# Department of Mathematics

The Department of Mathematics offers a Bachelor of Science degree in Mathematics. The degree is offered in two concentrations: Mathematics and General Mathematical Studies. The Mathematics Concentration offers students the opportunity to prepare to provide technical support and conduct research for high-technology industries, government, and private companies. Both concentrations prepare students to pursue advanced graduate study. The General Mathematical Studies Concentration includes a component for those students wishing to obtain state certification to teach mathematics at the secondary level. The department also offers a Minor in Mathematics. Students interested in electives in Statistics, a Minor in Applied Statistics, or a Bachelor of Science degree in Statistics, should refer to the Department of Management Science and Statistics in the College of Business section of this catalog.

## Bachelor of Science Degree in Mathematics

The Bachelor of Science (B.S.) degree in Mathematics is offered with two concentrations: Mathematics and General Mathematical Studies.

The minimum number of semester credit hours required for this degree, including the Core Curriculum requirements, is 120. Thirty-nine of the total semester credit hours required for the degree must be at the upper-division level.

Students choosing the General Mathematical Studies Concentration who wish to pursue teacher certification should satisfy the Core Curriculum requirements consistent with the State Board for Educator Certification.

All required and elective mathematics, computer science, and statistics courses must be completed with a grade of “C-” or better.

All candidates for this degree must fulfill the Core Curriculum requirements and the mathematics requirements, which are listed in the following pages. In addition, a candidate for the Bachelor of Science degree in Mathematics must complete the course requirements for the concentration declared by the candidate.

### Core Curriculum Requirements (42 semester credit hours)

Students seeking the B.S. degree in Mathematics must fulfill University Core Curriculum requirements. If courses are taken to satisfy both degree requirements and Core Curriculum requirements, then students may need to take additional courses in order to meet the minimum number of semester credit hours required for this degree.

MAT 1214 may be used to satisfy the core requirement in Mathematics as well as a major requirement.

For a complete listing of courses that satisfy the Core Curriculum requirements, see Core Curriculum Component Area Requirements.

### Core Curriculum Component Area Requirements

#### First Year Experience Requirement (3 semester credit hours)

All students must complete the following course, for a total of 3 semester credit hours:

AIS 1203 | Academic Inquiry and Scholarship | 3 |

#### Communication (6 semester credit hours)

Students must complete the following courses, for a total of 6 semester credit hours:

WRC 1013 | Freshman Composition I (Q) | 3 |

WRC 1023 | Freshman Composition II (Q) | 3 |

#### Mathematics (3 semester credit hours)

Students must complete one of the following courses, for a total of 3 semester credit hours:

MAT 1023 | College Algebra with Applications | 3 |

MAT 1033 | Algebra with Calculus for Business | 3 |

MAT 1043 | Introduction to Mathematics | 3 |

MAT 1073 | Algebra for Scientists and Engineers | 3 |

MAT 1093 | Precalculus | 3 |

MAT 1193 | Calculus for the Biosciences | 3 |

MAT 1214 | Calculus I | 4 |

STA 1053 | Basic Statistics | 3 |

#### Life and Physical Sciences (6 semester credit hours)

Students must complete two of the following courses for a total of 6 semester credit hours:

ANT 2033 | Introduction to Biological Anthropology | 3 |

AST 1013 | Introduction to Astronomy | 3 |

AST 1033 | Exploration of the Solar System | 3 |

BIO 1233 | Contemporary Biology I | 3 |

BIO 1243 | Contemporary Biology II | 3 |

BIO 1404 | Biosciences I | 4 |

BIO 1414 | Biosciences II | 4 |

ES 1113 | Environmental Botany | 3 |

ES 1123 | Environmental Zoology | 3 |

ES 1213 | Environmental Geology | 3 |

ES 2013 | Introduction to Environmental Science I | 3 |

ES 2023 | Introduction to Environmental Science II | 3 |

GEO 1013 | The Third Planet | 3 |

GEO 1123 | Life Through Time | 3 |

GES 2613 | Physical Geography | 3 |

PHY 1013 | Universes | 3 |

PHY 1943 | Physics for Scientists and Engineers I | 3 |

PHY 1963 | Physics for Scientists and Engineers II | 3 |

#### Language, Philosophy and Culture (3 semester credit hours)

Students must complete one of the following courses, for a total of 3 semester credit hours:

