The University’s general requirements for a bachelor’s degree are described in the Washington University Bulletin.

All math majors must complete Calculus I-II-III (Math 131-132-233) or the equivalent.  Each major must also complete one of five major tracks which are described below. No matter which track is followed, the student's permanent University record simply reads "Major in Mathematics."

In completing the major along any of the tracks, most students are required (or choose) to take

• Math 309 (Matrix Algebra)
• Math 318 (Calculus of Several Variables) or Math 308 (Mathematics for the Physical Sciences)  Students cannot count both 318 and 308 toward major requirements.
  
• Math 310 (Foundations for Higher Mathematics)
• Math 3200 (Elementary to Intermediate Statistics with Data Analysis
  

• An upper level mathematics course refers to a course with a number L24-300 or higher.  
  
• A Mathematics Department course with a number below 300 does not count toward upper level mathematics major requirements even if it is cross-listed with a higher number in some other department or program:  for example, if Math 2200 is cross-listed in another department as Lxx-3xx,  then taking the course under the number Lxx-3xx will not satisfy an upper-level mathematics requirement.
• Math 320 (no longer offered) was renumbered a few years ago as Math 2200 (not an upper level course), and Math 3200 was created as a stronger version of Math 320 for majors and minors.  Students with Math 320 already on their records are "grandfathered" and may still count Math 320 as an upper level course. But it is not possible to count both 320 and 3200 toward the upper level major requirements. 
• Generally speaking, courses from University College (the evening division of Arts & Sciences) do not count toward major requirements.
  
• Graduate level courses in mathematics are numbered in the 500's.  These courses are also open to qualified undergraduates. The introductory graduate sequences (5021-5022, 5031-5032, 5041-5042-5043, 5051-5052, 5061-5062) are the courses some undergraduates might consider.  Students who meet the prerequisites and who are willing to put in the extra effort for a course at this level can find it very rewarding.  But consultwith your advisor before registering.
• Transfer Courses   Department-approved courses transferred from other accredited colleges and universities may count toward the major requirements.  However,
  

  • courses transferred from a 2-year college (such as a community college) cannot be used to satisfy upper-level requirements in the major
    
  • both College and Department rules require at least half the upper level units required in a major be earned at Washington University (or at a Washington University approved Overseas Program).

• Counting lower level credits (such as Math 131-132-233 and Math 217) also to meet the requirements of another major or minor is OK.
• The Mathematics Department requires that each student's math major contain at least 18 "stand-alone" upper level math credits, that is, credits not counted to complete the requirements (including elective requirements) of any other major, minor, or program.  Because each math major track requires 7 or 8 upper level math courses, it is possible to double-count one of them (or perhaps two, depending on the major track) toward another major or minor.  

• A student should also check the double-counting policy of any other department involved. The statements above describe only  Mathematics Department policies.  

• An undergraduate with a plan for independent study and a faculty member to supervise the work can register for L24-400, Undergraduate Independent Study, using the section number corresponding to that faculty member.  (The section numbers are listed in the WUSTL Course Listing Book as part of the department header information.).
• Undergraduates should not register for L24-500 unless student and faculty member both agree that the independent study is clearly being done at the level of graduate work.
• No more than one 3-unit research/independent study course can count toward fulfilling major requirements.  However, additional independent studies that go beyond fulfilling the major requirements are welcome.

Since most majors take 309, 310, 318 (308) and frequently 3200, there is an overlap of courses in the tracks. Therefore, for most students, a decision on which track to follow by the end of the sophomore year is sufficient. Even after that, if courses have been planned carefully, a change of track might be possible.  Of course, making the decision as soon as it's practical will let a major choose courses in a specific direction and develop the strongest possible program.

Track A:  The Traditional Major
Math 310 (or 310W)	Foundations for Higher Mathematics
Math 4111-4121	Intro. to Analysis / Intro. to Lebesgue Integration
Math 429-430	Linear Algebra, Modern Algebra
Math 3200 (or Math 493)	Elementary to Intermediate statistics with Data Analysis  (or Probability)
Two other upper level math courses These courses could include Math 309 or 318 (308)	The topology courses Math 417-418 are recommended for students considering graduate study in mathematics.

Students planning on graduate school in mathematics are advised to get acquainted with and practice using TeX as undergraduates.  TeX is the premier word processsing and "typesetting" package in which nearly all professional papers and books are written nowadays.  Some versions of TeX are available free online.

