# Major Requirements

The mathematics major is designed around a core of required courses that provides a strong foundation in both computational and theoretical mathematics. Beyond this core, electives from both pure and applied mathematics serve to accommodate students whose aspirations may include double-majoring with any of the College’s other quantitative majors, pursuing graduate study in mathematics or a cognate field, or building a career that requires a strong mathematical background. Yet not all students who major in mathematics necessarily have long-term quantitative interests. Recent math majors have doubled with classics, English, language and culture studies, music, and theater and dance.

Students whose goals include graduate study in mathematics should supplement the core requirements with as many 300-level electives as possible and should consult with their mathematics adviser or with the department chair at the earliest possible date in order to plan a course of study.

LEARNING GOALS

The Math Department’s learning goals can be found HERE.

REQUIREMENTS

For a summary sheet of requirements for the Mathematics Major, click here.

To earn a major in mathematics, students must complete a total of ten courses of at least one credit each at the 200-level or above. These courses must be selected so as to satisfy the requirements below. Note that students may elect to complete the general mathematics major which provides the student a broad foundation in both pure and applied mathematics, or may choose to complete the major with a concentration in applied mathematics. In both cases, students must earn a grade of C- or better in each course that is counted toward these requirements. (In the case of Math 205, the minimum grade requirement is C+.)

Requirements for General Major in Mathematics

- Calculus requirement

MATH 231 - Linear Algebra requirement

Either MATH 228 or MATH 229. Students may take both courses for college credit but only one may be counted towards the ten courses required for the math major. - Introduction to Proof requirement

Math 205. Students must earn a grade of C+ or better in either Math 205 or Math 228. - Writing Intensive Part II requirement

MATH 307 and MATH 331. At least one of these courses must be taken at Trinity. - Electives
- Students must take two elective courses at the 200-level or above. Each course must carry a minimum of one credit. At most one course may be chosen from the list of cognate courses below.
- Students must take two additional elective mathematics courses at the 300-level or above, not including Math 399 or 497. No cognate course below will count toward the fulfillment of this requirement.

- Capstone requirement

Students must take one 400-level seminar course.

Requirements for Concentration in Applied Mathematics

- Calculus requirement

MATH 231 - Linear Algebra requirement

Either MATH 228 or MATH 229. Students may take both courses for college credit but only one may be counted towards the ten courses required for the math major. - Introduction to Proof requirement

Math 205. Students must earn a grade of C+ or better in either Math 205 or Math 228. - Writing Intensive Part II requirement

MATH 309 and MATH 331. At least one of these courses must be taken at Trinity. - Differential Equation Requirement

MATH 234 - Electives
- Students must take one elective course at the 200-level or above which carries a minimum of one credit. This course may be chosen from the list of cognate courses below.
- Students must take two additional elective mathematics courses at the 300-level or above, not including Math 399 or 497. No cognate course below will count toward the fulfillment of this requirement.
- Of these three electives:
- (i) one must be either MATH 316 or MATH 334
- (ii) another must be chosen from MATH 209, MATH 237, MATH 252, MATH 316, MATH 334

- Capstone requirement

Students must take one 400-level seminar course.

List of Approved Cognate Courses

- CHEM 309L. Physical Chemistry I
- CHEM 310. Physical Chemistry II
- CHEM 316L. Physical Biochemistry
- CPSC 320. Analysis of Algorithms
- ECON 312. Mathematical Economics
- ENGR 212L. Linear Circuit Theory
- ENGR 225. Mechanics I
- ENGR 301L. Signal Processing and Applications
- ENGR 303L. Analog and Digital Communication
- ENGR 312. Automatic Control Systems
- ENGR 337. Thermodynamics
- ENGR 346L. Computational Neuroscience
- ENGR 362L. Fluid Dynamics
- PHYS 232L. Physics III: Optics and Modern Physics
- PHYS 300. Mathematical Methods of Physics
- PHYS 301. Classical Mechanics
- PHYS 302. Electrodynamics
- PHYS 304. Statistical and Thermal Physics
- PHYS 313. Quantum Mechanics
- PSYC 221L. Research Design and Analysis

Not all mathematics courses are offered each year. To help students to plan their schedules, the following describes the frequency with which each course at the 200-level and above has recently been offered. These are subject to change according to student demand.

- Courses offered every semester: MATH 205, 207, 228, 229, 231, 234, 400
- Courses offered every year: MATH 307, 309, 331
- Courses offered every other year: MATH 209, 214, 237,

252, 253, 305, 306, 308, 316, 318, 326, 332, 334, 341

Although a student may begin the mathematics major as late as the fall semester of the sophomore year, the department recommends that prospective majors who have no prior calculus credit adopt the following typical schedule:

Year | Fall | Spring |

First | 131 | 132 |

Sophomore | 231, 205 | 228 or 229, elective |

Junior | 307 or 309, elective | 331, elective |

Senior | elective | 400 level seminar course |

ADDITIONAL OPPORTUNITIES

Study away: Students of mathematics have many

opportunities to study away, but all of them require a certain amount of early

planning. Students are strongly encouraged to discuss their plans with their advisers or the department chair as soon as possible since many courses in the Mathematics Department are not offered every year. Well-prepared students should consider the Budapest semester in mathematics; more information on this program can be found on the study-away website.

Many study away programs in English-speaking countries offer a wide range of mathematics courses that will count toward the major. For specific advice, please consult the department chair. Students who feel they are sufficiently proficient in a language to take mathematics courses in a foreign language should discuss this with their advisers. Students who take mathematics courses while away should be aware that universities that follow the European model cover the material in a somewhat different order than is done in the United States and that classes are primarily lectures with far less feedback from the instructor than is typical at Trinity.

Honors: Honors in mathematics, granted by departmental vote in the spring of the honors candidate’s senior year, is earned by:

- receiving a grade of at least a B- in all mathematics courses taken at the 200-level and above,
- receiving a grade of A- or better in at least four 300-level courses excluding MATH 399 and 497, and
- writing and presenting a suitable thesis on an area of mathematics that the student finds particularly interesting.

The student must apply to the department chair for honors candidacy in the second semester of the junior year. Upon acceptance, the candidate, together with the department chair, will select an honors adviser who will supervise the honors thesis. The student will then submit a thesis proposal by the last day of classes for the spring semester of the junior year.

The honors thesis need not be one of newfound mathematical results, but it is expected to be a balance of the historical, biographical, and mathematical aspects of the topic. The project will culminate with the submission of the final draft to the honors adviser no later than one week before the last day of classes of the spring semester. A formal presentation will be given by the candidate no later than one day prior to the earlier of (1) the deadline for verification of honors, and (2) the deadline for submission of senior grades. Guidelines for the completion of the honors thesis may be obtained from the department chair.