General Information

There are general requirements for majors described in the Washington University Bulletin.  In particular, note that

• in fulfilling the major requirements, there must be at least 18 "stand-alone" upper level credits, that is, credits not applied to fulfill the requirements of some other major, minor, or program. Students planning a double major should check with the College Office with any additional questions about double counting courses to fulfill the requirements of both majors.
• students with credits from other universities should note that College rules require at least half the upper level units required in a major (courses numbered 300 and above) be earned in Washington University programs.  Courses transferred from a 2-yr college (such as a community college) cannot count as upper level courses toward the minor. 

All majors are required to complete the introductory calculus sequence (Math 131-132-233, or its equivalent) and usually also Math 309, 318 and 310. We recommend that students consider taking Math 310 as early as possible. Stronger students who are comfortable with proof-oriented courses may be able to bypass Math 318 (with permission of an advisor) and instead take the 411-412 sequence directly.  In such cases, an upper level elective may be substituted for Math 318.

In addition, the department requires that each graduating senior participate in an exit interview during the senior year. Some seniors are invited to participate in a more detailed "extended exit interview."

Freshmen and Sophomores

Most majors should try to complete the calculus sequence and 309, 310 and 318 by the end of the sophomore year.  The following charts indicate possible course schedules for freshmen and sophomores, depend on where the student enters the calculus sequence, and assume the student will take Math 318 (see above).  Asterisks " *** " denote a possible elective such as 1201, 302, 320, or 331).  The courses 131, 132, 233 might be replaced by one of their alternate versions such as 1322, 1323, 201 or 2331 whenever these are offered.

 
The Major Tracks

In addition to the general requirements of the College of Arts and Sciences and the courses in the calculus sequence, each math major must fulfill the requirements listed under one of the major "tracks" described below. There is a overlap in the early requirements of all the tracks (most majors take 309, 318, 310), so the choice of a particular track doesn't need to be made immediately. For most students, a decision by the end of the sophomore year is sufficient. Of course, making the decision as soon as it's practical will let you focus your courses in a more specific direction and develop the strongest possible program.

• A grade of C- or better (CR/NCR = "pass/fail" not allowed) is required in each course fulfilling a major requirement.  The only exception is for courses (usually Calculus I or II) where the credit was earned through AP, IB, or a similar program.
  
• An upper level course means any 3-unit course numbered above 300
• No more than one 3-unit research/independent study course can count toward the requirements of the major.
• Students cannot receive credit toward the major for BOTH 308 and 318 toward the major.
• No University College mathematics course (U20-course) can be applied toward the major, even if the course is cross-listed "same as," except with prior approval by the Department's Undergraduate Committee.  Approval would involve consideration of the need for taking the course through University College and the Committee's judgment of the appropriateness of the course in a particular semester.
  

Track A:  The Traditional Major

In addition to the general requirements above:
 

Math 310	Foundations for Higher Mathematics
Math 411-412	Advanced Calculus I-II
Math 429-430	Linear Algebra, Modern Algebra
Math 320 or Math 493	Elementary Probability & Statistics,  or  Probability
Two other upper level math courses	(417-418 recommended but not required)

Track B:  Probability and Statistics

In addition to the general requirements above:
 

Math 1201, or one of CSE 126, 131, 200 (These CSE courses were formerly numbered as CS 136G, 101G, 265)	Programming in C,  or Introduction to Computing (The University College C-programming course, U20-123 may NOT be automatically substituted: that requires written permission from your advisor or Prof. Freiwald.)
Math 309	Matrix Algebra
Math 310	Foundations for Higher Mathematics
Math 318 or Math 308	Calculus of Several Variables
Math 493-494	Probability-Mathematical Statistics (University College U20 493-494 may NOT be automatically substituted)
Two other upper level probability and statistics courses**	***, ***

* *    For purposes of this requirement, the upper level probability and statistics courses are 320, 322, 420, 408, 434, 439, 475, 493, 494, 495.

NEW: students with an sufficient background in computing may substitute Math 475 for Math 1201 (or its alternatives).  In that case, however, Math 475 will not also count
as one of the required upper level probability and statistics electives.

In the fall semester, there is a special section of Math 320 (identified in the Course Listings) which is more intensive and introduces the SAS statistical package.  We strongly recommend that math majors taking 320 in the fall consider this section.