 

Track B:  Probability and Statistics
Computer Science: one of CSE 131 or 200 Please read the comments on choosing a CSE course.  This advice was formulated with the help of Professor Ron Cytron of the CSE Department. The University College C-Programming course, U20-123 may NOT be automatically substituted.	Students should check with the Department of Computer Science about the semesters in which each of these courses is offered.
Math 309 Math 310 or 310W Math 318 (or, Math 308)	Matrix Algebra Foundations for Higher Mathematics Calculus of Several Variables (or, Math for the Physical Sciences)
Math 493-494	Probability/Mathematical Statistics (University College U20 4931-4941 may NOT be substituted)
Two other upper level probability and statistics courses chosen from the list on the right.  (Often, one of these is Math 3200, taken before Math 493-494)	3200, 322, 420, 408, 434, 439, 459, 475, 493, 494, 495, 5061, 5062 Students who plan to use statistics in practical settings are strongly encouraged to learn to use SAS -- for example, by taking Math 475

Business students may substitute the pair of courses QBA 120 and 121 (Managerial Statistics I, II) for Math 3200.  In that case, Math 3200 cannot also count toward the major.  (But see the "one-only" rule at the bottom of this web page.) Students with a sufficient background in computing may use Math 475 to fulfill the computer science requirement in this track.  But in that case Math 475 cannot also count as one of the required upper level electives.

Track C:  Applied	Although 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, computer science, or engineering.
i)    Physics 117-118 or 197-198  or, ii)   Two more advanced physics courses approved by the Mathematics Department, or iii)   CSE 131+CSE (132 or 241),  or iv)   CSE 131+CSE200 Please read the comments on choosing CSE courses. This advice was formulated with the help of Professor Ron Cytron of the CSE Department.	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 Math 310* or 310W Math 318 (or Math 308)	Matrix Algebra Foundations for Higher Mathematics Calculus of Several Variables (or Math for the Physical Sciences)
Math 449-450 Matlab is generally used in Math 449.  With a little basic computing background, you can pick it up there as you go, but the whole experience would be more pleasant if you had some prior acquaintance with Matlab.  Applied track majors might consider fulfilling part of the computing requirement using CSE 200;  or they might consider the 1-unit course CSE 100B as an extra course to ease into Matlab.	Numerical Applied Mathematics / Topics in Applied Mathematics
One additional upper level mathematics course useful in applications, chosen from the list on the right. **	Math 312, 350, 370, 371, 410, 415, 416, 449, 450, 481, 495, , and all upper level probability/statistics courses from the Mathematics Department  (see list under Track B)  Home-based outside the Math Department: Math 440C, 501C-504C; ESE 317, ESE 326, ESE 403 (Operations Research) However, courses in the list not home-based in the Mathematics Department are subject to the "one-only" rule at the bottom of this web page.)
One other upper level math course **	This course may or may not be "applications oriented"--your choice!

*   Computer Science Majors doing a second major in mathematics and who have received a B or better in CSE 240 (Logic and Discrete Mathematics) may replace Math 310 with an upper level math elective of their choosing. **   At least one elective course in probability/statistics is a good idea for any student in the applied track. ***  For emphasis:  only one upper level course can "double-count" toward the requirements of the math major and any other major or minor program. For example, an engineering student could only count one upper level course (such as Math 309 or ESE 309 or ESE 317 or ESE 326) toward both math and engineering requirements.

Track D:  Secondary Education This track can be done only together with a second major in secondary education.	The courses required in this major track are typical of those required for secondary certification in mathematics.
One of CSE 131 or CSE 200.  Please read the comments on picking a CSE course.   This advice was formulated with the help of Professor Ron Cytron of the CSE Department. The University College C-Programming course, U20-123 may NOT be automatically substituted.	Students should check with the Department of Computer Science about the semesters in which each of these courses is offered.
Math 309 Math 310* or 310W Math 318 (or Math 308)	Matrix Algebra Foundations for Higher Mathematics Calculus of Several Variables (or Math for the Physical Sciences)
Math 3200	Elementary to Intermediate Statistics with Data Analysis
Math 302	Elementary Geometry from an Advanced Point of View
Math 331	Algebraic Systems
One additional upper level mathematics course

Students in the Secondary Education track need to finish the math major requirements by the end of the first semester of their senior year because of student teaching in their final semester.    For planning purposes, it is important to note that Math 302 is offered in even-numbered fall semesters; and Math 331 is offered in odd-numbered fall semesters. Students in this track should meet immediately with an advisor in the Education Department to understand its requirements and how to coordinate them with the Discovery Curriculum requirements of the College.  The Education Department may also have good advice about certification requirements in other states, the possibilities for teaching in private schools that do not require state certification, earning certificaiton in a post-A.B. program, and related issues.  Since this major track 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 math courses to make possible a later switch into one of the other tracks.  Also, permission to student teach from the Department of Education requires a higher mathematics GPA (approximately a B average--check with the Department of Education) than the math major itself.  If it becomes clear to a student that such a math GPA looks unlikely, the student needs to consider a switch of major track. With special permission from 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.  However, such students should be aware that the course scheduling of Math 302 and 331 is set up to accommodate the schedules (including student teaching) of students seeking secondary certification. There might be irreconcilable conflicts with required education courses or student teaching for those in elementary or middle school education.

