**PROGRAM PLANNING GUIDE**

for UNDERGRADUATE MATHEMATICS MAJORS

for UNDERGRADUATE MATHEMATICS MAJORS

** Contents**

I. Introduction

II. The Curriculum

A. Goals of the Math Major Program

B. General Requirements

C. First Year Courses

D. Mathematics Major Requirements

E. Sample Programs

F. Honors Program

G. Minors and Second Majors

H. Teaching Certification

III. Student Employment

A. Math Sciences Co-op Program

B. Math Department Jobs

A. Honors and Awards

B. Student-Department Relations

This guide is designed to inform you about the Mathematics Department at UTK and to help you plan your coursework. Although the curricular requirements (Section II) may be your primary concern, please read the other sections and consider taking advantage of the Co-op program and departmental employment opportunities. Activities like these can do much to enrich and broaden your mathematical experience, and give you an advantage in the job market when you graduate.

This guide is not a substitute for regular meetings with your faculty advisor. Your advisor, the best source for academic and professional advice, is also an excellent source for letters of recommendation when you graduate if you have given him or her the opportunity to become acquainted with you. You will be required to meet with your advisor each semester; you are strongly urged, however, to consult with him or her more often.

You will find additional information of interest to math majors in Ayres Hall 225B.

You may also be interested to learn that there is a special room, the Mathematics Undergraduate Reading Room, set aside exclusively for mathematics majors. This room, Ayres 229, provides you a chance to network with other mathematics majors, to study between classes, and to read recent periodicals in mathematics.

Should you choose to major in mathematics, we welcome you and hope you find this guide helpful. Get to know the Mathematics Department faculty and your educational experience will be enriched. We would appreciate your suggestions regarding additional information or services which the department can provide to its majors in the future.

A. GOALS OF THE MATHEMATICS MAJOR PROGRAM

The purpose of the mathematics degree program is to provide knowledge of the central concepts and techniques of mathematics, appreciation of the breadth of the mathematical sciences and their deep interconnecting principles, and understanding of the interplay between theory and applications. Mathematics majors should acquire reasoning, problem solving, computational and communication skills that can be adapted to and used with success in any professional field.

Logical reasoning and precise communication are closely linked, and lie at the core of an education in mathematics. Mathematical reasoning involves not only the ability to understand and produce rigorous mathematical arguments, but also the capacity to explore subtlety and discern patterns and significance. Communication of mathematical ideas ranges from intuitive description to formal proof. Mathematics majors should be able to use mathematical reasoning, express mathematical ideas in both written and spoken form, and obtain and analyze information effectively.

The power of mathematics is demonstrated by its wide applicability to concrete problems. Mathematics majors should be able to recognize mathematical ideas in diverse contexts and be able to apply mathematics to a broad spectrum of problems. Since computation is a central part of modern applied mathematics, mathematics majors should be able to use computers for numerical processing, modeling, simulation, and visualization.

THE DEVELOPMENT OF MATHEMATICAL THOUGHT

Mathematics majors should acquire an appreciation of contemporary mathematics, and the historical contexts in which mathematics has been developed and practiced. They should also be familiar with some of the important questions which have stimulated the evolution of mathematical thought.

To obtain a B.S. degree in Mathematics from UTK one must complete at least 124 credit hours divided as follows: prerequisites to the major (11 hrs), English Composition (6 hrs), distribution requirements (38-42 hrs), upper level distribution requirements (6 hrs), major courses (37 hrs), and electives (the remaining hours).

Prerequisites to the mathematics major (which serve as a foundation to all other math courses) are calculus of one variable (Math 141-142 or 147-148) and computer literacy (Math 171).

Distribution requirements (which are designed to ensure a broad education) fall into three categories: a laboratory science sequence (8 hrs), a non-US history sequence (6 hrs), social science courses from at least two different departments (6 hrs), humanities courses (6 hrs), and completion of the second year of a foreign language (normally, 12-16 hrs total). Although you may fulfil distribution requirements any way you wish, we recommend Physics 131-132 or 137-138 for the lab science and Economics 201 or 207 for the social science, since these courses all make substantial use of calculus. You may also wish to consider using French, German, or Russian for the foreign language requirement, since there is a vast body of mathematical literature available in each of them.