AAS 2013 | Introduction to African American Studies | 3 |

AAS 2113 | African American Culture, Leadership and Social Issues | 3 |

ANT 2063 | Language, Thought, and Culture | 3 |

ARA 1014 | Elementary Arabic I | 4 |

ARC 1113 | Introduction to the Built Environment | 3 |

ARC 1413 | Architecture and Culture | 3 |

CHN 1014 | Elementary Chinese I | 4 |

CLA 2013 | Introduction to Ancient Greece | 3 |

CLA 2023 | Introduction to Ancient Rome | 3 |

CLA 2323 | Classical Mythology | 3 |

CSH 1103 | Literary Masterpieces of Western Culture I | 3 |

CSH 1113 | Literary Masterpieces of Western Culture II | 3 |

CSH 1213 | Topics in World Cultures | 3 |

CSH 2113 | The Foreign Film | 3 |

ENG 2013 | Introduction to Literature | 3 |

ENG 2213 | Literary Criticism and Analysis | 3 |

ENG 2383 | Multiethnic Literatures of the United States | 3 |

ENG 2423 | Literature of Texas and the Southwest | 3 |

FRN 1014 | Elementary French I | 4 |

FRN 2333 | French Literature in English Translation | 3 |

GER 1014 | Elementary German I | 4 |

GER 2333 | German Literature in English Translation | 3 |

GLA 1013 | U.S. in the Global Arena | 3 |

GES 1023 | World Regional Geography | 3 |

GRK 1114 | Introductory Classical Greek I | 4 |

HIS 2123 | Introduction to World Civilization to the Fifteenth Century | 3 |

HIS 2133 | Introduction to World Civilization since the Fifteenth Century | 3 |

HIS 2533 | Introduction to Latin American Civilization | 3 |

HIS 2543 | Introduction to Islamic Civilization | 3 |

HIS 2553 | Introduction to East Asian Civilization | 3 |

HIS 2573 | Introduction to African Civilization | 3 |

HIS 2583 | Introduction to South Asian Civilization | 3 |

HUM 2093 | World Religions | 3 |

ITL 1014 | Elementary Italian I | 4 |

ITL 2333 | Italian Literature in English Translation | 3 |

JPN 1014 | Elementary Japanese I | 4 |

LAT 1114 | Introductory Latin I | 4 |

MAS 2013 | Introduction to Chicano(a) Studies | 3 |

PHI 1043 | Critical Thinking | 3 |

PHI 2023 | Introduction to Ancient Philosophy | 3 |

PHI 2033 | Introduction to Early Modern Philosophy | 3 |

PHI 2123 | Contemporary Moral Issues | 3 |

RUS 1014 | Elementary Russian I | 4 |

RUS 2333 | Russian Literature in English Translation | 3 |

SPN 1014 | Elementary Spanish I | 4 |

SPN 2333 | Hispanic Literature in English Translation | 3 |

WS 2013 | Introduction to Women’s Studies | 3 |

WS 2023 | Introduction to LGBTQ Studies | 3 |

#### Creative Arts (3 semester credit hours)

Students must complete one of the following courses, for a total of 3 semester credit hours:

AHC 1113 | Survey of Art and Architecture from Prehistoric Times to 1350 | 3 |

AHC 1123 | Survey of Art and Architecture in Europe and the New World from 1350 to 1750 | 3 |

AHC 1133 | Survey of Modern Art | 3 |

ARC 1213 | Design I | 3 |

ARC 1513 | Great Buildings and Cities of the World | 3 |

ART 1103 | Introduction to Visual Arts | 3 |

ART 1143 | Art for Non-Art Majors | 3 |

CLA 2033 | Introduction to Classical Literature | 3 |

DAN 2003 | Introduction to Dance | 3 |

ENG 1113 | Introduction to Creative Literary Arts | 3 |

HUM 2023 | Introduction to the Humanities I | 3 |

HUM 2033 | Introduction to the Humanities II | 3 |

HUM 2053 | History of Film | 3 |

MAS 2023 | Latino Cultural Expressions | 3 |

MUS 2243 | World Music in Society | 3 |

MUS 2623 | Fundamentals of Music for the Non-Music Major | 3 |

MUS 2633 | American Roots Music | 3 |

MUS 2663 | History and Styles of Jazz | 3 |

MUS 2673 | History and Styles of Rock | 3 |

MUS 2683 | Masterpieces of Music | 3 |

MUS 2693 | The Music of Latin America and the Caribbean | 3 |

MUS 2743 | Music and Film | 3 |

PHI 2073 | Philosophy of Art | 3 |

#### American History (6 semester credit hours)

Students must complete two of the following courses, for a total of 6 semester credit hours:

HIS 1043 | United States History: Pre-Columbus to Civil War Era | 3 |

HIS 1053 | United States History: Civil War Era to Present | 3 |

HIS 2053 | Texas History | 3 |

#### Government-Political Science (6 semester credit hours)

Students must complete two of the following courses, for a total of 6 semester credit hours:

POL 1013 | Introduction to American Politics | 3 |

and one of the following two courses: | ||

POL 1133 | Texas Politics and Society | 3 |

POL 1213 | Civil Rights in Texas and America | 3 |

#### Social and Behavioral Sciences (3 semester credit hours)

Students must complete one of the following courses, for a total of 3 semester credit hours:

AMS 2043 | Approaches to American Culture | 3 |

ANT 1013 | Introduction to Anthropology | 3 |

ANT 2043 | Introduction to Archaeology | 3 |

ANT 2053 | Introduction to Cultural Anthropology | 3 |

BBL 2003 | Language, Culture, and Society | 3 |

BBL 2243 | Globalizing the Local: Bilingual Families, Communities, and Schools | 3 |

