Mathematics Major Guide for 2012-2013

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: 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. Only engineering graduates rank consistently above mathematics majors in starting salaries. 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.

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 “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 will help determine the path that you follow towards completion of the major requirements. The only constraints on your choices from here on are the department’s breadth and depth requirements. At least one course must be taken from each of four fundamental areas of mathematics:

  • Analysis
  • Algebra
  • Numerical analysis
  • Probability

Each math major must also take a year­long sequence in one of the above areas.

Requirements for Mathematics

Prerequisites to the major are Mathematics 141-142 (or Honors version: 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).

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:

MATH 423 – Probability
MATH 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 II
 
MATH 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.

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.

Ready for the World logoReady 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.

 

Sample Curriculum

Following this four-year plan will help you stay on track to graduate in four years.  Milestone courses have been identified as the minimum courses that must be completed.

Freshman Year Credit Hours
English Composition 6
Foreign Language 6
Math 141, 142 or Math 147, 148 8
Math 171 or Computer Science 102 3-4
Natural Science Lab Sequence 8
Milestone courses: English 101 and Math 130 or higher
Sophomore Year Credit Hours
Foreign Language or General Electives 6
Non-US History Sequence 6
Social Science 6
Math 231, 241(247), 251(257), 300(307) 13
Milestone courses: English 102, Math 142, and Math 171 or COSC 102
Junior Year Credit Hours
Arts and Humanities 3
Upper Level Distribution 3
Math (major) 12
Upper Division Elective 3
General Electives 6-7
Senior Year Credit Hours
Communicating Through Writing 3
Communicating Orally 3
Upper Level Distribution 3
Math (major) 12
Arts and Humanities 3
Upper Division Electives 6
GRAND TOTAL (minimum) 120

For More Information

Charles Collins
Director of Undergraduate Studies
Mathematics Department
University of Tennessee
865-974-1478
ccollins@math.utk.edu
http://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.