# Course Options

This page gives the overall picture of the course offerings for the mathematics major. For the precise requirements for the various majors and minors offered in mathematics, please see the Mathematics Section of the Catalog.

There is also a joint Math/Computer Science major. Information about this can be found in the MACS Section of the Catalog.

**Warning:** the information contained on this page is no substitute for consulting an official advisor in the department of mathematics!

## Major Requirements

### Calculus Requirement

Calculus is a core area of mathematics, and is a prerequisite for many courses required by the major. The major can be thought of as requiring a year of calculus at the outset (material prior to calculus must be made up first if it was not taken before entering the university). There are several calculus options open to potential math majors.

- Our standard sequence is Math 251-253 which emphasizes mathematical and physical applications of calculus.
- A similar option is Math 246-247-253, which emphasizes applications in the life sciences and is equivalent to 251-253 for purposes of math majors.
- Our calculus with theory sequence (Math 261-263) covers the same material as 251-253 and in addition covers the theoretical grounding of calculus (WHY things work the way they do rather than just HOW things work). Because of this, Math 261-262 satisfy the bridge requirement and students who take Math 261-263 are exempt from the requirement for Math 315.

(Note that Math 241-242 is our calculus for business majors and does not satisfy the requirements for mathematics majors.)

### Bridge Requirement

Before taking most upper division courses, all students are required to take a course or courses that deal with some mathematical proof at an elementary level. There are three ways to satisfy this requirement.

- Math 307. This course is an introduction to proof. The mathematical focus is typically problems from set theory, combinatorics, logic and discrete math although the real point of the course is giving students practice and feedback so that they can learn how to do mathematical proofs. The prerequisite is Math 252 or equivalent.
- Math 261-262. This is the first two terms of our calculus with theory sequence (discussed briefly above). This includes not only the calculational techniques and applications of calculus, but also the theoretical underpinnings of the subject, and thus this course emphasizes proof.
- Math 231-232. This is two terms out of a year long course (Math 231-233) in discrete math. The entire sequence (Math 231-233) is essential for for students with a computer science major, but the material is of interest for mathematics students as well.

### Six Course Core

All majors except those in the secondary education option (that option is specifically for future high school teachers) will take a six course core mostly focussed on multivariable mathematics. The courses in this core are

- Math 256: Introduction to Differential Equations. This covers techniques for solving, and applications of, differential equations. Differential equations are analogous to algebraic equations, except the equations typically involve a function and its derivative, and a solution to such an equation is a formula for a function that satisfies the relevant equation. The prerequisite is Math 253 or equivalent.
- Math 281-281: Vector Calculus. This course concerns calculational techniques and applications of calculus generalized to functions with more than one variable. The prerequisite is Math 253 or equivalent.
- Math 341-342: Linear Algebra. This course is concerned with applications of groups of linear equations in more than one variable, vectors andvector spaces, matrices and matrix algebra, etc. The prerequisite is Math 252 or equivalent.
- Math 315: Elementary Analysis. This course is concerned with the definitions and theorems behind single variable calculus, focussed especially on the definition and importance of the limit. The prerequisite is Math 253 or equivalent and the bridge requirement.

### Pure, Applied and Design-your-own Options

To satisfy these major options, majors will satisfy the calculus requirement, the bridge requirement and take the six course core described above. They will then take at least 4 electives chosen appropriately from upper division (300 and 400 level) courses. For details about each option, consult the course catalog or an adviser.

### Secondary Teaching Option

Majors in this option will do the calculus requirement and the bridge requirement. Then they will complete the following list of courses.

- Math 341: First term of linear algebra. Prerequisitie: Math 252 or equivalent.
- Math 394-395: Geometries from an Advanced Viewpoint. Prerequisite: Math 253 or equivalent and bridge requirement.
- Math 391-393: Fundamentals of Abstract Algebra. Prerequisite Math 341 and bridge requirement.
- Math 346: Number Theory. Prerequisite: Math 253 and bridge requirement.
- Math 315: Elementary Analysis. Prerequisite: Math 253 and bridge requirement.
- Math 343: Statistical Models and Methods. Prerequisite: Math 252.
- CIS 122: This is meant to satisfy a requirement for a course involving computer programming. Prerequisite CIS 110 and Math 111.