BIO 1033 | Drugs and Society | 3 |

CRJ 1113 | The American Criminal Justice System | 3 |

ECO 2003 | Economic Principles and Issues | 3 |

ECO 2023 | Introductory Microeconomics | 3 |

EGR 1343 | The Impact of Modern Technologies on Society | 3 |

GES 1013 | Fundamentals of Geography | 3 |

GES 2623 | Human Geography | 3 |

HTH 2413 | Introduction to Community and Public Health | 3 |

HTH 2513 | Personal Health | 3 |

IDS 2113 | Society and Social Issues | 3 |

PSY 1013 | Introduction to Psychology | 3 |

SOC 1013 | Introduction to Sociology | 3 |

SOC 2013 | Social Problems | 3 |

SOC 2023 | Social Context of Drug Use | 3 |

#### Component Area Option (CAO) (3 semester credit hours)

Students must complete either one of the following courses or any additional Core Curriculum course not previously used to satisfy a core component area requirement, for a total of 3 semester credit hours:

COM 2113 | Public Speaking | 3 |

CS 1173 | Data Analysis and Visualization | 3 |

EGR 1403 | Technical Communication | 3 |

ENG 2413 | Technical Writing | 3 |

PAD 1113 | Public Administration in American Society | 3 |

PHI 2043 | Introductory Logic | 3 |

##### Core Curriculum Component Area Requirements

First Year Experience Requirement | 3 | |

Communication | 6 | |

Mathematics | 3 | |

Life and Physical Sciences | 6 | |

Language, Philosophy and Culture | 3 | |

Creative Arts | 3 | |

American History | 6 | |

Government-Political Science | 6 | |

Social and Behavioral Sciences | 3 | |

Component Area Option | 3 | |

Total Credit Hours | 42 |

### Gateway Courses

Students pursuing the B.S. degree in Mathematics must successfully complete each of the following Gateway Courses with a grade of “C-” or better in no more than two attempts. A student who is unable to successfully complete these courses within two attempts, including dropping a course with a grade of “W” or taking an equivalent course at another institution, will be required to change his or her major.

MAT 1214 | Calculus I | |

MAT 1224 | Calculus II |

### Mathematics Degree Requirements

All candidates for the B.S. degree in Mathematics, regardless of concentration, must complete the following 24 semester credit hours of required courses (this includes the 3 semester credit hours of the Core Curriculum requirement in mathematics).

MAT 1214 | Calculus I (The student who is not prepared to begin MAT 1214 must take MAT 1093 Precalculus.) | 4 |

MAT 1224 | Calculus II | 4 |

MAT 2214 | Calculus III | 4 |

MAT 2233 | Linear Algebra | 3 |

MAT 3013 | Foundations of Mathematics | 3 |

MAT 3213 | Foundations of Analysis | 3 |

MAT 4213 | Real Analysis I | 3 |

Total Credit Hours | 24 |

In addition, a candidate for the B.S degree in Mathematics must complete the course requirements for the concentration declared by the candidate.

### Mathematics Concentration

All candidates for this concentration must fulfill the Core Curriculum requirements, the mathematics degree requirements, as well as the course requirements necessary for this concentration.

A. Computer Science | ||

Select one of the following: | 3-4 | |

Introduction to Computer Programming I | ||

Introduction to Computer Programming II and Introduction to Computer Programming II Recitation | ||

Computer Programming with Engineering Applications | ||

B. Required courses | 21 | |

Differential Equations I | ||

Numerical Analysis | ||

Real Analysis II | ||

Modern Abstract Algebra | ||

Topology | ||

Applied Statistics | ||

Probability and Statistics | ||

C. Upper-division courses in mathematics or statistics | ||

Select 9 semester credits of upper-division courses in mathematics or statistics approved by the student's advisor | 9 | |

D. Electives | ||

Select 24 or 25 semester credit hours of electives | 24-25 | |

Total Credit Hours | 58 |

### General Mathematical Studies Concentration

All candidates for this concentration must fulfill the Core Curriculum requirements, the mathematics degree requirements, as well as the course requirements necessary for this concentration.

A. Support work | ||

3 semester credit hours of approved, supporting coursework that uses mathematics but is in a field other than mathematics. Courses in Computer Science, Statistics, Physics, Engineering or other disciplines may be used to satisfy this requirement. | 3 | |

B. Mathematics and/or Statistics | ||

24 semester credit hours of mathematics and/or statistics | ||

1. Mathematics | ||

MAT 3103 | Data Analysis and Interpretation | 3 |

MAT 3123 | Fundamentals of Geometry | 3 |

or MAT 4263 | Geometry | |

MAT 3233 | Modern Algebra | 3 |

or MAT 4233 | Modern Abstract Algebra | |

MAT 4113 | Computer Mathematical Topics | 3 |

MAT 4303 | Capstone Course for Mathematics | 3 |

2. 9 approved upper-division credit hours in mathematics or statistics | 9 | |

C. Electives | ||

Select 30 semester credit hours of electives. Students seeking teacher certification should use these hours for the required certification courses. Others students should include among these an additional 6 semester credit hours of upper-division mathematics or statistics courses approved by an undergraduate advisor for the Department of Mathematics. | 30 | |

Total Credit Hours | 57 |

* Certification requirements for students pursuing the General Mathematical Studies Concentration are different from degree requirements.* In addition to specific course requirements, teacher certification in Texas also requires passing scores on a Texas Success Initiative approved assessment instrument test and acceptable scores on the state-mandated exit competency test. Complete information may be obtained in the Teacher Certification Center at UTSA.

