## What is Mathematics?

A person who majors in mathematics is trained to solve problems by ignoring superfluous detail, looking for structure, and designing a logical method of attack that considers a wide range of possible outcomes and tries to eliminate preconceived notions. Mastering the content and techniques used in Mathematics is what makes this desirable outcome possible.

## Career Opportunities in Mathematics

Because math majors are trained to think clearly and logically, as well as to quantify, they are sought by business, government and industry. In particular, mathematics majors do many things besides teaching.

Recent graduates have ended up in the following fields: Physician, Actuarial Science (analyzing risks for insurance companies), Banking (designing programs so that computers can do lots of things, e.g., billing and payroll), Education (teaching at all levels, including college), Operations Research (finding the optimal way to schedule alternatively, organize industrial operations, e.g., refineries, assembly lines, and inventory control), Computer Industry (designing hardware and software), Health Professions (data mining and data compression), Cryptologist (discovering how to send messages difficult to decipher, or deciphering messages from hostile nations and groups), Law (Law schools appreciate the logical training math majors receive), Investment and Securities (research departments), and Systems Analyst (helping teams of engineers solve real world problems).

## Salary Trends in Mathematics

Mathematics majors typically receive some of the highest salaries among all college graduates. Even better, the kinds of jobs math majors typically fill rank near the top on job-satisfaction surveys because mathematicians usually have considerable autonomy in structuring their jobs.

## High School Preparation

Since the tools one uses to quantify problems are algebraic, geometric, and analytic (i.e., function driven) in nature, potential math majors should have had four years of high school mathematics: two courses in algebra, one in geometry, and one on functions (usually called precalculus). It is NOT necessary to have taken AP calculus, or even any calculus, in high school to successfully major in mathematics at the University of Tennessee.

Many math majors liked math in high school, but even if you didn’t, you may still want to major in math. In college courses, you will discover that mathematics is the language used by the world’s most creative minds to discuss the world’s most novel, exciting ideas. Math really can be the key to the cosmos.

## Highlights of Mathematics

The mathematics program at UT is designed to serve students with a broad range of interests and inclinations. Talented and highly motivated students may choose to participate in the departmental Honors Program, which features an accelerated curriculum leading to graduate courses as early as the junior year. Several recent graduates of this fast-track curriculum have received prestigious fellowships to some of the top graduate schools in the country.

Math major classes at the upper division level are small (rarely over 20 students per class), so math majors tend to know each other well. The departmental Junior Colloquium offers biweekly talks designed for undergraduates, given by mathematicians from UT and other universities.

The faculty of the Mathematics Department at the University of Tennessee is widely recognized for their internationally respected research programs and scholarly output. Therefore, math majors benefit from a well-informed, up-to-date faculty with multiple contacts throughout the national and international mathematical community.

## How to Major in Mathematics

There are only a few fixed requirements for a math major. During the first two years you will complete the calculus sequence and other basic courses that are prerequisites to higher level mathematics. These courses include Math 300, “Introduction to Abstract Mathematics,” which helps in the transition to the more abstract methods of thinking that take place in upper division mathematics courses. This course may be taken as early as the freshman year and generally should be taken no later than the second semester of the sophomore year.

**Warning: many upper division math courses required for the major have Math 300 or 307 as a prerequisite. Students who delay taking Math 300/307 until the junior year may need to take a large number of challenging upper-division courses in their senior year, and/or delay graduation. Students transferring after two years of college who haven’t had an equivalent course are strongly encouraged to take Math 300/307 during the summer prior to enrolling at UT, and no later than their first semester at UT. **

## Requirements for Mathematics

Prerequisites to the major are Mathematics 141-142 (or Honors equivalent: 147-148) and 171 or Computer Science 102.

The major consists of **37 hours** in twelve courses divided into four categories: (1) core courses, (2) courses for breadth, (3) courses for depth, and (4) additional courses (to reach 37 hours). Note: Courses used for depth (3) may also be used for breadth (2). In order to graduate, majors must take Math 495.

### 1. For the Core, complete all of the following (or honors equivalents):

MATH 231 – Differential Equations I MATH 241 – Calculus III MATH 251 – Matrix Algebra I MATH 300 – Introduction to Abstract Mathematics### 2. For Breadth, select one course from each category:

#### Algebra

MATH 351 – Algebra I MATH 455 – Abstract Algebra I MATH 456 – Abstract Algebra II MATH 457 – Honors: Abstract Algebra I MATH 458 – Honors: Abstract Algebra II#### Analysis

MATH 341 – Analysis I MATH 445 – Advanced Calculus I MATH 446 – Advanced Calculus II MATH 447 – Honors: Advanced Calculus I MATH 448 – Honors: Advanced Calculus II#### Numerical Analysis

COSC 370 – Introduction to Scientific Computing MATH 371 – Numerical Algorithms MATH 471 – Numerical Analysis MATH 472 – Numerical Algebra#### Probability and Statistics

