Mathematics Department
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Mathematics Advising Handbook

Department of Mathematics
Brandeis University
Fall 2007

Introduction

This is a supplement to the undergraduate Mathematics program description appearing in the annual Brandeis University Bulletin. It is intended to clarify some of the rules relating to the Mathematics program, and help students design their Mathematics concentration. Most of the "official" material may be found in the University Bulletin,but students can find additional advice and perspective on the Mathematics program here.

Students planning to take Math 10a or 10b, or to place into a course at the next level such as Math 15a, 20a, 21a or 22a, must take the online mathematics placement exam. This exam, along with instructions for scoring and interpreting the results, can found on the Placement Exam Page. Please read all the instructions carefully. Descriptions of Math 5a, 10a, 10b, 15a, 20a, 21a and 22a can also be found on this page.

Students, both majors and non-concentrators, are always welcome to discuss their own programs and other issues. The department members who are in charge of advising students for the academic year 2005-2006 are:

• Susan Parker: Elementary Mathematics Coordinator (EMC)
• Alan Mayer: Undergraduate Advising Head (UAH)--Fall 2007
• Dmitry Kleinbock: Undergraduate Advising Head (UAH)--Spring 2008.

1. Concentration Requirements

Regular track. The regular track to a degree with Mathematics Major requires a total of nine courses:

1. MATH 21a, 22a, or 15a; MATH 21b, 22b, or 20a.
2. MATH 23b (or exemption via examination; see special note below).
3. MATH 35a, 40a, or 45a.
4. MATH 28a or 30a.
5. Four additional courses from: MATH courses numbered at least 27, or cross-listed courses (currently COSI 88a, COSI 188a, and PHIL 106b).

Honors. A degree with Honors Mathematics Major requires a total of eleven courses:

1. MATH 21a, 22a, or 15a; MATH 21b, 22b, or 20a.
2. MATH 23b (or exemption via examination; see special note below).
3. MATH 35a, 40a, or 45a.
4. MATH 28a or 30a.
5. Six additional courses from: MATH courses numbered at least 27, or cross-listed courses (currently COSI 88a, COSI 188a, and PHIL 106b).

Special note regarding MATH 23b. Beginning in the academic year 1999-2000, students will be required to take a course (MATH 23b) on techniques of proof. The course is intended to better prepare students for the upper level courses, where they will be expected to write and understand moderately complicated proofs. Students may be exempted from this requirement by satisfactory performance on a placement exam to be given before pre-enrollment in October. Ordinarily, MATH 23b must be taken (or exemption granted) by the end of the sophomore year; permission to do otherwise must be given by the UA or UAH. The requirement of taking MATH 23b applies only to students who declare a major starting in September 1998. The content of MATH 23b is more fully described in the Bulletin.

Teacher preparation track. The teacher preparation track entitles students to gain certification to teach high school in Massachusetts. The requirements are:

1. MATH 21a, 22a, or 15a;MATH 21b, 22b, or 20a.
2. MATH 23b (or exemption via examination; see special note above).
3. MATH 35a, 40a, or 45a.
4. MATH 28a or 30a.
5. MATH 8a or 36a.
6. Two additional courses from: MATH courses numbered at least 27, or cross-listed courses (currently COSI 88a, COSI 188a, and PHIL 106b).
7. A computer science course numbered 10 or higher.
8. Completion of the High School Teacher Certification Program.

Minor in Mathematics. A degree with Mathematics Minor requires a total of five courses:

1. MATH 21a, 22a, or 15a; MATH 21b, 22b, or 20a.
2. Three additional courses from: MATH courses numbered at least 27, or cross-listed courses (currently COSI 88a, COSI 188a, and PHIL 106b).

Exclusions. A student may not receive credit for more than one of MATH 15a, 21a, and 22a; or MATH 20a, 21b, and 22b. or MATH 28a and 30a; or MATH 28b and 30b.

2. Substitutions

1. A course taken in other Brandeis departments or elsewhere may be substituted for one of the required math courses, only with permission of the UA or the UAH. No substitutions are allowed for the Mathematics Minor or for the courses in the Teacher Preparation Track.
2. No more than one course may be substituted for, and only for one of the electives (not from item A, B or C).
3. When a course substitution is proposed by a student, the UA or the UAH shall grant or deny the request on the basis of the merit of the proposed substitution. The substituted course must be at least comparable in substance, breadth and depth, to one of the elective MATH courses. A course which, say, simply applies some multivariable calculus to study problems in some other field would not be suitable; the course must actually teach the student some new mathematical ideas and techniques. Finally, the substituted course must not duplicate or overlap substantially with another course taken for credit.
4. Courses now being considered as possible valid substitutions for MATH courses are: ECON 184b, ECON 189a, IEF 284b, COSI 190a, COSI 240b, PHYS 110a (in lieu of MATH 35a).

3. Placement into elementary courses, calculus, and upper level courses

Placement into calculus courses can be confusing and occasionally needs to be adjusted after the first class or two. Instructors in MATH 10a and 10b give a diagnostic quiz on the first day of class to check placement. Any student who receives a low score on this test will be required to switch to the appropriate course.