### Course Sequence Guide for B.S. Degree in Mathematics with a Mathematics Concentration

This course sequence guide is designed to assist students in completing their UTSA undergraduate Mathematics degree requirements. *This is merely a guide and students must satisfy other requirements of this catalog and meet with their academic advisor for individualized degree plans. *Progress within this guide depends upon such factors as course availability, individual student academic preparation, student time management, work obligations, and individual financial considerations. Students may choose to take courses during Summer terms to reduce course loads during long semesters.

#### B.S. in Mathematics, Mathematics Concentration – Recommended Four-Year Academic Plan

First Year | ||
---|---|---|

Fall | Credit Hours | |

AIS 1203 | Academic Inquiry and Scholarship (core) | 3 |

MAT 1214 | Calculus I (core and major) | 4 |

WRC 1013 | Freshman Composition I (Q) (core) | 3 |

American History core | 3 | |

Life & Physical Sciences core | 3 | |

Spring | ||

MAT 1224 | Calculus II | 4 |

WRC 1023 | Freshman Composition II (Q) (core) | 3 |

Life & Physical Sciences core | 3 | |

Select one of the following: | 3-4 | |

CS 1063 | Introduction to Computer Programming I | |

CS 1713 & CS 1711 | Introduction to Computer Programming II | |

CS 2073 | Computer Programming with Engineering Applications | |

Second Year | ||

Fall | ||

MAT 2214 | Calculus III | 4 |

MAT 2233 | Linear Algebra | 3 |

Government-Political Science core | 3 | |

Free elective | 3 | |

Free elective | 3 | |

Spring | ||

MAT 3013 | Foundations of Mathematics | 3 |

STA 3003 | Applied Statistics | 3 |

Creative Arts core | 3 | |

Government-Political Science core | 3 | |

Free elective | 3 | |

Third Year | ||

Fall | ||

MAT 3613 | Differential Equations I | 3 |

STA 3513 | Probability and Statistics | 3 |

Social & Behavioral Sciences core | 3 | |

Upper-division MAT or STA elective | 3 | |

Free elective | 3 | |

Spring | ||

MAT 3213 | Foundations of Analysis | 3 |

MAT 4233 | Modern Abstract Algebra | 3 |

Component Area Option core | 3 | |

Free elective | 3 | |

Upper-division MAT or STA elective | 3 | |

Fourth Year | ||

Fall | ||

MAT 3633 | Numerical Analysis | 3 |

MAT 4213 | Real Analysis I | 3 |

MAT 4273 | Topology | 3 |

Free elective | 3 | |

Upper-division Free elective | 3 | |

Spring | ||

MAT 4223 | Real Analysis II | 3 |

Free elective ^{1} | 2-3 | |

Upper-division MAT or STA elective | 3 | |

American History core | 3 | |

Language Philosophy & Culture core | 3 | |

Total Credit Hours: | 120.0 |

^{1} | Only 2 semester credit hours are needed if CS 1713 and CS 1711 are taken. |

Note: Some courses are only offered once a year; Fall or Spring. Check with the Department of Mathematics for scheduling of courses.

### Course Sequence Guide for B.S. Degree in Mathematics with a General Mathematical Studies Concentration

This course sequence guide is designed to assist students in completing their UTSA undergraduate Mathematics degree requirements. *This is merely a guide and students must satisfy other requirements of this catalog and meet with their academic advisor for individualized degree plans.* Progress within this guide depends upon such factors as course availability, individual student academic preparation, student time management, work obligations, and individual financial considerations. Students may choose to take courses during Summer terms to reduce course loads during long semesters.

#### B.S. in Mathematics, General Mathematical Studies Concentration – Recommended Four-Year Academic Plan

First Year | ||
---|---|---|

Fall | Credit Hours | |

AIS 1203 | Academic Inquiry and Scholarship (core) | 3 |

MAT 1214 | Calculus I (core and major) | 4 |

WRC 1013 | Freshman Composition I (Q) (core) | 3 |

Life & Physical Sciences core | 3 | |

Free elective | 3 | |

Spring | ||

MAT 1224 | Calculus II | 4 |

WRC 1023 | Freshman Composition II (Q) (core) | 3 |

Free elective | 3 | |

Life & Physical Sciences core | 3 | |

Approved support work | 3 | |

Second Year | ||

Fall | ||

MAT 2214 | Calculus III | 4 |

MAT 2233 | Linear Algebra | 3 |

Free elective | 3 | |

American History core | 3 | |

Spring | ||

MAT 3013 | Foundations of Mathematics | 3 |

MAT 3103 | Data Analysis and Interpretation | 3 |

POL 1133 or 1213 | Texas Politics and Society (core) | 3 |

Free elective | 3 | |

Free elective | 3 | |

Third Year | ||

Fall | ||

MAT 3123 or 4263 | Fundamentals of Geometry (or Geometry) | 3 |

POL 1013 | Introduction to American Politics (core) | 3 |

Free elective | 3 | |

Upper-division free elective | 3 | |

Social & Behavioral Sciences core | 3 | |

Spring | ||

MAT 3213 | Foundations of Analysis | 3 |

MAT 3233 or 4233 | Modern Algebra (or Modern Abstract Algebra) | 3 |

Component Area Option core | 3 | |

Upper-division free elective | 3 | |

Upper-division MAT or STA elective | 3 | |

Fourth Year | ||

Fall | ||

MAT 4213 | Real Analysis I | 3 |

MAT 4303 | Capstone Course for Mathematics | 3 |

Free elective | 3 | |

Free elective | 3 | |

Upper-division MAT elective (not MAT 3253) | 3 | |

Spring | ||

MAT 4113 | Computer Mathematical Topics | 3 |

Upper-division MAT or STA elective | 3 | |

American History core | 3 | |

Creative Arts core | 3 | |

Language, Philosophy & Culture core | 3 | |

Total Credit Hours: | 120.0 |

Note: Some courses are only offered once a year; fall or spring. Check with the Department of Mathematics for scheduling of courses.

