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Home > Undergraduate > Degree Requirements

Undergraduate Program: Degree Requirements

Major | Minor | Special Program Requirements
Courses in Other Departments | Independent Study (399) | Departmental Honors
 

MAJOR

There are special major requirements for ISP and MMSS Majors.

Basic courses: 220 and 224 (or 212, 213, 214); 230, 234, and 240 (or 281-1,2,3 or 285-1,2,3 or 290-1,2,3 or 291-1,2,3); or equivalent

Required major courses: a total of nine 300-level courses offered by the department, among these must be one of the complete sequences

• 310-1,2,3
• 320-1,2,3
• 321-1,2,3
• 330-1,2,3
• 331-1,2,3.
• In addition, those who have NOT taken and passed at least one quarter of Math 320, Math 321, Math 330, or Math 331 with a grade of C- or better must take Math 334-0.

Math 334-0 is also strongly recommended for students considering graduate school, as well as for those (such as potential actuaries) considering certain other careers.. As usual, you should seek advice from the department about whether you should take 334.

With the prior approval of the department, as many as 3 of these 9 courses may be 300-level courses offered by other departments which focus on serious applications of mathematics or have substantial mathematical content.

Important note: those who took 330-1 (337-1 before Fall 2005) prior to academic year 2004/2005 may use that course to substitute for 334. The courses 334 and 330-1 (337-1 before Fall 2005), if taken prior to academic year 2004/5, cannot both be counted for the major without consent of the department (although both may count toward the 45 courses required for graduation).

Some advice

Most mathematics majors should take 300-0 as early as possible in their course of study. Those with a bent for abstraction may be able to skip this course and should consult with the director of undergraduate studies. Students who passed 291-1 with a grade of A- or above may skip 300.

While 250 is not required of mathematics majors, it is strongly recommended for those with a second major or a minor in a science, and, of course, for those planning to take a 300-level course which has 250 as a prerequisite.

Students considering graduate school in mathematics should take all of 321 (or 320) and 331 (or 330) as well as 344.

Math majors with a second major in Economics should consider taking Math 310-1. Those who do so are usually exempted from Stat 210 by the Economics department, and are advised to skip Econ 281 and go directly into Econ 381-1. (Before acting on this advice, they should check with the Director of Undergraduate Studies in Economics.)

MINOR

Basic courses: 220 and 224 (or 212, 213, 214); 230, 234, and 240 (or 281-1,2,3 or 285-1,2,3 or 290-1,2,3 or 291-1,2,3); or equivalent

Required minor courses: a total of six 300-level courses offered by the department, including at least one 2-quarter sequence chosen from:

• 310-1,2
• 320-1,2
• 321-1,2
• 330-1,2
• 331-1,2

To fulfill the sequence requirement, students may, with the prior approval of the director of undergraduate studies, substitute:

• 310-2,3, 320-2,3, 321-2,3, 330-2,3, or 331-2,3 where appropriate
• other 2-quarter sequences regularly offered by the department that provide a focused, in-depth introduction to a subfield of mathematics

Up to 2 of these 6 courses may, with the prior approval of the director of undergraduate studies, be 300-level courses offered by other departments which focus on serious applications of mathematics or have substantial mathematical content. No such course, however, may be simultaneously counted toward the student's major requirements or, if the course is offered in a school other than Weinberg College, toward the student's school requirements.

SPECIAL PROGRAM REQUIREMENTS

Mathematics major requirements for students who complete an ISP or MMSS major differ from the standard ones; MMSS majors may also obtain a minor in Mathematics by completing a special set of requirements.

Mathematics Major Requirements for ISP Majors

Students majoring in ISP who wish to complete a second major in mathematics may not substitute ISP 398 for any mathematics course in the ISP curriculum, and must, in addition complete one of the complete sequences:

• 320-1,2,3 Real Analyis or 321-1,2,3 MENU: Real Analysis
• 330-1,2,3 Abstract Algebra or 331-1,2,3 MENU: Abstract Algebra.