The MATH AP exams (AB and BC) provide additional information which is often useful in determining placements in the first year. Note that there are several different (but related) issues surrounding the AP exams: Credit towards the degree, mathematics requirements for other departments, and placement into Math courses. Credits (in all fields) for AP exams are described in a table in the Bulletin; look under "Advanced Placement Credit" in the index. Some departments (Chemistry and Psychology, for instance) require a year or a semester of Calculus as part of their concentration; students should consult with the Undergraduate Advising Head in the relevant department about satisfying such requirements. The Math Placement Exam, being self-administered, cannot be used as a means of fulfilling a requirement in another department.

Here are some guidelines relating to the AP exams. Note that in general, a student cannot receive credit for both a Brandeis course and an AP course which is equivalent to it.

1. Students receiving a score of 5 on the MATH AB exam or at least 4 on the MATH BC exam would not ordinarily take MATH 5a or either of the first-year calculus courses: MATH 10a or 10b.
2. Students receiving a score of 4 on the MATH AB exam or a score of 3 on the MATH BC exam would not ordinarily take MATH 5a or 10a. These students must take the department placement exam if they wish to bypass MATH 10b.
3. Students whose AP scores are not sufficient for credit for MATH 10a may still wish to take MATH 10b. These students must take the department placement exam if they wish to bypass MATH 10a. Note that placement into MATH 10b does not give credit for MATH 10a, unless the AP scores warrrant such credit. Similarly, students whose AP scores are not sufficient for credit for MATH 10b may still wish to go directly into MATH 15a or 20a. These students must take the department placement exam if they wish to bypass MATH 10b.

Placement into courses beyond calculus is best determined in consultation with the department. Students who have completed a year of calculus (or placed out of MATH 10) are strongly urged to discuss their course selection at the next level (MATH 15,20,21, or 22) with the Departmental advisors. Faculty members who teach MATH 20a, 21a, 21b, 22a, and 22b, often give an early diagnostic exam to help ensure that students who are taking the courses are properly prepared. Students who do not have the proper background will be advised to transfer to lower level courses. Incoming students should be advised that any upper level (above 22) MATH course will require, as a minimum prerequisite, one or more of MATH 15, 20, 21 or 22, plus MATH 23b. It is therefore essential for students who intend to pursue the math major to get started on these courses as soon as possible. It is certainly possible for students to become math majors after taking MATH 10ab in the first year; students who are pursuing this route are urged to consult with the department early on to plan their course of studies.

4. Declaring a Major

1. A general University rule is that students must declare one or more majors by the end of the second semester of the sophomore year. To declare a major, students file the ``Declaration of Field of Study'' form (available at the Academic Affairs), after consultation with and approval by the Undergraduate Administrator or Advising Head.
2. Before meeting with the UA or UAH, the student should carefully read the major requirements, and have some idea of what might constitute a reasonable program in line with his or her interests. The UA or UAH will discuss the proposed program from the point of view of its intellectual content, and make sure that various practical issues (all requirements can be fulfilled, prerequisites are taken at the proper time, etc.) are settled. At the end, the candidate's declaration of major and course plan must be approved in writing by the UA/UAH when they are deemed appropriate. The UA/UAH will also assign to the candidate a department member as a faculty advisor. The candidate should in the future consult with his or her faculty advisor on specific matters pertaining to courses and academic plans. Any future change on the course plan beyond substitution of one elective course for another must be approved by the UA/UAH. In particular, any substitution of a course from another Brandeis department, or from summer school at another institution, must be approved in advance.
3. All information pertaining to the candidate's academic performance, progress and granted requests in subsequent years shall be made available to and be kept on file by the department secretary, the UA, the UAH, and the faculty advisor to the candidate.

5. Sample Course Plans

1. For students interested in graduate school or an intensive program in Mathematics:
   1. MATH 21a, and 21b; 23b.
   2. MATH 30a, 30b, 32a, and 34a.
   3. MATH 38b, 40a, 40b, and COSI 88a or COSI 188a.
   4. MATH 37a, 45a, 98a, and two 100 series courses.
2. For students interested in a Mathematics major plus one other major such as Computer Science, Physics, Economics, etc:
   1. MATH 21a and 21b; 23b.
   2. MATH 30a, 30b, and 32a.
   3. MATH 38b, 40a, and 40b.
   4. MATH 37a and 45a.
3. For students interested in a career in applied sciences such as Applied Mathematics, Applied Physics, Engineering etc:
   1. MATH 15a and 20a; 23b.
   2. MATH 28a, 28b, and 36a.
   3. MATH 35a, 35b, and 36b.
   4. MATH 37a and 45a.
4. For students interested in a career in teaching high school Mathematics (see Bulletin for more information):
   1. MATH 15a and 20a; 23b.
   2. MATH 28a, 28b, and 36a.
   3. MATH 35a, 35b, 37a, and a COSI course.
5. For students interested in a Mathematics Minor:
   1. MATH 15a and 20a.
   2. MATH 28a and 28b.
   3. MATH 35a and 36a.