### Course Sequence Guide for B.S. Degree in Mathematics with a General Mathematical Studies Concentration (with teacher certification)

This course sequence guide is designed to assist students in completing their UTSA undergraduate Mathematics degree requirements. *This is merely a guide and students must satisfy other requirements of this catalog and meet with *their *academic advisor* *for individualized degree plans.* Progress within this guide depends upon such factors as course availability, individual student academic preparation, student time management, work obligations, and individual financial considerations. Students may choose to take courses during Summer terms to reduce course loads during long semesters.

#### B.S. in Mathematics, General Mathematical Studies Concentration with teacher certification – Recommended Four-Year Academic Plan

First Year | ||
---|---|---|

Fall | Credit Hours | |

AIS 1203 | Academic Inquiry and Scholarship (core) | 3 |

GEM 1011 | GEEMS Mathematics/Science I | 1 |

MAT 1214 | Calculus I (core and major) | 4 |

WRC 1013 | Freshman Composition I (Q) (core) | 3 |

Approved support work | 3 | |

Life & Physical Sciences core | 3 | |

Spring | ||

GEM 1021 | GEEMS Mathematics/Science II | 1 |

MAT 1224 | Calculus II | 4 |

WRC 1023 | Freshman Composition II (Q) (core) | 3 |

Life & Physical Sciences core | 3 | |

Social & Behavioral Sciences core | 3 | |

Second Year | ||

Fall | ||

EDU 2103 | Social Foundations for Education in a Diverse U.S. Society ^{1} | 3 |

GEM 1031 | GEEMS Mathematics/Science III | 1 |

MAT 2214 | Calculus III | 4 |

MAT 3013 | Foundations of Mathematics | 3 |

American History core | 3 | |

Spring | ||

EDP 3203 | Learning and Development in the Secondary School Adolescent | 3 |

MAT 2233 | Linear Algebra | 3 |

MAT 3103 | Data Analysis and Interpretation | 3 |

Creative Arts core | 3 | |

Summer | ||

POL 1013 | Introduction to American Politics (core) | 3 |

Language, Philosophy & Culture core | 3 | |

Third Year | ||

Fall | ||

BBL 3403 | Cultural and Linguistic Equity for Schooling ^{1} | 3 |

MAT 3123 or 4263 | Fundamentals of Geometry (or Geometry) | 3 |

MAT 3233 or 4233 | Modern Algebra (or Modern Abstract Algebra) | 3 |

POL 1133 or 1213 | Texas Politics and Society (core) | 3 |

Upper-division MAT or STA elective | 3 | |

Spring | ||

MAT 3213 | Foundations of Analysis | 3 |

SPE 3603 | Introduction to Special Education ^{1} | 3 |

Upper-division MAT elective (not MAT 3253) | 3 | |

Upper-division MAT or STA elective | 3 | |

Component Area Option core | 3 | |

Summer | ||

MAT 4113 | Computer Mathematical Topics | 3 |

American History core | 3 | |

Fourth Year | ||

Fall | ||

C&I 4203 | Models of Teaching in the Content Areas of the Secondary School | 3 |

EDP 4203 | Assessment and Evaluation | 3 |

MAT 4213 | Real Analysis I | 3 |

MAT 4303 | Capstone Course for Mathematics | 3 |

LTED 3773 | Reading and Writing Across the Disciplines-Grades 7–12 | 3 |

Spring | ||

C&I 4646 | Clinical Teaching: Grades 7–12 | 6 |

Total Credit Hours: | 120.0 |

^{1} | BBL 3403, EDU 2103, and SPE 3603 are not required if student is in the Generating Educational Excellence in Mathematics and Science (GEEMS) program. However, these courses must be replaced with upper-division MAT/STA electives. |

Note: Some courses are only offered once a year; fall or spring. Check with the Department of Mathematics for scheduling of courses.

## Minor in Mathematics

All students pursuing the Minor in Mathematics must complete 24 semester credit hours. All required and elective mathematics, computer science, and statistics courses must be completed with a grade of “C-” or better.

A. Required courses | ||

MAT 1214 | Calculus I | 4 |

MAT 1224 | Calculus II | 4 |

MAT 2214 | Calculus III ^{1} | 3-4 |

or CS 3333 | Mathematical Foundations of Computer Science | |

MAT 2233 | Linear Algebra | 3 |

MAT 3613 | Differential Equations I ^{2} | 3 |

B. Approved upper-division mathematics electives | ||

Select a minimum of 6 semester credit hours of approved upper-division mathematics electives | 6-7 | |

Total Credit Hours | 24 |

^{1} | For Computer Science majors, substitute CS 3333 Mathematical Foundations of Computer Science and Recitation. |

^{2} | Computer Science majors may substitute 3 hours of an approved upper-division mathematics elective. |

To declare a Minor in Mathematics, obtain advice, or seek approval of substitutions for course requirements, students should consult their academic advisor and the Undergraduate Advisor of Record for the Department of Mathematics.

