# School of Natural Sciences and Mathematics

## Mathematics (BS)

Mathematics is both a profession and an indispensable tool for many types of work. As a tool, mathematics is a universal language that 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 BS in Mathematics and Teacher Certification in the state of Texas should consult the Teacher Development Center or UTeach Dallas office for specific requirements as soon as possible after formal admission to the University. See the Teacher Education Certification Programs section of the catalog for additional information.

The Mathematics degree program also prepares students for graduate studies. An accelerated BS/MS 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, Vladimir Dragovic, Sam Efromovich, Matthew J. Goeckner, M. Ali Hooshyar, Wieslaw Krawcewicz, Susan E. Minkoff, Dmitry Rachinskiy, Viswanath Ramakrishna, Robert Serfling, Janos Turi, John Zweck

**Professors Emeritus:** Patrick L. Odell, Istvan Ozsváth, Ivor Robinson, John W. Van Ness

**Associate Professors:** Zalman I. Balanov, Yan Cao, Pankaj K. Choudhary, Mieczyslaw K. Dabkowski, Yulia Gel

**Clinical Associate Professor:** Natalia Humphreys

**Assistant Professors:** Mohammad Akbar, Swati Biswas, Bhargab Chattopadhyay, Min Chen, Tobias Hagge, Qingwen Hu, Oleg Makarenkov, Qiongxia (Joanna) Song

**Senior Lecturers III:** Bentley T. Garrett, David L. Lewis, Paul Stanford

**Senior Lecturers II:** Manjula Foley, Yuly Koshevnik, William M. Scott

**Senior Lecturers I:** Diana Cogan, Malgorzata Dabkowska, Anatoly Eydelzon, Brady McCary, Jigarkumar Patel

**Affiliated Faculty:** Hervé Abdi, Titu Andreescu, Alain Bensoussan, Raimund J. Ober, John J. Wiorkowski

**Adjunct Faculty from the Research for Mathematics of the Mexican Council and Technology (CIMAT):** José Carlos Gómez Larrañaga, Adolfo Sánchez Valenzuela

### The Program in Mathematics

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

Mathematics Specialization: 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 Specialization: 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 Specialization: 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.

The UTeach option may be added to the BS degree in Mathematics. UTeach Dallas Option degree plans are streamlined to allow students to complete both a rigorous Bachelor of Science or Bachelor of Arts degree and all coursework for middle or high school teacher certification in four years. Teaching Option degrees require deep content knowledge combined with courses grounded in the latest research on math and science education. While most graduates go on to classroom teaching, UTeach alums are also prepared to enter graduate school and to work in discipline related industry.

### Bachelor of Science in Mathematics

#### Degree Requirements (120 hours)

All majors with specialization in either Mathematics or Statistics are strongly urged to meet with assigned departmental advisors every semester.

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

**Communication (6 hours)**

3 hours Communication (RHET 1302)

3 hours Communication Elective (NATS 4310 or MATH 4390 or MATH 4399)^{2}

**Social and Behavioral Sciences (15 hours)**

6 semester credit hours Government (GOVT 2301 and GOVT 2302)

6 hours American History

3 hours Social and Behavioral Science Elective

**Humanities and Fine Arts (6 hours)**

3 hours Fine Arts (ARTS 1301)

3 hours Humanities (HUMA 1301)

**Mathematics and Quantitative Reasoning (6 hours)**

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

**Science (9 hours)**

*Mathematics/Applied Mathematics Specialization*

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 Wave

or PHYS 2422 Honors Physics II - Electromagnetism and Waves

Plus an additional science course approved by the assigned departmental advisor.

*Statistics Specialization*

(PHYS 2325 Mechanics and PHYS 2125 Physics Laboratory I and PHYS 2326 Electromagnetism and Waves and PHYS 2126 Physics Laboratory II)

or (PHYS 2421 Honors Physics I - Mechanics and Heat and PHYS 2125 Physics Laboratory I and PHYS 2422 Honors Physics II - Electromagnetism and Waves and PHYS 2126 Physics Laboratory II)

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

Plus an additional science course approved by the assigned departmental advisor.