6. Transfer credits

1. The student must fill out a form at the registrar's office. In addition to the official evidence required by the registrar's office, the student will need to present a detailed description and syllabus for each math course for which he wishes to receive credit at Brandeis. Text books used in those courses may also help determine their merits. The UA and the UAH shall make the decision on granting credits on the basis of the information presented. Students who do not have the relevant material at hand often find that they can obtain it from the mathematics department of their previous schoo; sometimes this material is available from a web site. It is the student's responsibility to make sure that all relevant materials are submitted.
2. Credit towards the MATH major shall be granted only if the course taken elsewhere is nearly equivalent, in breadth, and depth, to a course offered by the Brandeis Math Dept. Courses on subjects which are not offered at Brandeis may be considered, but they must meet the same criteria. The student must receive a `B' (or its equivalent) or better in that course.

Credit cannot be given for courses with substantial overlap with a Brandeis course which a student has taken.

7. Career information and opportunities

• Posters advertising graduate study in mathematics and other related fields are displayed on the bulletin boards around the department.
• Announcements of summer research opportunities, some of which are funded by the National Science Foundation, are displayed as they arrive on the wall near the mailboxes on the second floor.
• We get an assortment of announcements of job opportunities, including some summer internships. Starting in the fall of 1998, these will be kept on a shelf in room 200; we will make every effort to keep students up to date on new arrivals. Students who wish to look at this information should contact the UA/UAH.
• One particular item which may be of interest is information pertaining to the Actuarial exams, which are given three times a year: November, January and April. Students who are interested in these exams, or in the actuarial profession, can get some information from the UA/UAH.

8. Miscellaneous other questions

1. What are the rules governing repeating classes? Specifically, students often ask about taking Math 10a or 10b over to replace a bad grade, typically D or E. If they are allowed to do so, what goes on their transcript, and which grade is used in computing their GPA?
   Answer. If the course was taken initially with a passing grade (D- or better) and repeated, both grades appear on the transcript but only the first receives credit and only the first goes into the GPA. (The only advantage to doing this is that it is mildly cosmetic. Designed to discourage repeating under these circumstances.) See Bulletin, p. 25, Exceptions to Rate of Work. If course was taken initially with a failing grade (E, F) and repeated, both grades appear on the transcript. If the second try yields a passing grade, it will generate credit. Both attempts go into the GPA.

2. Are all courses listed in the Bulletin offered every year?
   Answer. Some are, and some aren't. MATH 5a, 8a, 10ab, 15a, 20a, 21ab, 22ab, 23b, 28a, 30ab, 35ab, 36ab, 40ab, and 45a are offered every year. MATH 28b is usually offered every year. The other courses are offered in alternate years, according to the chart in the bulletin.

3. Can I still major in math if I take Math 10a and 10b during my freshman year?
   Answer. Yes, you can. You'll need to do some planning, to make sure you can fulfill all the requirements in three years.

4. What is the difference between MATH 15a, 20a, 21ab and 22ab?
   Answer. This is a question which is best discussed with the department advisers, so that notions like `more theoretical' can be fully explained. Math 15a covers linear algebra, with emphasis on calculational techniques and applications. Some theoretical issues are discussed, but these are in the background. Math 21a and 22a also cover linear algebra, but are much more theoretical, with the emphasis being on proofs and more conceptual thinking than computation. The material in 21a and 22a is similar, with greater depth and a faster pace in 22a. Math 20a covers multivariable calculus, and like Math 15a focusses on calculation and applications. Math 21b and Math 22b have a much more conceptual and theoretical orientation, and cover some more advanced subjects.

   As a rule, students who are able to handle the more difficult courses (21ab/22ab as opposed to 15 and 20) find that they are better prepared for the upper level courses in the department. One final difference: Math 21 and 22 meet for four hours per week, whereas Math 15 and 20 meet for the usual three.

5. If I've taken (or placed out of) calculus and plan to take Math 15a and 20a, which should I take first?
   Answer. Either order is fine. Note however that Math 21a and 21b must be taken in that order.

6. Can I take Math 21b after taking Math 15a?
   Answer. Yes, but only with permission from the Math 21b instructor.

7. Can I switch from a Teacher Track program to a Math major in my Senior year?
   Answer. Yes, as long as all of the requirements are satisfied.

8. What MATH courses are offered at Brandeis during the summer?
   Answer. Ordinarily, MATH 5a and MATH 10ab are offered.

9. If I wish to take math courses outside of Brandeis during a summer, do I have to get permission before?
   Answer. You are strongly advised to do so, because credit for courses taken outside of the University is not granted automatically. If you do not get approval before the summer, you run the risk of the course not being approved, and wasting your time and money.

10. What are the rules governing a `level change' between courses?
    Answer. Level change refers to the fact that changes between certain courses are routinely granted by the Committee on Academic Standing (COAS), beyond the usual add/drop dates, if this has been approved in advance by the department. Currently, level changes are permitted between MATH 21a (or b) and 22a (or b), and MATH 28a (or b) and 30a (or b).

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Last updated: August , 2007.