Students who wish to use statistics in practical settings are strongly encouraged to learn to use SAS, e.g., via Math 475.

Strong incoming students should also look at the Honors Program in Statistics
 

Track C:  Applied

In addition to the general requirements above:
 

Physics 117-118,  or CSE 131-132   or CSE 126  and (CSE 200 or CSE 131) (Note: CSE 131-132, CSE 126, and CSE 200 were formerly known as CS 101G-102G, CS 136G, and CS 265	Two substantially mathematical courses in a different department can sometimes be substituted, with departmental approval, if the substitution forms part of a coherent "applications" program
Math 217	Differential Equations
Math 309	Matrix Algebra
Math 310*	Foundations for Higher Mathematics
Math 318 or Math 308	Calculus of Several Variables
Three upper level mathematics courses useful in applications**	***, ***, ***
One other upper level math course	This course may or may not be applications oriented

*       Computer Science Majors who are doing a second major in math and who have received a B or better in CS 201 (Formal Foundations of Computer Science) may replace 310 with an upper level math elective of their choosing.
**    Courses counting for the "applications" requirement include: any upper level course in probability and statistics (see list under Track B);  Math 312, 350, 404, 405, 415, 416, 4361, 450, 481, 495, 501-502 (= Physics 501-502);  And from engineering: SSM 317 (Engineering Mathematics), SSM 481 (or CS353: not both) (Operations Research),
CS 465A (Numerical Methods).  Students cannot use BOTH SSM 465A and Math 404 toward the major requirements without special permission.
      
        NEW for majors declared after December 2003:  at least two of the upper level courses required in the applied track beyond 309-310-(308/318) must be courses taught by faculty in the department of mathematics (as opposed to courses taught in other departments, or courses cross-listed with math but taught by a faculty member of another department.) 
         While the applied track can be done as a "stand-alone" major, most students following this track combine it with substantial work in a math-related area such as physics, engineering, or economics.

Track D:  Secondary Education  This track can be done only as a double major with secondary education (or, with special permission, elementary or middle school education).

In addition to the general requirements above:

 

Math 1201 or one of CSE 131, CSE 126 or CSE 200 (These CSE courses were formerly numbered CS 101G, CS136G, CS265)	Programming in C,  or Introduction to Computing (The University College C-programming course, U20-123 may NOT be automatically substituted: that requires written permission from your advisor or Prof. Freiwald.)
Math 302	Geometry
Math 309	Matrix Algebra
Math 310	Foundations for Higher Mathematics
Math 318	Calculus of Several Variables
Math 320	Elementary Probability and Statistics
Math 331	Algebraic Systems
One other upper level math course	***

Students in the Secondary Education track usually need to finish the math major requirements by the end of the first semester of their senior year (because of student teaching in the second semester). Therefore, for planning purposes, it is important to note that Math 1201 and Math 302 are offered only in the fall semesters, and that
Math 331 is offered only during the spring semesters.

Since this version of the major requires an additional major in secondary education (including student teaching), students pursuing this track who are uncertain about continuing with the education major should plan their courses to make possible a later switch into one of the other tracks.

With special permission for the department's Undergraduate Committee, students who complete a major in elementary or middle school education may also complete a mathematics major using the "Secondary Education" track and subject to the same requirements.

Additional Comments About Major Requirements

• Occasional substitutions may be made in one of the sets of requirements above if they serve a reasonable purpose. Such substitutions must have prior approval of the department's Undergraduate Committee.
• There are a number of courses in other departments which, with the prior approval of your advisor, can sometimes be used to satisfy one of the department requirements for "upper level math courses". These include: CS 353 (Operations Analysis I),  SSM 465A (Numerical Methods), Philosophy 401 (Set Theory), Philosophy 403-404 (Mathematical Logic I, II)
• The introductory graduate level math courses (421-422, 431-432, 441-442, 451-452) are open to qualified undergraduates. Undergraduates who have satisfied the prerequisites and who are willing to put in the extra effort often find these courses very rewarding.
• Sometimes undergraduates can enroll in supervised independent study. A student who has a plan for independent work and who has found a faculty member who will supervise the work should discuss the possibility with his/her advisor.
  
• Students are encouraged to consider a senior project (whether or not for honors).  Some of our faculty have listed ideas (some much harder, some easier) for projects at various levels.
• Students planning on spending a semester or year abroad should consult with their advisors or Prof. Ron Freiwald as early as possible.