# Mathematics Requirements

**Required for the Major in Mathematics**: (Eleven courses total, at least six of which must be taken at Middlebury College in Vermont):

I. Core courses: MATH 0122, MATH 0200, MATH 0223, MATH 0302, and MATH 0323 (at least one of the latter two to be completed by the end of the junior year);

II. Electives: five MATH electives at the 0200-level or above;

III. Senior thesis work: A 0700-level MATH seminar in the senior year.

**Note**: Students are strongly encouraged to include a proof-based course such as MATH 0241 or MATH 0247 early in their programs. This is especially helpful prior to taking MATH 0302 or MATH 0323.

**Required for the Mathematical Sciences Option in the Mathematics Major**: (Eleven courses total, at least six of which must be taken at Middlebury College in Vermont)

I. Core courses: MATH 0122, MATH 0200, and MATH 0223;

II. Computing-intensive course: CSCI 0150 or MATH 0216 or MATH 0228;

III. Electives. Six courses from categories A and B. At least four of the six courses must have the MATH designation, and at least two must be from category B, and at least one of those two must be MATH 0302 or MATH 0323, to be completed by the end of the junior year. Non-MATH courses must all have the same designation (ECON or PHYS or CSCI)

A. Courses in applied specialization: MATH 0218, MATH 0225, MATH 0310, MATH 0315, MATH 0318, ECON 0280, PHYS 0212, CSCI 0201, CSCI 0463;

B. Advanced electives: MATH 0302, MATH 0311, MATH 0323, MATH 0325, MATH 0410, CSCI 0302, ECON 0390, ECON 0411, MATH 0500 (with prerequisite: at least one course from categories A or B);

IV. Senior work: A 0700-level MATH seminar in the senior year.

**Note**: Students should consult the mathematics department for examples of course sequences in the mathematical sciences option recommended for emphases in Mathematical Economics, Computer Science, or Physical Sciences/Engineering. For students completing double majors, electives used towards a major in another department cannot also be counted as electives in the mathematical sciences option.

Students planning a "3-2" engineering program who wish to major in Mathematics will complete the 700-level MATH course in their sixth semester at Middlebury. These students should normally choose the Mathematical Sciences Option in the major.

**Honors Program**: A student who wishes to be considered for departmental honors in mathematics must submit a proposed plan of study during his or her junior year. Candidates for departmental honors should include one additional elective in their programs (12 courses total). For the mathematical sciences option, an honors program must include an elective sequence such as MATH 0310-0410 or MATH 0310-0311. Students should consult their advisors as they develop proposals for honors study.

**Required for the Minor in Mathematics** **(six courses total at least half of which must be taken at Middlebury College in Vermont)**: MATH 0121, MATH 0122, MATH 0200, and three courses at the 0200-level or above.

**Joint Majors**: The Department of Mathematics does not offer a joint major.

**Advanced Placement**: Advanced placement in the department is offered to first-year students whose secondary training indicates they can commonly bypass one or more of the beginning courses in mathematics. Majors typically begin their study of mathematics in MATH 0122 or MATH 0200. Mathematics majors who need to begin the study of calculus with MATH 0121 may arrange with their advisors to use this course as one of the required electives. Credits for MATH 0121 and 0122 may be earned through the College Board AP exams or international exams such as the A-Levels or IB. At the discretion of the chair, additional courses may be waived in recognition of exceptional secondary school preparation. However, in all cases the major must include at least 7 Middlebury College or approved transfer courses, and the minor must include at least 4. Students who have earned grades on advanced placement calculus exams that are eligible for credit may not register for the equivalent course at Middlebury College. Thus students who have earned 4 or 5 on the Calculus AB exam or a 3 on the Calculus BC exam may not register for MATH 0121, students who have earned 4 or 5 on the Calculus BC exam may not register for MATH 0121 or MATH 0122. This policy applies irrespective of whether students choose to use their AP credits toward meeting Middlebury's graduation requirements. The following international credentials carry the same credit as a 4 or 5 on the Calculus BC Exam: A-level exam with a mathematics grade of A, B, or C; or IB Higher Level Mathematics with a grade of 6 or 7.