Upper level distribution requirements ensure additional breadth at the junior or senior level. Part of this requirement can be fulfilled by taking Math 400 (History of Mathematics), usually offered Spring and Summer Semesters, or Math 411 (Mathematical Modeling), usually offered Fall Semester. Although neither of these courses count as part of the mathematics major, either one of them will give you a broader perspective on mathematics. Moreover, they will sharpen your skills at communicating mathematics because each of them is a writing emphasis capstone course. The remaining hours of this requirement can be taken from an extensive set of courses in U.S. or foreign studies, or from literature courses in a foreign language. In particular, if you enjoyed the first two years of foreign language study and wish to improve your skills in this area, an upper division literature course in the language you have been studying is an excellent choice. (Note: literature-in-English-translation courses do not fulfill this requirement.)

Major courses will be discussed in sections C and D below.

Elective courses provide you with an opportunity to strengthen your major and to shape your own program to fit your interests and career goals. These courses should include selections from mathematics and other departments as well. Please plan this portion of your curriculum with care. Seek input from your mathematics faculty advisor. He or she can offer professional guidance which will enhance your degree and increase your marketability when you finish your education.

The prerequisites to the mathematics major are calculus (Math 141-142 or 147-148) and computer literacy (Math 171).If you studied two years of algebra, a year of geometry, and at least a half year of trigonometry, and your ACT score in Mathematics is 28 or higher, your first math course should be Math 141. (If your score is 32 or higher, we urge you to take the honors version 147). If your ACT score in Mathematics falls below 28, you should take Math 130 before enrolling in Math 141. (If you have not studied trigonometry, first take the non-credit trigonometry course Math 015.)

If you had a year of calculus in high school, you may consider taking additional calculus a waste of time. However, you will find that calculus courses taught in college are significantly different from the course you took in high school. Nevertheless, if you took the AB Advanced Placement Test in calculus and received a score of "3" or better, we will give you credit for Math 141 and you may take Math 142 as a first course here. If you took the BC Advanced Placement Test in Calculus and received a score of "3" or better, we will give you credit for Math 141-142 and you may take Math 241 as a first course here, or (after consulting with the Mathematics Department) the honors version Math 247. In any event, do not postpone beginning your mathematical coursework because you have received advanced credit. Mathematics is like an iron tool. It gets rusty if not used regularly.

D. MATHEMATICS MAJOR REQUIREMENTS

In addition to 141-142 (or 147-148) and 171 (or their equivalents), every math major must take some required math courses (13 hrs) and some elective math courses (24 hrs).

The required math courses are

Math 241 or 247 (Calculus of Several Variables)

Math 231 (Differential Equations)

Math 251 or 257 (Linear Algebra and Matrices)

Math 300 (Introduction to Abstract Mathematics)

These courses are designed to broaden your knowledge and sharpen your skills in preparation for more advanced and, in some cases, more theoretical courses at the junior and senior level.

The elective math courses must satisfy the following conditions:

(A) At least one course must be taken from each of the following categories:

ALGEBRA: 351, 455-56 (457-58)

ANALYSIS: 341, 445-45 (447-48)

NUMERICAL ANALYSIS: 371, 471-72

PROBABILITY/STATISTICS: 323, 423-24 (423-25)

(B) At least one 400 level two-semester sequence must be taken from the list in Part A.

These conditions are designed to ensure additional breadth and depth to the major, and to provide a broad introduction to four of the core components of mathematics.

Because of fixed requirements, the first two years of any math major's schedule will look about the same. Here is a typical example:

Freshman

Fall: Math 141; English Composition; Foreign Lanugage I; Laboratory Science

Spring: Math 142; Math 171; English Composition; Foreign Language I; Laboratory Science

Sophomore

Fall: Math 241; Math 231; Non-US History; Social Science Distribution; Foreign Language II

Spring: Math 251; Math 300; Non-US History; Elective; Foreign Language II

Because there are many careers one can pursue with a mathematics major, the rest of the program will vary from student to student. It should be designed carefully, in consultation with a Mathematics Faculty Advisor, to reflect special interests or career goals of each individual. Here are several options and sample programs to go with them. Math courses in parentheses are recommendations for electives which fall outside the minimal requirements. In each case these additional courses have been designed to strengthen your preparation toward the intended goal.