### Generating Educational Excellence in Math and Science (GEM) Courses

**GEM 1011. GEEMS Mathematics/Science I. (1-2) 1 Credit Hour.**

This course introduces students to the prospect of mathematics and science secondary teaching as a career choice through hands-on experiences observing and teaching in an elementary classroom. Students will work in teams with an exemplary elementary teacher at one of the local school districts participating in mathematics and science classes. Class activities will emphasize the qualities of good mathematics and science teaching, including standards-based instruction and the integration of resources into effective class planning. Field-based experiences required. Restricted course; GEEMS Office approval required for registration. (Formerly UTE 1011. Credit cannot be earned for both GEM 1011 and UTE 1011.) Generally offered: Fall, Spring.

**GEM 1021. GEEMS Mathematics/Science II. (1-2) 1 Credit Hour.**

Prerequisite: GEM 1011.
Builds on the teaching practices, lesson plan design, and instructional models used in GEM 1011, but in a middle school setting. Students become familiar with the reform movements in the middle school concept and philosophy. Through class activities and observations of middle school mathematics and science teachers, students identify the instructional and management strategies and assessment techniques appropriate to early adolescence. Students work in teams with an exemplary middle school teacher to design and deliver lessons appropriate to middle school students. Field-based experiences required. Restricted course; GEEMS Office approval required for registration. (Formerly UTE 1021. Credit cannot be earned for both GEM 1021 and UTE 1021.) Generally offered: Spring.

**GEM 1031. GEEMS Mathematics/Science III. (1-2) 1 Credit Hour.**

Prerequisite: GEM 1021.
Builds on the teaching practices, lesson plan design, and instructional models used in GEM 1021, but in a high school setting. Students become familiar with the reform movements in the high school concept and philosophy. Through class activities and observations of high school mathematics and science teachers, students identify the instructional and management strategies and assessment techniques appropriate to adolescence. Students work in teams with an exemplary high school teacher to design and deliver lessons appropriate to high school students. Field-based experiences required. Restricted course; GEEMS Office approval required for registration. (Formerly UTE 1031. Credit cannot be earned for both GEM 1031 and UTE 1031.) Generally offered: Fall.

### Mathematics (MAT) Courses

**MAT 0203. Basic Mathematics. (3-0) 3 Credit Hours.**

A course intended for students with minimal mathematical skills who need a comprehensive review before they can successfully complete an algebra course. Topics include the Fundamental Mathematics and Geometry objectives of the Texas Success Initiative (TSI), with an introduction to algebra. Intensive review and maintenance of computational skills with integers, fractions, decimals, percentages, ratios, and proportions; reading and interpreting information presented in graphs, tables, and charts; solving word problems, elementary algebraic equations, problems with two- and three-dimensional geometric figures; and inductive and deductive reasoning skills. Course does not count toward any degree at UTSA. This course may be repeated. (Formerly MTC 0103).

**MAT 0213. Intermediate Algebra. (3-0) 3 Credit Hours.**

Introductory algebra course that includes the Texas Success Initiative (TSI) Algebra and Problem Solving objectives. Operations with algebraic expressions; solving one- and two-variable equations; solving word problems involving one and two variables; graphing number relationships; and solving problems involving quadratic equations. Course does not count toward any degree at UTSA. This course may be repeated. (Formerly MTC 0113).

**MAT 1023. College Algebra with Applications. (3-0) 3 Credit Hours. (TCCN = MATH 1314)**

Prerequisite: Satisfactory performance on a placement examination.
Topics include algebraic expressions; equations; inequalities over the real numbers; relations, functions and graphs; polynomial and rational functions; systems of linear equations and inequalities; complex numbers; and matrices and determinants. A wide range of applications will be included in this course. Students majoring in areas that require MAT 1214 Calculus I are encouraged to take MAT 1073 instead of MAT 1023. (Formerly MTC 1023. Credit can be earned for only one of the following: MAT 1023, MTC 1023, MAT 1063, MTC 1073, or MAT 1073.) This course is designed for majors outside sciences and engineering. May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer.

**MAT 1033. Algebra with Calculus for Business. (3-0) 3 Credit Hours. (TCCN = MATH 1325)**

Prerequisite: Satisfactory performance on a placement examination.
An introduction to business calculus with an emphasis on the algebra of functions. Concentration is on the algebraic manipulations of functions and includes volume and profit functions, both linear and quadratic; root finding and graphical analysis; matrices; and differentiation and integration. (Formerly MTC 1033. Credit cannot be earned for both MAT 1033 and MTC 1033.) May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer.