## Families of Courses

We make an attempt here to divide the courses in our undergraduate curriculum roughly into classical mathematical areas. Any such division is subjective, furthermore because most areas of mathematics have interesting and deep relationships with many other areas of mathematics, this attempt at such a division may be sometimes misleading. But these general terms are often used, and it is useful to understand how mathematicians use them.

#### Analysis

The branch of mathematics dealing with calculus and its generalizations is called analysis. Courses in this area include advanced calculus, Introduction to Analysis, Functions of a Complex variable, Differential Equations, Fourier series, and Numerical Analysis.\ Someone interested in a career in technology, applied mathematics, physics or economics will generally include plenty of analysis or applied analysis in his or her degree program, as well as numerical analysis (including approximate solution techniques and error analysis) and computer science.

#### Algebra

Most of mathematics which does not involve limits or continuity in some way can be generally thought of as belonging to the area of algebra. Our courses in this area include Math 341, Math 342 and Math 441 in linear algebra; two sequences of abstract algebra (Math 391-393 and Math 444-446); and number theory (Math 346).

#### Statistics

Besides Math 243 and Math 425-426 (which are aimed at mathematically unsophisticated students and thus unsuitable for majors), the department offers Math 461-463 on probability, inference, regression and analysis of variance, Math 467 on stochastic processes, and a new one-term course (not yet numbered) on applied inference.

#### Topology, Geometry and Others

The department offers two terms of topology Math 431-432 and term of differential geometry (Math 433) as well as two terms of more classical geometry (Math 394 and 395). There are also courses in combinatorics, mathematical modeling, dynamical systems (including some chaos theory) and occasional special courses.

Students planning on graduate work are encourage to take courses in several fields to get some feeling for the breadth of mathematics.

## Courses Outside the Major

Language courses (French, German and Russian are the classical languages of mathematics besides English, and many Ph.D. programs require some fluency in some of these languages) and a thorough grounding in English composition have always been valuable to mathematicians. A concentration in pedagogy or one of the sciences has also been useful when beginning a career. A strong background in economics, business or finance is valuable, as is a background in computers science, although the situation is constantly changing. Students should have the goal of being able to relate mathematics to something outside of mathematics.

Physics courses (like Physics 251-253) make a natural complement to calculus courses both at the single variable and more advanced level, and we encourage all mathematics majors to take courses like this, especially those majors considering future careers in the physical sciences.

The discipline of economics is highly dependent on mathematics and quantitative methods, and majors who may want a career in the business or financial world should explore options in the Economics department as well as the business school.

Quantitative methods are finding increasing applications in biology as modern lab techniques produce mountains of data allow measurement of systems that can be productively modeled mathematically. Students interested in careers in this rapidly growing area should consider courses in biology as a complement to a mathematics major.

## General Education Requirements

Besides satisfying the departmental requirements in the major as summarized above (and discussed in detail in the Mathematics section of the Catalog), students must satisfy the university’s General Education Requirements. These requirements are discussed in detail in the Catalog and in the university’s Student Handbook.

- The Group Requirements are four course requirements in each of three areas (Arts and Letters; Social Sciences; and Science). Not all courses in these areas satisfy these requirements and the list of courses which do is in the Student Handbook. There are additional restrictions which are detailed in the catalog and student handbook. This provides an opportunity to concentrate on a field that is related to mathematics, and also provides an opportunity to learn about areas completely unrelated. The chance to study humanities, the arts and social science should not be passed up, as a student may never have the opportunity for formal study of these subjects after leaving college.
- The Multicultural Requirement is a requirement for one course in each of two out of three categories (American Cultures; Identity, Pluralism, and Tolerance; International Cultures). Again, the courses which satisfy this requirement are listed in the Student Handbook.
- The Writing Requirement, WR 121 and either WR 122 or WR 123.
- The Mathematics Requirement for the BS will be filled automatically by any math major, and if a student wishes to get a BA instead, there is a foreign language requirement.

Besides these there are various credit requirements for graduation. Transfer students need to be aware of the requirement for at least 62 credits of upper-division work (courses at the 300-level and above), and similarly, students who are attempting to finish their degrees while non-resident need to be aware of the requirement that at least 45 credits of work AFTER the first 120 credits be done in residence at the university.