Minors Offered

The Mathematical Sciences minor

The Minor includes six courses. 21-127 Concepts of Mathematics is a prerequisite for 21-228 and recommended for 21-241 . The minimum preparation required for 21-355 Principles of Real Analysis I  is 21-120 /21-122 or equivalent courses. Students planning to include 21-373 Algebraic Structures as a Mathematical Sciences Elective should choose 21-341 Linear Algebra. 21-241 or 21-242, and 21-341 cannot both count toward the minor.

Minor in Mathematical Sciences Courses		Units
21-127	Concepts of Mathematics	9
21-228	Discrete Mathematics	9
or	21-301 Combinatorics
or	21-484 Graph Theory
21-241	Matrices and Linear Transformations (10 units)	9 or 10
or	21-242 Matrix Theory (10 units)
or	21-341 Linear Algebra (9 units)
21-355	Principles of Real Analysis I	9
21-3xx	Mathematical Sciences Elective
21-3xx	Mathematical Sciences Elective

To avoid excessive double counting, the two Mathematical Sciences Electives may not also count toward the student's major.

A student who completes the Mathematical Studies sequence plus two recommended electives (typically 21-470 Selected Topics in Analysis and 21-374 Field Theory ) will receive a Minor in Mathematical Sciences. Excluded as acceptable electives are the following: 21-105 , 21-111 , 21-112 , 21-120 , 21-122 , 21-259 or 21-268 or 21-269, and 21-260 or 21-261, and courses intended for H&SS or undergraduate business students, such as 21-110 , 21-256 and 21-257 .

The Discrete Mathematics and Logic Minor

This minor develops the fundamentals of discrete mathematics and logic necessary to understand the mathematical foundations of many computer related disciplines. Required courses are:

Minor in Discrete Mathematics and Logic		Units
21-300	Basic Logic	9
21-301	Combinatorics	9
21-341	Linear Algebra	9
21-484	Graph Theory	9

Two of the following:

21-329	Set Theory	9
21-374	Field Theory	9
21-441	Number Theory	9
21-602	Introduction to Set Theory I	12
21-603	Model Theory I	12
21-610	Algebra I	12
21-700	Mathematical Logic II	12

The Computational Finance Minor

The requirements for the Computational Finance Minor are listed below. Beginning in Fall 2006, a student must satisfy one of the following requirements to declare a minor:

1. Completion of 21-270 Introduction to Mathematical Finance with a grade of A and an overall QPA of at least 3.2., or

2. Completion of 21-270 Introduction to Mathematical Finance and 21-370 Discrete-Time Finance with an average grade of B and an overall QPA of at least 3.0.

When a student has met the necessary requirements, he or she may declare the minor by contacting the Associate Dean of the Mellon College of Science.

21-241 Matrices and Linear Transformations (or 21-341 Linear Algebra I)
21-259 Calculus in Three Dimensions (or 21-256 Multivariate Analysis)
21-260 Differential Equations
21-270 Introduction to Mathematical Finance
21-370 Discrete-Time Finance
21-420 Continuous-Time Finance

To avoid excessive double counting, Mathematical Sciences majors must also take 21-365 Projects in Applied Mathematics or an approved substitute.

The pre-requisite for 21-370 is 21-270, and either 21-256 or 21-259, and the co-requisite is 70-207, 21-325, 36-225, or 36-217. Students in 21-370 are expected to read and write proofs.

The pre-requisite for 21-420 is 21-260, 21-370 and one of the following three calculus based probability courses: 21-325, 36-225, or 36-217. Note that 70-207 is not a sufficient preparation in probability. Also note that 21-122 is a pre-requisite for 21-260 and that 21-127 is a prerequisite for 21-341 and is recommended for 21-241.

Note that these are corrections of the pre-requisites listed in the 2004-06 catalog.

Students minoring in Computational Finance are strongly encouraged to take one or two economics courses, e.g., 73-100, 73-150, 73-200 and 73-251