**MAT 1043. Introduction to Mathematics. (3-0) 3 Credit Hours. (TCCN = MATH 1332)**

Prerequisite: Satisfactory performance on a placement examination.
This course is designed primarily for the liberal arts major to satisfy the Core Curriculum mathematics requirement. Topics may include logic; proofs; deductive and inductive reasoning; number theory; fundamentals of statistics; basic statistical graphs; causal connections; financial management; functions; linear graphs and modeling; exponential growth and decay; logarithms; fundamentals of probability; fundamentals of geometry; and basic ideas from trigonometry, calculus, and discrete mathematics. (Formerly MTC 1043. Credit cannot be earned for both MAT 1043 and MTC 1043.) May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer.

**MAT 1073. Algebra for Scientists and Engineers. (3-0) 3 Credit Hours. (TCCN = MATH 1314)**

Prerequisite: Satisfactory performance on a placement examination.
This course is designed to prepare the student for MAT 1093 Precalculus and MAT 1214 Calculus I. Topics may include algebraic expressions; equations; inequalities over the real numbers; relations; functions; polynomial and rational functions; logarithmic and exponential functions; systems of linear equations and inequalities; matrices and determinants; complex numbers; sequences; series binomial expansion; mathematical induction; permutations, and combinations. (Formerly MTC 1073. Credit can be earned for only one of the following: MAT 1073, MTC 1073, MAT 1063, MTC 1023, or MAT 1023.) May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer.

**MAT 1093. Precalculus. (3-0) 3 Credit Hours. (TCCN = MATH 2312)**

Prerequisite: MAT 1073 or the equivalent course or satisfactory performance on a placement examination.
Exponential functions, logarithmic functions, trigonometric functions, complex numbers, DeMoivre’s theorem, and polar coordinates. May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer.

**MAT 1153. Essential Elements in Mathematics I. (3-0) 3 Credit Hours. (TCCN = MATH 1350)**

Prerequisite: MAT 1023 or MAT 1073.
Numeration systems; properties of the systems of whole numbers, integers, rational numbers, and real numbers; problem solving; logic. May not be applied toward a major in mathematics. (Credit cannot be earned for both MAT 1153 and MAT 1143.) Generally offered: Fall, Spring, Summer.

**MAT 1163. Essential Elements in Mathematics II. (3-0) 3 Credit Hours. (TCCN = MATH 1351)**

Prerequisite: MAT 1153.
Algebra, statistics and probability; geometric shapes; measurement; coordinate and transformational geometry. May not be applied toward a major in mathematics. Generally offered: Fall, Spring, Summer.

**MAT 1193. Calculus for the Biosciences. (3-0) 3 Credit Hours. (TCCN = MATH 2313)**

Prerequisite: MAT 1093 or an equivalent course or satisfactory performance on a placement examination.
An introduction to calculus is presented using discrete-time dynamical systems and differential equations to model fundamental processes important in biological and biomedical applications. Specific topics to be covered are limits, continuity, differentiation, antiderivatives, definite and indefinite integrals, the fundamental theorem of calculus, differential equations, and the phase-plane. (Formerly MAT 1194. Credit can be earned for only one of the following: MAT 1193, MAT 1194, or MAT 1214.) May apply toward the Core Curriculum requirement in Mathematics.
Generally offered: Fall, Spring, Summer.

**MAT 1214. Calculus I. (4-0) 4 Credit Hours. (TCCN = MATH 2413)**

Prerequisite: MAT 1093 or an equivalent course or satisfactory performance on a placement examination.
An introduction to the concepts of limit, continuity and derivative, mean value theorem, and applications of derivatives such as velocity, acceleration, maximization, and curve sketching; introduction to the Riemann integral and the fundamental theorem of calculus. (Credit can be earned for only one of the following: MAT 1214, MAT 1193, or MAT 1194.) May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer.

**MAT 1224. Calculus II. (4-0) 4 Credit Hours. (TCCN = MATH 2414)**

Prerequisite: MAT 1193 or MAT 1214.
Methods of integration, applications of the integral, sequences, series, and Taylor expansions. (Formerly MAT 1223. Credit cannot be earned for both MAT 1224 and MAT 1223.) Generally offered: Fall, Spring, Summer.

**MAT 2113. Functions and Modeling. (3-0) 3 Credit Hours.**

Prerequisites: MAT 1093 or consent of instructor and admission to the UTeachSA teacher preparation program.
In-depth study of concepts needed to teach secondary school mathematics at various levels. Emphasizes the development of the concept of function, exploring function patterns in data sets, and the connections between the main topics of mathematics associated with a secondary school curriculum. Use of appropriate technology is explored. May not be applied toward the Mathematics Concentration of the B.S. degree in Mathematics. (Same as UTE 2113. Credit cannot be earned for both MAT 2113 and UTE 2113).

**MAT 2214. Calculus III. (4-0) 4 Credit Hours. (TCCN = MATH 2415)**

Prerequisite: MAT 1224.
Vectors, functions of several variables, partial derivatives, line, surface and volume integrals, Green’s, Stokes’ and the Divergence theorems. (Formerly MAT 2213. Credit cannot be earned for both MAT 2214 and MAT 2213.) Generally offered: Fall, Spring, Summer.

**MAT 2233. Linear Algebra. (3-0) 3 Credit Hours. (TCCN = MATH 2318)**

Prerequisite: MAT 1224 or EGR 2323.
Vector spaces and matrix algebra, matrices and determinants, characteristic values of matrices, and reduction to canonical forms. Emphasis on applications.
Generally offered: Fall, Spring, Summer.