It is highly recommended (but not required) that ISP students planning graduate work in mathematics take both a real analysis (320/321) and an algebra (330/331) sequence.

Mathematics Major Requirements for MMSS Majors

Students majoring in MMSS who wish to obtain a major in mathematics must complete all 300-level mathematics courses in the MMSS curriculum (300-0; 385-0, 386-1,2), a social science major of their choice, and six additional mathematics courses.

Three of these courses must be one of the full-year sequences:

• 320-1,2,3 Real Analyis, or
• 321-1,2,3 MENU: Real Analysis

The other 3 must be chosen from

• 310-2,3 Probability and Stochastic Processes (even though MMSS students cannot receive credit for 310-1, those planning to take 310-2,3 would be well advised to sit in on 310-1)
• 330-1,2,3 Abstract Algebra or 331-1,2,3 MENU: Abstract Algebra
• 334-0 Linear Algebra: second course
• 344-1,2 Introduction to Topology
• 360-3 MENU: Applied Analysis (Complex Variables)
• 366-1 Mathematical Models in Finance
• 368-0 Introduction to Optimization

Those MMSS students who are given permission to skip Math 300 (which is normally part of their MMSS requirements) must substitute another 300-level mathematics course for Math 300 in order to complete a Mathematics major.

It is highly recommended (but not required) that MMSS students planning graduate work in mathematics take one of the algebra sequences (330/331).

Mathematics Minor Requirements for MMSS Majors

MMSS students who fulfill all of the requirements for the MMSS major, including Math 385-0, Math 386-1,2, and Math 300 may complete a minor in mathematics by taking one of the full-year sequences:

• 320-1,2,3 Real Analyis, or
• 321-1,2,3 MENU: Real Analysis

Those MMSS students who are given permission to skip Math 300 (which is normally part of their MMSS requirements) must substitute another 300-level mathematics course for Math 300 in order to complete a Mathematics minor.

COURSES IN OTHER DEPARTMENTS

With the prior approval of the Director of Undergraduate Studies in Mathematics (dus@math.northwestern.edu), up to three 300-level courses which focus on serious applications of mathematics or have substantial mathematical content offered by other departments may be counted towards a Mathematics major. Below is a list of courses which have been approved in the past for this purpose.

Before registering for one of these courses, be sure that you have taken the necessary prerequisites, that you are not counting the course towards another major, and that you have received the necessary approval.

INDEPENDENT STUDY (399)

1. General Requirements

Students interested in a mathematical topic or area not covered in our standard curriculum may wish to pursue Independent Study. There are several general conditions that must be met:

• the topic should be mathematics at the 300-level or higher
• the topic must not be one covered in a course that is normally offered in the department
• written materials (texts and/or mathematics papers) must be available covering the topic
• the work must be supervised by a member of the Mathematics Department
• the student must have mastered any prerequisite material required for the independent study topic
• the student and his/her supervisor must submit a 399 petition to the Director of Undergraduate Studies for approval

2. Choosing a topic and a supervisor

Independent study most often arises from a student's desire to continue deeper study of a topic encountered in course work. For example, someone fascinated by the material in our one-quarter topology course (344-0) might want to learn more about that subject. In such a case, the first step is to have a discussion with the professor who taught the course. Even if s/he is unable to supervise an independent study project, s/he might be able to suggest another instructor who can.

The desire to understand the mathematics underlying another subject, such as relativity theory or finance sometimes leads to independent study. Browsing the faculty list is a way of identifying a faculty member with expertise in the relevant mathematics.

Topics not covered in our current curriculum, such as algebraic geometry, can make interesting material for independent work.

Students who need help in pinpointing exactly what to study, as well as those seeking help in finding a supervisor, should consult the Director of Undergraduate Studies.

