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The Math Major

General Information

The general University requirements for a bachelor’s degree can be found in the Washington University Bulletin; these will vary between schools (Arts & Sciences, Engineering, Business, Art, Architecture).

Study Abroad  Students planning to spend a semester or year abroad should consult with their advisors or Prof. Ron Freiwald as early as possible.  If the plan is for just one semester abroad, then there needs to be a discussion about which semester, fall or spring, is preferable to go. This may depend on the courses a student has already taken and also on the major track the student is following.  For example: what are the prerequisites for courses available at the school where the student wants to go?  does their spring semester have a selection of math courses that aren't continuations of course from the earlier semester?  or, if the student goes in the fall, what math courses will be available at W.U. when the student returns in the spring?  

The Budapest Semesters in Mathematics program is an excellent opportunity abroad for serious mathematics students.  For some students, the Math in Moscow program might also be of interest.

Latin Honors and Distinction in Mathematics Award  Strong students may want to look ahead in the Handbook at the requirements for "Honors" and "Distinction" and perhaps build those requirements into their major plans.

Major Requirements

A math major must complete Calculus I-II-III (Math 131-132-233) or the equivalent, and meet the course requirements in one of the five major tracks.  The major tracks and the courses required are described below.  Be sure to look at the rules about double-counting, independent study, courses from other departments, … that are listed at the end of this section.  No matter which track is followed, the student’s permanent university record simply reads “Major in Mathematics.”

The department also requires that each graduating major participate in an exit interview late in the senior year.  Some seniors are asked to participate instead in a more detailed extended exit interview.

A major must complete one of the following major tracks.  The choice should be discussed with an advisor.  It depends partly on the student's plans after graduation, but also on the student's tastes and abilities.  Since most majors take 309, 310, 318 (308) and 3200, there is overlap among the tracks, and for most students a decision by the end of the sophomore year about which track to follow is soon enough.  Even after that, if courses have been planned carefully, a change of track can be possible.  Of course, making the decision as soon as it's practical will let a major choose courses to develop the best possible program.

The requirements listed below for each track assume that the student has completed  the Calculus I-II-III sequence, or the equivalent.  

Be sure to look at the rules about double-counting, independent study, courses from other departments, … that are listed at the bottom of this web page. 

If you need to choose a Computer Science course, please read these comments on picking a CSE course.   This advice was formulated with the help of Professor Ron Cytron of the CSE Department.

Comments about each track

Be sure to look at the rules about double-counting, independent study, courses from other departments, … that are listed at the end of this section.

Track A) Traditional  

• Students planning on graduate school in mathematics should get acquainted with using TeX. TeX is the premier software package for technical typesetting and word processing in mathematics. It is used nowadays to prepare manuscripts for nearly all professional papers and books.  See, for example, the Wikipedia entry for TeX.  Some versions of TeX are available free online.
• The topology sequence Math 417-418 is also recommended for students considering graduate study in mathematics.

• Students who plan to use statistics in practical settings are strongly encouraged to learn to use SAS—for example, by taking Math 475.
• 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. 
• University College U20 4931-4941 may NOT be substituted for L24 Math 493-494, and U20-1201 cannot be substituted for the required computer science course.
• Business School students who enrolled at WU as full-time students before Fall 2010 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.   For students entering WU in Fall 2010 or later, QBA 120 and 121 can no longer be counted as an upper level mathematics course to fulfill major requirements.

• 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.  With departmental approval, two substantially mathematical courses in a different department can sometimes be substituted for the physics or computer sciences requirement if the substitution forms part of a coherent “applications” program. In some other departments, “sufficiently mathematical” may require that the courses be upper level.
• 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 early-on using CSE 200;  or they might consider the 1-unit course CSE 100B as an extra course to ease into Matlab.
• Computer Science Majors doing a second major in mathematics who receive a B or better in CSE 240 (Logic and Discrete Mathematics) may replace Math 310 with an upper level math elective of their choosing.  Conversely, the CSE Department may allow some majors to substitute Math 310 for their CSE 240 requirement (check with the CES Department).