(1) PURE MATHEMATICS

This plan, which emphasizes abstract mathematics, provides good preparation for students who wish to pursue an advanced degree in mathematics.

Junior

Fall: Math 431 or 435; Math 423; Math 371; Humanities Distribution; Social Science Distribution

spring: Math 421 or 461; (Mth 424 or 425), (Math 341 or 351); Humanities Distribution; Elective

Senior

Fall: Math 445; Mth 455; (Mth 443); Upper Level Distribution; Elective

Spring: Math 446; Math 456; Math 400; Elective; Elective

This plan is appropriate for students who wish to pursue an advanced degree in applied mathematics or some other field which uses mathematics extensively (e.g., economics), or who intend to seek industrial employment after completing the B.S. degree.

Junior

Fall: Math 351, 431, (423), Humanities Distribution, Social Science Distribution

Spring: Math 371, 435, (424 or 425), Humanitties Distribution, Elective

Senior

Fall: Math 471, 411, 445, (443), Elective

Spring: Math 472, 475, (446 or 404), Upper Level Distribution, Elective

(3) ACTUARIAL AND STATISTICAL MATHEMATICS

This program, which emphasizes probability and mathematical statistics, is designed to prepare a student for graduate study or industrial employment in actuarial or managerial science.

Junior

Fall: Math 351, 423, (453), Humanities Distribution, Social Science Distribution

Spring: Math 371, 424 or 425, (421), Humanities Distribution, Elective

Senior

Fall: Math 445, 471, (443), 411, Elective

Spring: Math 446, 472 or 475, (435, Upper Level Distribution, Elective

This program is designed for students who intend to teach high school mathematics.

Junior

Fall: Math 323, 351, Humanities Distribution, Social Science Distribution,

Psychoeducational Studies 210, Ed.S.Math.R. & Tech 304

Spring: Math 371, 341, Humanities Distribution, Ed.S.Math.R. & Tech 352,

Ed.S.Math.R. & Tech 355, Elective

Senior

Fall: Math 445 (or 455), 460, Upper Level Distribution, Education 400, 401, (453)

Spring: Math 446 (or 456), 421 or 431, 400, Education 403, Elective

F. HONORS PROGRAM

An honors B.S. degree is available to any mathematics major who fulfills all of the requirements for a B.S. degree in mathematics, but takes 27 hrs of math electives (instead of 24 hrs) and two 400 level two-semester sequences (instead of one). The grade point average, computed on the 27 hours of mathematics elective courses will determine the honors category as follows:

G.P.A. at least 3.4 - Honors

G.P.A. at least 3.6 - High Honors

G.P.a. at least 3.8 - Highest Honors

Students with credit for more then 27 hours of mathematics electives may designate which courses will be used to compute these averages.

Candidates for an honors degree must apply to the Chair of the Undergraduate Honors Committee the semester before they expect to graduate (e.g., in fall for May graduation or in spring for December graduation). Their application should list the courses comprising the required 27 hours. A note of successful completion of the honors program will be entered on the transcript.

Students interested in pursuing an honors degrees should consult with their advisors as early as possible.

A minor or second major in a field which makes substantial use of mathematics can help you get into graduate school or get a better job at graduation. Requirements for minors and majors can be found in the general catalogue under the appropriate departmental heading.

Two departments, Computer Science and Statistics, are closely allied to mathematics. Because courses counting toward your major can also be used to satisfy minor and second major requirements, it follows that a math major can pick up a minor or second major in Computer Science or Statistics with just a few extra courses. For your convenience, the minor and major requirements for these two departments are listed below together with an indication of which courses can be shared.

