Mathematics

www.math.uiuc.edu

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
	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.