3. Procedural Matters

Once a topic has been chosen, an appropriate member of the department should be asked to supervise the independent study. The same person may be consulted about finding a specific topic within a general area. (Suggestions for identifying potential supervisors are in the preceding paragraph.) Agreement should be reached on what texts will be used, what specific chapters or sections will be read, what specific work must be done, and how often meetings with the supervisor will take place. That agreement should be formalized on a copy of the 399 petition. The petition should then be submitted to the Director of Undergraduate Studies (in most cases, it will be sufficient to leave it in the Math office for the DUS) for approval.

The staff in the Math office will assign a section number and a permission number for registration in Math 399-0 upon presentation of the approved petition.

These steps take time! The process of finding a supervisor should commence at least 3 weeks before registration opens for the quarter in which the independent study is to take place.

DEPARTMENTAL HONORS

1. General Requirements

Majors with outstanding records may be nominated for graduation with department honors. To be eligible for such nomination, a student must:

• complete 320 (or 321) and 330 (or 331) or the equivalent (in exceptional cases, students who have not completed these courses may also be considered for honors)
• complete with distinction two quarters of independent study or two quarters of a 400-level course
• complete a project which culminates in an honors thesis
• have a grade point average greater than or equal to 3.5 in courses which satisfy major requirements (in this calculation, courses such as those in the calculus sequence which are prerequisites for the major are not counted)

2. The Honors Project

An honors project must be an independent work by the student, devoted to some sharply focused subject in pure or applied mathematics not covered in normal course work. It should attest to the student's in-depth understanding of the material and his or her ability to use the material in a substantial manner.

There are three general forms such a project may take, in part or in combination; other possibilities may be considered if sufficiently original in concept.

• The project may be a thesis written after intense immersion in some specialized topic in advanced mathematics. The thesis itself should be an extended exploration of this topic leading the reader to the cutting edge of research in the area.
• The project may be a thesis written after historical investigation of important mathematical concepts in which the mathematical results themselves are described and their development explained and set in the proper historical framework.
• The project may involve an experimental investigation of some interesting mathematical phenomena through the use of a computer program or programs. For such a project, the student should present, in addition to the program, an explanation of the nature of the algorithm, together with a discussion of the results of the calculation and their meaning.

A student's work towards an honors project/thesis shall be supervised by a faculty member of the department (the "advisor"), who helps the student frame the project and provides necessary guidance and motivation. The honors thesis must be evaluated independently by at least one other faculty member in the department. Both these faculty members shall present their recommendations in writing to the Departmental Honors Committee, which votes on whether or not to nominate the candidate for honors. The department's Director of Undergraduate Studies appoints the Departmental Honors Committee each year, in the absence of such an appointment, the Undergraduate Committee of the department shall constitute the department's Honors Committee.

3. Procedural Matters

Students interested in pursuing work that may lead to nomination for department honors should speak with the department's Director of Undergraduate Studies by the end of the junior year (in exceptional circumstances, they may do so no later than the fall quarter of the senior year). Students should come prepared with some ideas of what they may wish to pursue as a topic for honors work (in which case the Director of Undergraduate Studies will assist the student in locating a member of the faculty with whom the student can frame an appropriate project) and/or the names of faculty members who they may wish to have as their honors advisor (this might be someone who has taught the student in a 300-level course, or an expert in the subject which the student wishes to pursue). A student might also locate a faculty supervisor independently; if so, the Director of Undergraduate Studies should be informed of the arrangement immediately, certainly no later than the end of the fall quarter of the student's senior year.

Two paper copies of the student's completed honors project must be submitted to the Director of Undergraduate Studies by a due date (usually early in the last week of April to allow adequate time to examine the project) which is communicated to students and their advisers in November of each academic year. The thesis should be typed in the TEX markup language and bound in a spiral binding. Students may, if they wish, also submit their theses electronically as a .pdf file (in addition to the paper copies).

A student with concerns about the supervision he or she is receiving should speak with the Director of Undergraduate Studies, unless the honors advisor is the Director of Undergraduate Studies, in which case the student should speak with the Chair of the Department.

In case of a dispute between the project supervisor and the student as to the merits of the project, the Director of Undergraduate Studies and the department Chair shall act as a committee of appeal. This two person group has final authority with respect to the department's nomination.