COMPUTER SCIENCE:

Major:

i) CS 102, 140, and 160 are prerequisites

ii) CS 302, 311, 365, 380, and two of the three courses 340, 360, and 370.

[CS 311 and 380 can be used as math electives. Math 371 will substitute

for CS 370].

iii) 6 additional hours of CS Advanced Topics courses

[Math 471-472 will satisfy this requirement].

iv) A student may progress to the major only after completing courses specified by the C.S. Department. These courses are listed in the Undergraduate Handout available from the C.S. Department. Students must apply to the C.S. Department in order to be officially enrolled in this program.

THEREFORE, you can pick up a double major in C.S. by taking only five courses in addition to a carefully planned math major curriculum: C.S. 140, 160, 302, 365, and 340 or 360.

Minor: C.S. 140 and 160 plus 15 hours of 300 or 400 level courses in C.S. [371, 471-472 fulfills 9 of these 15 hours]

THEREFORE, you can pick up a minor in C.S. by taking only four courses in addition to a carefully planned math major curriculum: C.S. 140, 160 plus 6 hours of 300 or 400 level courses in C.S.

STATISTICS

Major:

i) Stat 201 or 251

[Math 323 will substitute for either one]

ii) Stat 320 and 365

iii) Stat 330 and 471

iv) two 400-level electives

[Math 423-424 or math 423-425 can be used for these 400-level electives].

THEREFORE, you can pick up a double major in Statistics by taking only four courses in addition to a carefully planned math major curriculum.

Minor:

i) Stat 201 or 251

[Math 323 will substitute for either one]

ii) 12 hours from Stat 320, 330, 364, 471, 472, 473, 475 and Math 423, 424, 425

[If Math 323 has been substituted for 201 or 251, your first statistics course should be

370 or 365, not 330].

THEREFORE, you can pick up a minor in Statistics by taking only two courses in addition to a carefully planned math major curriculum.

A secondary teaching certificate requires a B.A. or B.S. degree in an academic subject area plus an intern year in the College of Education. For endorsement in mathematics in grades 7-12, the Baccalaureate degree does not necessarily have to have a major in mathematics but must include at least 24 semester hours of mathematics including courses in certain areas. The Mathematics Department recommends the following 36 hours: Math 141-42, 241, 251, 300, 323, 341, 351, 400, 401, and 460. These courses exceed the requirements for a mathematics minor and satisfy Tennessee state minimum requirements for mathematics teaching in grades 7-12. More detailed information may be obtained from Ayres 225B and the College of Education. If you are interested in a teaching career, you should seek information early in your sophomore year.

A. MATH SCIENCES CO-OP PROGRAM

In September 1979, the three mathematical sciences department (Computer Science, Mathematics and Statistics) began a co-op education program. The program locates jobs for students who alternate periods of full-time employment with periods of full-time study. After each period on campus,the student returns to the same employer and the cycle repeats. The total number of semesters of work ranges from 2 to 5, depending on when the student begins.

All co-op assignments provide professional training and on-the-job experience. Some of these jobs are in the Knoxville area, others are at various locations in the southeast. In some cases, jobs can be found near a student's home.

Many students find that co-op employment pays for most, (if not all), of their educational expenses. At the same time, there are other advantages: professional experience, opportunity to make contacts valuable for finding permanent employment, exposure to problems and ideas different from those available in academic courses, and perhaps a chance to live and work in a different part of the country.

Most co-op jobs require at least one semester of computer science (C.S. 102). Thus, if you are interested in the co-op program, you can improve your chances greatly by taking C.S. 102 early, preferably during your first year. In addition, most employers want students who have a background in one of the following skills:

I) programming (C.S. 111, 112, and 320);

ii) math modeling (Math 231 plus C.S. 102);

iii) applied math (C.S. 102, Math 371 and knowledge of a natural science such as biology or physics);

iv) statistics (Math 251, 323, Stat. 411).

Interested students who plan their programs accordingly can begin co-op jobs sometime during the sophomore year. It is a good idea to apply early, however, and first-year students are encouraged to apply.

Information about the program is available from Ayres 225 and from the Career Co-op Programs office, Alumni Hall.