**Other Credits:**

Because of the wide variation in course offerings at other institutions, students wishing to substitute a course from another college for any course in mathematics must seek approval from the department before registering for the course. In addition, students seeking MATH 0121 credit for a summer course taken elsewhere must pass a written examination given by the department in the fall. Check with the department early in the first week of classes for details.

**Requirements Prior to Fall 2016 Required for the Major in Mathematics**: (Ten courses total at least half of which must be taken at Middlebury College in Vermont):

I. Core courses: MATH 0122, MATH 0200, MATH 0223, MATH 0302, and MATH 0323;

II. Electives: four MATH electives at the 0200-level or above;

III. Senior thesis: MATH 0704 in the senior year.

**Note**: Students are strongly encouraged to include a proof-based course such as MATH 0241, or MATH 0247 early in their programs. This is especially helpful prior to taking MATH 0302 or MATH 0323. **Required for the Mathematical Sciences Option in the Mathematics Major**: (Ten courses total at least half of which must be taken at Middlebury College in Vermont)

I. Core courses: MATH 0122, MATH 0200, and MATH 0223;

II. Electives. Six courses from categories A and B. At least four of the six courses must have the MATH designation, and at least two must be from category B.

A. Courses in applied specialization: MATH 0225, MATH 0310, MATH 0315, MATH 0318, ECON 0380, PHYS 0212, CSCI 0201, CSCI 0463;

B. Advanced electives: MATH 0302, MATH 0311, MATH 0323, MATH 0325, MATH 0410, CSCI 0302, ECON 0390, ECON 0411, MATH 0500 (with prerequisite: at least one course from categories A or B);

III. Senior thesis: MATH 0704 in the senior year.

**Note**: Students should consult the mathematics department for examples of course sequences in the mathematical sciences option recommended for emphases in Mathematical Economics, Computer Science, or Physical Sciences/Engineering. For students completing double majors, electives used towards a major in another department cannot also be counted as electives in the mathematical sciences option.

Students planning a "3-2" engineering program who wish to major in Mathematics will complete the thesis course MATH 0704 in their sixth semester at Middlebury. These students should normally choose the Mathematical Sciences Option in the major.**Honors Program**: A student who wishes to be considered for departmental honors in mathematics must submit a proposed plan of study during his or her junior year. Candidates for departmental honors should include two additional electives in their programs (12 courses total). For the mathematical sciences option, an honors program must include one of MATH 0302/0323 and an elective sequence such as MATH 0310-0410 or MATH 0310-0311. Students should consult their advisors as they develop proposals for honors study.**Required for the Minor in Mathematics (six courses total at least half of which must be taken at Middlebury College in Vermont)**: MATH 0121, MATH 0122, MATH 0200, and three courses at the 0200-level or above.

Joint Majors: The Department of Mathematics does not offer a joint major.**Advanced Placement**: Advanced placement in the department is offered to first-year students whose secondary training indicates they can commonly bypass one or more of the beginning courses in mathematics. Majors typically begin their study of mathematics in MATH 0122 or MATH 0200. Mathematics majors who need to begin the study of calculus with MATH 0121 may arrange with their advisors to use this course as one of the required electives. Credits for MATH 0121 and 0122 may be earned through the College Board AP exams or international exams such as the A-Levels or IB. At the discretion of the chair, additional courses may be waived in recognition of exceptional secondary school preparation. However, in all cases the major must include at least 7 Middlebury College or approved transfer courses, and the minor must include at least 4. Students who have earned grades on advanced placement calculus exams that are eligible for credit may not register for the equivalent course at Middlebury College. Thus students who have earned 4 or 5 on the Calculus AB exam or a 3 on the Calculus BC exam may not register for MATH 0121, and students who have earned 4 or 5 on the Calculus BC exam may not register for MATH 0121 or MATH 0122. This policy applies irrespective of whether students choose to use their AP credits toward meeting Middlebury's graduation requirements. The following international credentials carry the same credit as a 4 or 5 on the Calculus BC Exam: A-level exam with a mathematics grade of A, B, or C; or IB Higher Level Mathematics with a grade of 6 or 7.**Other Credits**:

Because of the wide variation in course offerings at other institutions, students wishing to substitute a course from another college for any course in mathematics must seek approval from the department before registering for the course. In particular, this applies to calculus courses taken at other institutions over the summer.