# School of Natural Sciences and Mathematics

## Mathematics (B.S.)

Mathematics is both a profession and an indispensable tool for many types of work. As a tool, mathematics is a universal language which has been crucial in formulating and expressing ideas not only in science and engineering, but also in many other areas such as business and the social sciences. As probably the oldest and most basic science, it provides the key to understanding the major technological achievements of our time.

Of equal importance, knowledge of mathematics may help provide a student with the type of uncompromising and clear-sighted thinking useful in considering the problems of many other disciplines. The Mathematics degree program encompasses mathematics, statistics, and applied mathematics.

Applied mathematics and statistics continue to enjoy a rapid growth. Students have the opportunity of applying their expertise to any of a number of fields of application. For the student to be more effective in such applications, Mathematics also offers degree programs allowing additional emphasis in the areas of actuarial science, computer science, electrical engineering, and management.

Those interested in obtaining both a B.S. in Mathematics and Teacher Certification in the state of Texas should consult the Office of Teacher Education for specific requirements as soon as possible after formal admission to the University. See the Teacher Education section of this catalog for additional information.

The Mathematics degree program also prepares students for graduate studies. An accelerated B.S./M.S. Fast Track program is available which provides the opportunity for undergraduate students to satisfy some of the requirements of the master’s degree while they are completing the bachelor’s degree in Mathematics.

### Faculty

**Professors: **Larry P. Ammann, Michael I. Baron, Sam Efromovich, M. Ali Hooshyar, Wieslaw Krawcewicz, Patrick L. Odell (Emeritus), Istvan Ozsvath, Viswanath Ramakrishna, Ivor Robinson (Emeritus), Robert Serfling, Janos Turi, John W. Van Ness (Emeritus)

**Associate Professor:** Zalman I. Balanov, Pankaj Choudhary, Mieczyslaw Dabkowski

**Assistant Professor**: Yan Cao, Tobias Hagge, Quiongxia (Joanne) Song

**Affiliated Faculty**: Herve Abdi (BBS), Titu Andreescu, Alain Bensoussan (JSOM), Thomas Butts (SME), Raimond Ober (EE), John Wiorkowski (JSOM)

**Senior Lecturers**: Malgorzata Dabkowska, Anatoly Eydelzon, Bentley Garrett, Yuly Koshevnik, David L. Lewis, Joanna R. Robinson, William Scott, Paul Stanford

### The Programs in Mathematics

Students seeking a degree in Mathematics may specialize in Traditional Mathematics, Statistics, or Applied Mathematics. Each specialization allows some flexibility in electives so that students can better adapt their degree plans to their educational goals.

Mathematics: For students interested in a career in mathematics and for students interested in continuing on to graduate work in mathematics, applied mathematics, math education, and related areas.

Statistics: For students interested in probability and statistical models and their use in data analysis and decision making and for students interested in continuing on to graduate work in statistics, biostatistics, actuarial science, and other statistics related areas.

Applied Mathematics: For students interested in mathematics for the purpose of using it broadly in various areas of application and for students interested in continuing on to graduate work in applied mathematics and related areas.

## Bachelor of Science in Mathematics Degree Requirements (120 hours)

### I. Core Curriculum Requirements^{1}

- Communication (6 hours)
- Social and Behavioral Sciences (15 hours)
- Humanities and Fine Arts (6 hours)
- Mathematics and Quantitative Reasoning (6 hours)
- Science (9 hours)

*Statistics Option*

or PHYS 2421 Honors Physics I - Mechanics and Heat with Laboratory and PHYS 2422 Honors Physics II -

Electromagnetism and Waves with Laboratory

or CHEM 1311/1111 and CHEM 1312/1112 General Chemistry I and II with Laboratory

^{1} Curriculum Requirements can be fulfilled by other approved courses from accredited institutions of higher education. The courses listed in parenthesis are recommended as the most efficient way to satisfy both Core Curriculum and Major Requirements at UT Dallas.

