER | |
MATH 347—Fundamental Mathematics |
|
or |
|
MATH 348—Fundamental Mathematics-ACP |
|
and |
|
12 hours of courses chosen from at least two of the following lists of courses. |
|
| OR | |
15 hours of courses chosen from at least two of the following lists of courses. |
|
| Algebra: | |
MATH 415—Linear Algebra |
|
MATH 417—Intro to Abstract Algebra |
|
MATH 418—Advanced Linear Algebra |
|
MATH 421—Symbolic Algebra |
|
MATH 426—Honors Linear Algebra |
|
MATH 427—Honors Abstract Algebra |
|
MATH 453—Elementary Theory of Numbers |
|
| Discrete Mathematics: | |
MATH 412—Graph Theory |
|
MATH 413—Intro to Combinatorial |
|
MATH 414—Mathematical Logic |
|
MATH 482—Linear Programming |
|
| Analysis: | |
MATH 380—Advanced Calculus |
|
MATH 385—Intro Differential Equations |
|
MATH 386—Intro to Differential Eq with Plus |
|
MATH 424—Honors Real Analysis |
|
MATH 425—Honors Advanced Analysis |
|
MATH 441—Differential Equations |
|
MATH 442—Intro Partial Diff Equations |
|
MATH 444—Elementary Real Analysis |
|
MATH 446—Applied Complex Variables |
|
MATH 447—Real Variables |
|
MATH 448—Complex Variables |
|
CS 450—Numerical Analysis Intro |
|
MATH 484—Nonlinear Programming |
|
MATH 489—Differential Equations II |
|
| Geometry: | |
MATH 402—Non Euclidean Geometry |
|
MATH 403—Euclidean Geometry |
|
MATH 423—Differential Geometry |
|
MATH 428—Honors Geometric Analysis |
|
MATH 432—Set Theory and Topology |
|
MATH 481—Vector and Tensor Analysis |
|
| Probability and Statistics: | |
MATH 461—Probability Theory I |
|
STAT 400—Statistics and Probability I |
|
STAT 410—Statistics and Probability II |
|
MATH 466—Probability Theory II |
|
| 18 | Minimum total hours required |
Teacher Education Minor in Mathematics
For students in teacher education curricula other than mathematics who wish to be qualified to teach mathematics at the high school or middle school level.
E-mail: office@math.uiuc.edu
Web address for department: http://www.math.uiuc.edu
| Hours | Requirements to Teach Mathematics in Grades 9-12 |
|---|---|
| 8 | MATH 220—Calculus I |
| MATH 230—Calculus II; or equivalent | |
| 3 | Methods courses in the teaching of mathematics: |
CI 401—Intro Tchg in a Diverse Societ |
|
| 14 | At least 14 hours of work including the following: |
MATH 242—Calculus of Several Variables |
|
MATH 402—Non Euclidean Geometry |
|
| 8 | Courses from at least two areas other than applied mathematics and geometry, to be chosen from the following list: |
| Computer Science: | |
CS 101— Intro to Computing, Eng & Sci |
|
CS 105— Intro to Computing, Non-Tech |
|
| Linear Algebra: | |
MATH 125—Elementary Linear Algebra |
|
MATH 225—Introductory Matrix Theory |
|
MATH 415—Linear Algebra |
|
| Modern Algebra: | |
MATH 413—Intro to Combinatorics |
|
MATH 417—Intro to Abstract Algebra |
|
MATH 453—Elementary Theory of Numbers |
|
| Advanced Aspects of Euclidean Geometry: | |
MATH 403—Euclidean Geometry |
|
| Applied Mathematics: | |
MATH 347—Fundamental Mathematics or MATH 348- Fundamental Mathematics-ACP |
|
MATH 380—Advanced Calculus |
|
MATH 385—Intro Differential Equations |
|
MATH 441—Differential Equations |
|
MATH 444—Elementary Real Analysis |
|
MATH 446—Applied Complex Variables |
|
| Probability-Statistics: | |
STAT 400/MATH 463—Statistics and Probability I |
|
| History of Calculus: | |
MATH 406—History of Calculus |
| Hours | Requirements to Teach Mathematics in Grades 6-8 |
|---|---|
| 3 | CI 431— Tchg Elementary Mathematics |
| 15 | Courses from at least four of the following areas: |
| Math For Elementary Teachers: | |
MATH 117—Elementary Mathematics |
|
MATH 103—Theory of Arithmetic |
|
| Calculus: | |
MATH 220—Calculus I |
|
MATH 230—Calculus II |
|
| Modern Algebra: | |
MATH 413—Intro to Combinatorics |
|
MATH 417—Intro to Abstract Algebra |
|
MATH 453—Elementary Theory of Numbers |
|
| Topics on Geometry: | |
MATH 402—Non Euclidean Geometry |
|
| Computer Science: | |
CS 101— Intro to Computing, Eng & Sci |
|
CS 105 — Intro to Computing, Non-Tech |
|
| Probability-Statistics: | |
STAT 100/MATH 161—Statistics |
|
STAT 400/MATH 463—Statistics and Probability I |
|
| History of Mathematics: | |
MATH 406—History of Calculus |
Students are advised that additional course work is necessary to teach in grades six through eight. Consult the certification officer in 130 Education Building for additional information.