II. Major Requirements: 48 hours

**Major Preparatory Courses (15 hours)**

CS 1337 Computer Science I^{4}

MATH 2417 Calculus I^{3}^{, }^{5}

MATH 2419 Calculus II^{3}^{, }^{5}

MATH 2420 Differential Equations with Applications^{4}

MATH 2451 Multivariable Calculus with Applications^{4}

**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 Mathematics 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 3380 Differential Geometry

MATH 4341 Topology

3 hours upper-division guided elective^{6}

*Statistics Specialization*

STAT 3355 Data Analysis for Statisticians and Actuaries

STAT 4352 Mathematical Statistics

STAT 4382 Stochastic Processes

3 hours upper-division guided elective^{6}

III. Elective Requirements: 30 hours

**Electives (30 hours)**

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

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

**BS in Actuarial Science**

The department offers a BS in Actuarial Science (see the program within this catalog for additional information).

**Mathematics or Statistics 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 3376 C/C++ Programming in a UNIX Environment

CS 3345 Data Structures and Introduction to Algorithmic Analysis

CS 4337 Organization of Programming Languages

CS 3340 Computer Architecture

**Mathematics or Statistics 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

**Mathematics or Statistics with Management Emphasis**

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

ACCT 2301 Introductory Financial Accounting

ACCT 2302 Introductory Management Accounting

BLAW 2301 Business and Public Law

FIN 3320 Business Finance

MIS 3300 Introduction to Management Information Systems

OBHR 3310 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.

### Bachelor of Science in Mathematics with UTeach Option

#### Degree Requirements (120 hours)

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

**Communication (6 hours)**

3 hours Communication (RHET 1302)

3 hours Communication Elective (NATS 4390)^{2}

**Social and Behavioral Sciences (15 hours)**

6 semester credit hours Government (GOVT 2301 and GOVT 2302)

6 hours American History

3 hours Social and Behavioral Science Elective

**Humanities and Fine Arts (6 hours)**

3 hours Fine Arts (ARTS 1301)

3 hours Humanities (HUMA 1301)

**Mathematics and Quantitative Reasoning (6 hours)**

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

**Science (9 hours)**

*Mathematics/Applied Mathematics Specialization*

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 Specialization*

(PHYS 2325 Mechanics and PHYS 2125 Physics Laboratory I and PHYS 2326 Electromagnetism and Waves and PHYS 2126 Physics Laboratory II)

or (PHYS 2421 Honors Physics I - Mechanics and Heat and PHYS 2125 Physics Laboratory) I and PHYS 2422 Honors Physics II - Electromagnetism and Waves and PHYS 2126 Physics Laboratory II)

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

Plus an additional acceptable science course approved by the assigned departmental advisor.

II. Major Requirements: 50 hours

**Major Preparatory Courses (17 hours beyond core curriculum)**

CS 1337 Computer Science I^{4}

MATH 2420 Differential Equations with Applications^{4}

MATH 2451 Multivariable Calculus with Applications^{4}

**Major Core Courses (21 hours beyond core curriculum)**

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 4390 Research Methods^{2}

STAT 4351 Probability

**Major Related Courses (12 hours)**

*Applied Mathematics 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 4341 Topology

3 hours upper-division guided elective^{6}

*Statistics Specialization*

STAT 3355 Data Analysis for Statisticians and Actuaries

STAT 4352 Mathematical Statistics

STAT 4382 Stochastic Processes

3 hours upper-division guided elective^{6}

III. Elective Requirements: 28 hours

**Electives (6 hours)**

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

**UTeach Requirements (18 hours beyond core curriculum and electives)**

NATS 1141 UTeach STEP 1

NATS 1143 UTeach STEP 2

NATS 3341 Knowing and Learning in Mathematics and Science

NATS 3343 Classroom Interactions

HIST 3328 History and Philosophy of Science and Medicine

NATS 4390 Research Methods^{2}

NATS 4341 Project-Based Instruction

NATS 4694 UTeach Apprentice Teaching, 8-12 Science and Mathematics

or NATS 4696 UTeach Apprentice Teaching, 4-8 Science and Mathematics

NATS 4141 UTeach Apprentice Teaching Seminar

MATH 3303 Introduction to Mathematical Modeling

**Free Electives (4 hours)**

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

### Minor in Mathematics

Students not majoring in Mathematics or Statistics 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 and MATH 4334 and two more upper-division mathematics courses that satisfy degree requirements by students in Mathematics.

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

### Fast Track Baccalaureate/Master's Degrees

For students interested in pursuing graduate studies in Mathematics, the Mathematics Department offers an accelerated BS / MS 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 that 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 mathematics with specializations in applied mathematics and statistics.

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

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

5. MATH 2417 and MATH 2419 requirements can be fulfilled by completing MATH 2413, MATH 2414, and MATH 2415.

6. Approval of Mathematics department advisor required.

7. Another MATH course, i.e. MATH 3380, may be substituted if MATH 3321 is not offered.