Track E:  Mathematics (Economics Emphasis) This track provides an opportunity for math majors to acquire a strong mathematics background in a track resembling the "traditional" Track A, but with less algebra and an added emphasis in probability/statistics.   This track would be excellent mathematical preparation for a graduate program in finance or economics.  Such students should also consult with the Business School or Economics Department to see what additional work in those subject areas would be required. The track could also be a good background, for a career in investment banking where pure math/economics candidates are sometimes attractive. Of course, rather than following this track, a student interested in economics might follow one of the other major tracks combined with a minor or second major in economics or finance.

Math 309 Math 310, or 310W	Matrix Algebra Foundations for Higher Mathematics
Math 3200, or Math 493	Elementary to Intermediate statistics with Data Analysis,  or Probability
Math 4111-4121	Introduction to Analysis - Introduction to Lebesgue Integration
Two other upper level mathematics courses chosen from the list on the right.	Math 429, 439, 456, 493, 494, 475, 495
In addition, the following Economics courses are required: Economics 103 and 104 (Microeconomics and  Macroeconomics) (the Economics Department recently renamed these as Econ 1011 and 1021) Economics 413  (Econometrics) At least one of Economics 401/402 (Price Theory / Income and Employment Theory) (the Economics Department recently renamed these courses 4011/4021 and modified the course titles to Intermediate Micro/Macro Theory)

***  For emphasis:  only one upper level mathematics course can "double-count" toward the requirements of the math major and any other major or minor program. For students in the Business School only: MECO 290 (Microeconomics) may substitute for Economics 103.  According to the Business School, students who take MECO 290 should probably not also take Economics 401. For the purposes of this major, they may take 402 or may propose another mathematically oriented upper level economics course for approval instead of 402  (Examples might include Economics 4111  (Optimization and Economic Theory) or Economics 467 (Game Theory)) MECO 292 (Global Economy) may be used in place of Economics 104.  However, such students might want to consider taking Economics 402. The pair of courses QBA 120 + QBA 121 (Managerial Statistics I, II) may replace Math 3200. In that case, Math 3200 cannot also count toward the major.  See also the "one-only" rule that follows, below.

• The "One-Only Rule"   For majors graduating after May 2010 at most one upper level mathematics requirement can be fulfilled by an approved course that is not home-based in the Mathematics Department.  Up through the May 2010 graduation, one exception to this rule can be discussed with Professor Ron Freiwald.   (This change was posted well in advance (May 20, 2008) so that students who were, at that time, finishing their sophomore years, would not need to upset their planning.)                                                                                                                            
•  A course is home-based in Mathematics if

i)   The department number of the course is L24, and

ii)  The course number does not end in a "C".  ( A terminal  "C" indicates that the course belongs to another department but is cross-listed as a math course. )

For example, the following courses are not home-based in the Mathematics Department:  E35-317, E35-326, QBA 120-121, L24-501C (home-based in the Physics Department), L24-440C (home-based in the Department of Computer Science & Engineering).

• Subject to this "one-only" rule,  students may substitute a course from the list below. Any other proposed substitutions, or any other variation from this rule, must be approved by the Department's Undergraduate Committee.

Approved courses for use in satisfying major requirements

• Any course from another department that is cross-listed as a mathematics L24 course: for example L24-501C, or L24-403C.  Such L24 courses always end with a "C".
• Philosophy 401  (Set Theory, as an upper level elective)
• Economics 413  (as an upper level p/stat elective)
• ESE 317  (as an upper level elective, but not a substitute for Math 318 or 308)
• ESE 326  (as an upper level elective, or in place of Math 3200;  but ESE 326 and Math 3200 cannot both be used to satisfy major requirements)
• ESE 403  (Operations Research, as an upper level elective)
• ESE 411  (Numerical Methods, as an upper level elective or to replace Math 449)  However, in this case, be sure to check with the instructor scheduled to teach Math 450 (a variable "topics" course) to be sure the next offering of Math 450 won't be assuming some special material from Math 449.)  Math 449 and ESE 411 cannot both be used to satisfy major requirements.
• CSE 441T (Advanced Algorithms)
  
• QBA 120 + QBA 121 (for Business students only, in place of Math 3200).  In this case, Math 3200 cannot also count toward major requirements.

• University College  (the evening division of Arts & Sciences) mathematics courses do not apply toward the major. University College math courses have department number U20 rather than L24.  This restriction applies even if course numbers or names match with L24 courses.  Any exceptions must be made, in advance, by the Department's Undergraduate Committee.  Approval would require a compelling special need for taking the course through University College and the Committee's judgment of the appropriateness of the course in a particular semester.