Track D) Mathematics & 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 certification as a secondary school mathematics teacher.
• Majors in this track should meet immediately with an advisor in the Education Department to understand its requirements and how to coordinate them with fulfilling the general education 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 certification 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, placement by the Department of Education for student teaching requires a higher mathematics GPA than the math major itself (approximately a B average--check with the Department of Education).  If it becomes clear to a student that such a math GPA looks unlikely, the student needs to consider a switch of major track.
• Majors in this track need to finish the math major requirements by the end of the first semester of the senior year since they will be student teaching and taking special education courses during their eighth semester.  Therefore some careful planning is needed:  in particular,             

• With special permission from the department's Undergraduate Committee, students who complete a major in elementary or middle school education, including student teaching, may also complete a mathematics major using the “Secondary Education” track and subject to the same requirements. But such students should be aware that the course scheduling of Math 302 and 331 is planned to work together with the schedules (including student teaching) of students seeking secondary certification. There very well could be irreconcilable conflicts between math course requirements and  required education courses or student teaching for elementary or middle school education majors.

• This track provides a strong mathematics background that resembles the “traditional track,” but with less algebra and more probability/statistics.  It was designed after consultation with the Department of Economics and Olin Business School and should be particularly useful as a “second major” to economics majors planning to go to graduate school in economics, or to students planning to enter a graduate program in finance.  Both these options will make use of the required analysis sequence (4111-4121).  The track could also be a good background, for a career in investment banking where pure math/economics candidates are sometimes attractive.
• For students in the Business School only:

         MECO 290 (Microeconomics) may substitute for Economics 1011.  According to the Business School, students who take MECO 290 should probably not also take Economics 4011.  So for the purposes of this major, these students may instead Economics 4021 or may propose, instead, another mathematically oriented upper level economics course for approval instead of 4021.  (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 1021.  However, such students might want to consider taking Economics 4021.

        Business School students who enrolled at WU as full-time students before Fall 2010 may substitute the pair of courses QBA120 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 end of this section.)   For students entering WU in Fall 2010 or later QBA 120 and 121 can no longer be counted as an upper level mathematics course for the purpose of fulfilling major requirements.

• An “upper level” mathematics course is one numbered L24-300 or higher.  A course with a lower number does not count toward upper mathematics requirements even if it is cross-listed as an upper level course in another department or program:  for example, if Math 2200 were cross-listed by another department as Lxx-3xx, then registering for Lxx-3xx would not satisfy an upper-level mathematics requirement.
•  Required courses must be completed with a letter grade of C- or better.
•  Math 318 and 308 cannot both be used.
• Courses transferred from other accredited colleges and universities with department approval can be counted toward the major.  However,

• courses transferred from a 2-year college (such as a community college) cannot be used to satisfy upper level requirements.  For example, if you took a community college course that seemed roughly similar to 309, we might transfer the credit “as” 309 but the course would not count toward the major.  However, in such a case, you may ask the Mathematics Department for permission to allow you to substitute an additional elective in place of 309 rather than retaking the course.
• at least half the upper level units required in a major or minor must be earned at Washington University or in a Washington University approved Overseas Study Program.

• Courses from University College cannot be used.  Any exceptions must be made, in advance, by the Department's Undergraduate Committee.  Approval requires 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.
• 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.  At most 3 units for independent study or research work can count to fulfill major requirements.  However, additional independent study credits that go beyond fulfilling the major requirements are welcome.
• At least 18 of the required upper level units in a major must be satisfied using courses not double-counted toward the requirements (including "elective requirements") of any other major or minor program.  However, double-counting lower level courses (such as Math 131-132-233 and Math 217) to also meet the requirements of another major or minor is OK.   Students should also check the double-counting policy of any other department involved. The statements above describe only the policy of the Mathematics Department.   
• 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 consult with your advisor before registering.
• Approved course substitutions in each track are listed below.  In all cases at most one substitution can be made using a course not home-based in the Department of Mathematics.

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:  ESE-317, ESE-326, QBA 120-121, L24-501C (home-based in the

        Physics Department), L24-440C (home-based in the Department of Computer   

        Science & Engineering), L24-403C (home-based in the Philosophy Department

Majors may substitute at most one 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 “one-only” courses that can satisy major requirements:

• Any course from another department that is cross-listed as a mathematics L24 course:  for example, L24-501C, L24-440C, or L24-403C.  Such L24 courses always end with a "C".
• Philosophy 401, 403 or 404  (Set Theory, Mathematical Logic I or II) 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 course whose topic can vary) 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.
• For Business School students (only) who entered WU as full time students before fall 2010: QBA 120 + QBA 121 in place of Math 3200).  In this case, Math 3200 cannot also count toward major requirements. 
  For all students entering WU in fall 2010 or later, QBA 120-121 can no longer count as an upper level mathematics course.