### II. Major Requirements: 48 hours

** Major Preparatory Courses (15 hours)**

- CS 1337* Computer Science I

MATH 2417 Calculus I

^{3}

MATH 2418* Linear Algebra

MATH 2419 Calculus II

^{3}

MATH 2420* Differential Equations with Applications

MATH 2451* Multivariable Calculus with Applications

** Major Core Courses (21 hours)**

- MATH 3310 Theoretical Concepts of Calculus

MATH 3311 Abstract Algebra I

MATH 3379 Complex Variables

MATH 4301 Mathematical Analysis I

MATH 4302 Mathematical Analysis II

MATH 4334 Numerical Analysis

NATS 4310 Advanced Writing in the Natural Sciences and Mathematics

^{2}

STAT 4351 Probability

** Major Related Courses (12 hours)**

*Applied Math Specialization*

- MATH 4341 Topology

MATH 4355 Methods of Applied Mathematics

MATH 4362 Partial Differential Equations

STAT 4382 Stochastic Processes

*Mathematics Specialization*

- MATH 3312 Abstract Algebra II

MATH 3321 Geometry

MATH 4341 Topology

3 hours upper-division guided elective

^{4}

*Statistics Specialization*

- STAT 3355 Data Analysis for Statisticians and Actuaries

STAT 4352 Mathematical Statistics

STAT 4382 Stochastic Processes

3 hour upper-division guided elective

^{ 4}

^{2} A Major course requirement that also fulfills a Core Curriculum requirement. If hours are counted in the Core Curriculum, students must complete additional coursework to meet the minimum requirements for graduation. Course selection assistance is available from the undergraduate advisor.

^{3} Two hours of Calculus are counted as electives; six hours are counted in Core Curriculum.

^{4} Approval of Mathematical Science department advisor required.

* Indicates a prerequisite class to be completed before enrolling in upper-division classes.

### III. Elective Requirements: 30 hours

**Advanced Electives (6 hours)**

** Free Electives (24 hours)**

Both lower- and upper-division courses may count as electives, but the student must complete at least 51 hours of upper-division credit to qualify for graduation.

**Mathematics Programs with Actuarial Science Emphasis**

Refer to the Actuarial Science B.S. degree program.

**Mathematics Programs with Computer Science Emphasis **

- CS 2305 Discrete Mathematics for Computing I

CS 2336 Computer Science II

CS 3305 Discrete Mathematics for Computing II

CS 3335 C and C++

CS 3345 Data Structures and Introduction to Algorithmic Analysis

CS 4337 Organization of Programming Languages

CS 3340 Computer Architecture

**Mathematics Programs with Electrical Engineering Emphasis **

- EE 3101 Electrical Network Analysis Laboratory

EE 3111 Electronic Circuits Laboratory

EE 3120 Digital Circuits Laboratory

EE 3301 Electrical Network Analysis

EE 3311 Electronic Circuits

EE 3320 Digital Circuits

EE 4301 Electromagnetic Engineering I

**Mathematics Programs with Management Emphasis **

- AIM 2301 Introductory Financial Accounting

AIM 2302 Introductory Management Accounting

BA 2301 Business and Public Law

BA 3341 Business Finance

BA 3351 Introduction to Management Information Systems

BA 3361 Organizational Behavior

NOTE: Students transferring into Mathematics at the upper division level are expected to have completed all of the 1000- and 2000- level mathematics core course requirements.

### Minor in Mathematics

Students not majoring in Mathematics may obtain a minor in Mathematics or Statistics by satisfying the following requirements:

18 credit hours of mathematics or statistics, 12 hours of which must be chosen from the following courses:

- Mathematics Minor: MATH 3310, MATH 4334 and two more upper-division mathematics courses that satisfy
degree requirements by students in Mathematics.

Statistics Minor: STAT 4351, STAT 4352 and two more upper-division mathematics courses that satisfy degree; requirements by students in Mathematics.

### Fast Track Baccalaureate/Master’s Degrees

For students interested in pursuing graduate studies in Mathematics, the Mathematics Department offers an accelerated B.S. /M.S. Fast Track that involves taking graduate courses instead of several advanced undergraduate courses. Acceptance into the Fast Track is based on the student’s attaining a GPA of at least 3.200 in all mathematics classes and being within 30 hours of graduation. Fast Track students may, during their senior year, take 15 graduate hours which may be used to complete the baccalaureate degree. After admission to the graduate program, these 15 graduate hours may also satisfy requirements for the master’s degree. Fast Track programs are offered in math, applied math, and statistics.