MATH 323 – Probability and Statistics MATH 423 – Probability MATH 424 – Stochastic Processes MATH 425 – Statistics### 3. For Depth, select one of the following pairings or a two-course graduate math sequence. These courses may also be used to satisfy the Breadth requirement:

MATH 423 – ProbabilityMATH 424 – Stochastic Processes MATH 423 – Probability

MATH 425 – Statistics MATH 421 – Combinatorics

MATH 423 – Probability MATH 445 – Advanced Calculus I

MATH 446 – Advanced Calculus II MATH 447 – Honors: Advanced Calculus I

MATH 448 – Honors: Advanced Calculus II MATH 443 – Complex Variables

MATH 445 – Advanced Calculus I MATH 455 – Abstract Algebra I

MATH 456 – Abstract Algebra II MATH 457 – Honors: Abstract Algebra I

MATH 458 – Honors: Abstract Algebra II MATH 471 – Numerical Analysis

MATH 472 – Numerical Algebra MATH 471 – Numerical Analysis

MATH 475 – Industrial Mathematics MATH 472 – Numerical Algebra MATH 475 – Industrial Mathematics MATH 431 – Differential Equations II

MATH 435 – Partial Differential Equations MATH 431 – Differential Equations II

MATH 453 – Matrix Algebra IIMATH 462 – Differential Geometry

MATH 467 – Honors: Topology

**Honors Concentration
**

The requirements to graduate with honors in mathematics are the same as those for the mathematics major except the total requirement is 38 hours and includes:

- For Depth (3), complete 2 pairings, one of which must be an honors sequence (MATH 447-MATH 448, MATH 457-MATH 458) or a math graduate sequence.
- Graduate with an overall GPA of at least 3.25 and an MGPA of at least 3.4.
- Complete at least 4 hours of MATH 497.
- Complete at least 3 hours of MATH 498 and submit a completed thesis at least 30 calendar days prior to the end of the final semester of enrollment.
- Complete a total of 24 hours of honors courses or mathematics courses numbered 510 or higher (except seminars), which may include courses used to fulfill other requirements to graduate with a mathematics honors concentration.

Please see the undergraduate catalog for specific information on the Honors Concentration.

## Special Programs, Co-ops, and Internships

The Mathematics Department has a tutorial center, which is staffed primarily by undergraduate math majors that provides part-time employment and educational experience for students interested in teaching after they graduate.

Students interested in industrial employment should look into our Co-operative Education Program in which, beginning at the Sophomore level, students alternate periods (usually semesters) of full-time jobs with periods of full-time study. This program provides professional training, on-the-job experience, and income for math majors and other applied majors, e.g., computer science, engineering, and statistics. Frequently, successful students end up taking their first job after graduation from a company where they had co-operative experience. If you are interested in this program, take several courses from the Computer Science Department and/or the Statistics Department, along with your math major courses, and contact the Co-op office in 100 Dunford Hall early during your first year here.

## Ready for the World

“Ready for the World” is part of a long-range plan to transform the UTK campus into a culture of diversity that best prepares students for working and competing in the 21st century. Thus students are encouraged to actively participate in the diverse cultural programs offered on campus. Some of these events include the guest lecture series, cultural nights at the International House, and international film screenings. Visit the Center for International Education web site (http://web.utk.edu/~globe/about.shtml) or the Ready for the World web site (http://www.utk.edu/readyfortheworld/) for more information on upcoming cultural programs and activities. Learn more about UT’s Ready for the World initiative to help students gain the international and intercultural knowledge they need to succeed in today’s world.

Students are also encouraged to develop a global perspective within their academic program through study abroad. Studying abroad options do exist for mathematics and statistics majors! Possibilities include (but are not limited to) studying abstract algebra in Fiji, Galois theory in Hungary, linear programming in Malaysia, advanced stochastic processes in South Africa, or Bayesian inference in London. In addition to taking major-related courses abroad, many math or statistics majors have elected to fulfill their language requirement and/or general education courses overseas.

Consult an academic advisor early in your academic career about the best time for you to study abroad as well as what courses you may need to take. For more information about program options, the application process, and how to finance study abroad, please visit the Programs Abroad Office website.

## Academic Plan and Milestones

Following an academic plan will help students stay on track to graduate in four years. For first-time, first-year, full-time, degree-seeking students, UT has implemented Universal Tracking (uTrack), an academic monitoring system designed to help students stay on track for timely graduation. In order to remain on track, students must complete the minimum requirements for each tracking semester, known as milestones. Milestones may include successful completion of specified courses and/or attainment of a minimum GPA.

To see a sample academic plan and milestones for this major, please visit the undergraduate catalog.

## For More Information

Director of Undergraduate Studies:Dr. Nikolay Brodskiy

nbrodski@utk.edu Honors Director:

Dr. Remus Nicoara

rnicoara@utk.eduMathematics Department

University of Tennessee

(865) 974-2461

www.math.utk.edu

## Note

The information on this page should be considered general information only. For more specific information on this and other programs refer to the UT catalog or contact the department and/or college directly.