## The Mathematics Major

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The purpose of the major is to immerse students in the content and methodology of mathematics as it is practiced by active mathematicians. The basic requirements in the major introduce the central ideas of the discipline. Electives within the major permit students to pursue further areas of special interest.

The course in Linear Point Set Theory is an important bridge into the major. In it students begin the immersion into the mathematical process, and the foundation is built for later work in Algebra, Analysis, Topology, and other courses. Linear Point Set Theory, along with Abstract Algebra and Analysis, highlight methods of proof, raising and settling of questions, developing precise definitions of concepts, and thinking and writing concisely in mathematical terms. Students who immerse themselves in these mathematical ideas are able to approach the other courses in the major with the perspective of the working mathematician.

Mathematical concepts have a profound influence on the world outside of mathematics. Equally important, the world external to mathematics has helped shape the discipline. It is important for majors to experience this interaction and to see the power and limitations of mathematics. Courses such as Calculus I, II, and III, Linear Algebra, Differential Equations, Probability, Statistics, Numerical Analysis, and Introduction to Computer Science as well as the physics requirement aid in the development of this perspective.

A major in mathematics opens many doors. Majors go on to graduate work in fields such as mathematics, computer science, statistics, physics, economics, or biology. They pursue careers in business, actuarial science, linguistics, medicine, law, and teaching. Most importantly, the major allows the budding mathematician to see the world in a creative, beautiful, and profound way.

## Advising

All majors are urged to seek advice from the Department concerning selection of courses. Students considering a major in mathematics should consult with the Department as soon as possible. A faculty member can suggest courses that may help students make a decision. Mathematics majors should go to Rome in the spring of the sophomore year, as many required courses for the major are only offered in the fall semester.

## Major Requirements

### Bachelor of Arts in Mathematics

**Mathematics:**

1404,1411, 2412 (Calculus I, II, III)

3159 (Junior Workshop)

3310 (Linear Algebra)

3321 (Linear Point Set Theory)

4332 (Abstract Algebra I)

4341 (Analysis I)

4333 or 4342 (Abstract Algebra II or Analysis II)

one of 3324, 3325, 3326, 4315, or an approved 3V50 course; (Differential Equations,
Complex Analysis, Probability, Numerical Analysis, Applied Mathematics, or an approved
Special Topic.)

Three credits at any level; and six credits in courses numbered 3000 or above including
advanced courses in computer science (only six hours of computer science may count
toward the major); participation in 2107, 3107, 3190, and 3V50 (Mathematics Colloquium,
Problem Solving, and Special Topics) as often as it is offered is encouraged.

**Physics:** 2311-2111, 2312-2112 (General Physics I, II, Calculus based)

### Bachelor of Science in Mathematics

Twelve additional advanced hours in mathematics are required including 4315; 4333 or 4342, excluding the choice for the B.A.; and 4V43 (Research).

## Comprehensive Examination

A comprehensive exam is required of all majors in their final year. It is administered by the mathematics faculty and consists of a written exam and an oral exam. The written exam is offered once in the fall semester and twice in the spring semester and covers four major disciplinary areas: Algebra, Analysis, Pure Math, and Applied Math. A score of 70% or better qualifies the student to proceed to the oral exam. The oral exam is intended to explore further the students' understanding of mathematics, their facility with the concepts and processes of mathematical thought, their approach to problems using the mathematical tools they have been given, and their ability to communicate their thoughts and ideas.

### Suggested Sequence

The following is a representative sequence of the courses to be taken by students in the mathematics major.

#### Year I

Physics 2311 | 3 | Physics 2312 | 3 |

Physics 2111 | 1 | Physics 2112 | 1 |

English 1301 | 3 | English 1302 | 3 |

Language 2311 | 3 | Language 2312 | 3 |

Mathematics 1404 | 4 | Mathematics 1411 | 4 |

Philosophy 1301 | 3 | Theology 1310 | 3 |

TOTAL | 17 | TOTAL | 17 |

#### Year II (Rome)

English 2312 | 3 | English 2311 | 3 |

Mathematics 2412 or 3310 | 3-4 | History 2301 | 3 |

Mathematics 3321 | 3 | Theology 2311 | 3 |

Economics 1311 | 3 | Philosophy 2323 | 3 |

History 2302 | 3 | Art 2311 | 3 |

TOTAL | 16-17 | TOTAL | 15 |

#### Year III

Mathematics 3310 or 2412 | 3-4 | Mathematics Elective | 3 |

Mathematics 4341 or 4332 | 3 | Mathematics 4342 or 4333 | 3 |

History 1311 | 3 | Philosophy 3311 | 3 |

Life Science | 3 | History 1312 | 3 |

Mathematics 3159 | 1 | Mathematics 3159 | 1 |

TOTAL | 13-14 | TOTAL | 13 |

#### Year IV

Mathematics 4332 or 4341 | 3 | Mathematics Elective | 3 |

Mathematics Elective | 3 | Electives | 9 |

Politics 1311 | 3 | ||

Electives | 6 | ||

TOTAL | 15 | TOTAL | 12 |