# School of Natural Sciences and Mathematics

## Mathematical Sciences (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 Mathematical Sciences 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, Mathematical Sciences 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 Mathematical Sciences 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 Mathematical Sciences 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 Mathematical Sciences.

### Faculty

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

**Assistant Professor:** Yan Cao, Pankaj Choudhary, Mieczyslaw Dabkowski

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

**Senior Lecturers:** Frank R. Allum, Bentley Garrett, Yuly Koshevnik, Grigory Kramer, David L. Lewis, Charles R. McGhee, Joanna R. Robinson, William Scott, Paul Stanford

### The Programs in Mathematical Sciences

Students seeking a degree in the Mathematical Sciences may specialize in Mathematics, Statistics, or Applied Mathematics, and receive a B.S. degree in these areas. 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.

### Fast Track Baccalaureate/Master's Degrees

For students interested in pursuing graduate studies in Mathematical Sciences, 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 3.20 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.

### Bachelor of Science in Mathematical Sciences

Degree Requirements (120 hours)

#### I. Core Curriculum Requirements^{1}: 42 hours

A. Communication (6 hours)

3 hours Communication (RHET 1302)

3 hours Communication Elective (NATS 4310, or MATH 4390 or MATH 4398)^{2}

B. Social and Behavioral Sciences (15 hours)

6 hours Government (GOVT 2301 and 2302)

6 hours American History

3 hours Social and Behavioral Sciences Elective

C. Humanities and Fine Arts (6 hours)

3 hours Fine Arts (ARTS 1301)

3 hours Humanities (HUMA 1301)

D. Mathematics and Quantitative Reasoning (6 hours)

6 hours Calculus (MATH 2417 and 2419)^{3}

E. Science (9 hours)

*Math/Applied Math Options*

PHYS 2125 Physics Laboratory I

PHYS 2126 Physics Laboratory II

PHYS 2325 Mechanics

*or* PHYS 2421 Honors Physics I - Mechanics and Heat

PHYS 2326 Electromagnetism and Waves

*or* PHYS 2422 Honors Physics II - Electromagnetism and Waves

And an additional acceptable science course

*Statistics Option*

PHYS 2325/2125 Mechanics with Laboratory and PHYS 2326/2126 Electromagnetism and Waves with Laboratory

*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* 1312/1112 General Chemistry I and II with Laboratory

And an additional acceptable science course

^{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)

All students are required to take at least six hours of advanced electives outside their major field of study. These must be either upper-division classes or lower-division classes that have prerequisites.

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.

### Mathematical Sciences Programs with Actuarial Science Emphasis

*Statistics Specialization together with following courses:*

- AIM 2301 Introductory Financial Accounting
- BA 3341 Business Finance
- BA 3351 Introduction to Management Information Systems
- BA 4345 Financial Markets and Institutions
- BA 4346 Investment Management
- STAT 4372 Actuarial Science
- And any two of the following courses:
- AIM 2302 Introductory Management Accounting
- AIM 3331 Intermediate Financial Accounting I
- BA 4347 Applied Corporate Finance
- ECON 4330 Law and Economics

Notes: AIM 2301 must be taken before BA 3341, 4345, 4346 and 4347.

MATH 1325 or MATH 2417 relates to Exam 100 of Society of Actuaries (SOA) and Exam 1A of the Casualty Actuarial Society (CAS) and MATH 4334 relates to Exam 135 of SOA.

STAT 4351 and STAT 4352 relate to Exam 110 of SOA and Exam 1B of CAS. STAT 3355 and STAT 4382 relate to Exam 120 of SOA and Exams 3F, 3G, 4A, 4B, 4C of CAS. STAT 4372 relates to Exams 3E, 3H and the rest of Exam 4 of CAS and Exam 150 of SOA.

### Mathematical Sciences Programs with Computer Science Emphasis

*Applied Mathematics Specialization or Statistics Specialization together with following courses:*

- 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

### Mathematical Sciences Programs with Electrical Engineering Emphasis

*Applied Mathematics Specialization or Statistics Specialization together with following courses:*

- 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

### Mathematical Sciences Programs with Management Emphasis

*Mathematics Specialization, Applied Mathematics Specialization or Statistics Specialization together with following courses:*

- 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 Mathematical Sciences at the upper-division level are expected to have completed all of the 1000- and 2000-level mathematics core course requirements.

### Minor in Mathematical Sciences

Students not majoring in Mathematical Sciences 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 Mathematical Sciences.

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