B. MATHEMATICS DEPARTMENT JOBS

The Mathematics Department has several employment opportunities for undergraduate students. These jobs provide not only money, but also valuable experience and an opportunity to work with other math majors and faculty members. Although math majors are given preference for these positions, students with other majors are often hired if they have the necessary qualifications.

1. Math Lab Tutors

The Math Lab is a free individualized tutorial service available to all students enrolled in lower division mathematics courses. The lab, which is located in Ayres G012, operates about 40 hours per week.

During the academic year, 25-40 students are employed as proctors in the Math Lab from six to ten hours per week, compensated at a fixed hourly rate. Math and Math Education majors are given preference. Application forms are available online; for more information on proctoring, see the Math Lab directors in Ayres G012.

2. Paper Graders

Students are needed to grade papers, both for calculus sections and for certain upper division courses. Graders are paid by the hour, with higher rates for the more advanced courses. College Work-Study students are preferred for these positions; others may be hired if funds are available.

3. Federally Funded Work-Study Positions

Many students with grants from the College Work-Study Program, funded by the U.S. Office of Higher Education, have been hired to work in the department office, to proctor, to tutor or to grade papers. It is hoped that funds will continue to be available for this program, which has been highly advantageous to both the students and the department. Applications are taken at the University's Financial Aid Office in the Student Services Building. Anyone with a work-study grant who is interested in working for the Mathematics Department may inquire at the department office.

4. Teaching Assistantships

Each year the Mathematics Department offers several new graduate teaching assistantships to students beginning work towards the Master's and Ph.D. degrees. Information and application materials can be obtained in Ayres 225A. Your application should be submitted here (and to other graduate schools) no later than February 1 of your senior year. Graduate work is worth considering; it can be very rewarding, both intellectually and monetarily.

Each spring the Mathematics Department presents several awards and scholarships to outstanding students at an honors ceremony. The following awards are available to undergraduate students.

1. The John M. Allen Mathematics Prize is awarded annually to the most outstanding first year mathematics student. Any first year student enrolled in a mathematics course below the 300 level is eligible. The award is based on the results of a competitive exam, given during the spring semester on the content of the courses 141-142 and 147-148. Time and place of the exam will be announced in all appropriate classes.

2. The J.A. Cooley Memorial Scholarship is awarded to the outstanding junior mathematics major interested in pursuing a career in the teaching of mathematics. The scholarship is for use during the senior year of study. Interested students may obtain application forms from Ayres 227.

3. The Lucille and Herbert Lee Mathematics Scholarships are awarded to one or more outstanding sophomore or junior mathematics majors. Interested students may obtain application forms from Ayres 227.

4. The Cooper D. Schmidt Mathematics Scholarships are awarded to one or more outstanding sophomore or junior mathematics majors. Interested students may obtain application forms from Ayres 227.

5. John H. Barrett Prize, one of our most prestigious awards, is awarded annually to the most outstanding senior mathematics student. (Non-majors are eligible for this award.) The faculty is asked to nominate candidates each year.

B. STUDENT-DEPARTMENT RELATIONS

Every semester (except summer), more than 7,000 students enroll in a mathematics class at UTK. Although complaints are rare, sometimes situations arise which can only be solved through mediation by a third party. If you have a problem in a specific class that you and your instructor are unable to resolve, you may seek help by coming to Ayres Hall 225B or calling 974-1478 to make an appointment with the Associate Head in charge of the undergraduate mathematics program.

In any huge institution, it is easy to feel lost among the masses. There is a simple antidote for this: get acquainted with your professors and mathematics advisor. They, not the student grapevine, can help you with their advice, knowledge, and experience. Many questions of a general nature can be answered by the staff in the Mathematics Department office (Ayres Hall 227). Someone is there from 7:30 a.m. to 5:00 p.m., Monday through Friday. Curricular problems can be solved by using this guide and scheduling a conference each semester with your faculty advisor.

Mathematics Department

225B Ayres Hall

University of Tennessee

Knoxville, TN 37996-1320

865-974-1478