**MAT 3013. Foundations of Mathematics. (3-0) 3 Credit Hours.**

Prerequisite: MAT 1214.
Development of theoretical tools for rigorous mathematics. Topics may include mathematical logic, propositional and predicate calculus, set theory, functions and relations, cardinal and ordinal numbers, Boolean algebras, and construction of the natural numbers, integers, and rational numbers. Emphasis on theorem proving. (Formerly MAT 2243. Credit cannot be earned for MAT 3013 and MAT 2243.) Generally offered: Fall, Spring, Summer.

**MAT 3023. Perspectives on Science and Mathematics. (3-0) 3 Credit Hours.**

Prerequisite: MAT 1193, MAT 1214, STA 1053, or consent of instructor.
An examination of important episodes in the history of mathematics and science that illustrate the nature of scientific inquiry and convey that scientific and mathematical concepts are not static. Topics may include Galileo’s conflict with the Catholic Church, Isaac Newton’s formulation of the laws of motion and invention of calculus, Charles Darwin’s proposal of the theory of evolution by natural selection, the development of the atomic bomb, and the discovery of the double helix structure of DNA, or others chosen by the instructor. May not be applied toward the Mathematics Concentration of the B.S. degree in Mathematics. (Same as UTE 3023. Credit cannot be earned for both MAT 3023 and UTE 3023. Credit cannot be earned for both MAT 3023 and MAT 4123).

**MAT 3103. Data Analysis and Interpretation. (3-0) 3 Credit Hours.**

Prerequisite: MAT 1093 or consent of instructor.
Measurement, sampling, summarizing and displaying data, types of data, inferential methods, nonparametric methods, qualitative research designs and methods, interpreting research results, and research design. Applications to research techniques in school-based settings will be emphasized. May not be applied toward the Mathematics Concentration of the B.S. degree in Mathematics. Generally offered: Fall, Spring, Summer.

**MAT 3123. Fundamentals of Geometry. (3-0) 3 Credit Hours.**

Prerequisite: MAT 1093 or consent of instructor.
A survey of geometric concepts, including axiomatic development of advanced Euclidean geometry, coordinate geometry, non-Euclidean geometry, three-dimensional geometry, and topology. May not be applied toward the Mathematics Concentration of the B.S. degree in Mathematics. Generally offered: Fall, Spring.

**MAT 3213. Foundations of Analysis. (3-0) 3 Credit Hours.**

Prerequisites: MAT 1224 and MAT 3013.
Axiomatic definition of real numbers, including order properties and completeness; infinite sequences and their convergence; basic notions related to series and their convergence; functions and function limits. Introduction to topology of the real line. Emphasis on theorem proving. Generally offered: Fall, Spring, Summer.

**MAT 3223. Complex Variables. (3-0) 3 Credit Hours.**

Prerequisites: MAT 2214 and MAT 3213.
An introduction to complex variables, including elementary functions, line integrals, power series, residues and poles, and conformal mappings. Generally offered: Spring.

**MAT 3233. Modern Algebra. (3-0) 3 Credit Hours.**

Prerequisite: MAT 3013.
Topics will include the development of groups, integral domains, fields, and number systems, including the complex numbers. Divisibility, congruences, primes, perfect numbers, and some other problems of number theory will be considered. Generally offered: Fall, Spring, Summer.

**MAT 3273. Applied Mathematics for Sciences and Engineering. (3-0) 3 Credit Hours.**

Prerequisite: MAT 2214 or MAT 3613 or consent of instructor.
Mathematical applications in biology, physics, engineering or other scientific disciplines. Topics may employ techniques of complex analysis, harmonic analysis, Fourier series, Fourier transforms, and partial differential equations.

**MAT 3613. Differential Equations I. (3-0) 3 Credit Hours.**

Prerequisite: Completion of or concurrent enrollment in MAT 2233.
Basic notions of differential equations, solution of first-order equations and linear equations with constant coefficients, nth-order initial value problems, Laplace transforms, and may include additional topics such as power series solutions of differential equations, linear systems, and stability. Generally offered: Fall, Spring, Summer.

**MAT 3623. Differential Equations II. (3-0) 3 Credit Hours.**

Prerequisite: MAT 3613.
Continuation of MAT 3613. May include topics in stability, linear systems, power series solutions, partial differential equations, and boundary value problems. Generally offered: Spring.

**MAT 3633. Numerical Analysis. (3-0) 3 Credit Hours.**

Prerequisites: MAT 2233, MAT 3213, and one of the following: CS 1063, CS 1713, or CS 2073.
Solution of linear and nonlinear equations, curve-fitting, and eigenvalue problems.
Generally offered: Fall, Spring.

**MAT 3653. Stochastic Calculus. (3-0) 3 Credit Hours.**

Prerequisite: STA 3513.
Probability, random walk, Brownian motion, stationary and evolutionary processes and stochastic differential equations.

**MAT 4013. Graphing Calculator Topics. (3-0) 3 Credit Hours.**

Prerequisite: MAT 1214 or consent of instructor.
Mathematical topics from algebra, trigonometry, calculus, modeling, and probability and statistics will be investigated using the graphing calculator. Assessment and evaluation techniques using technology will also be included. May not be applied toward the Mathematics Concentration of the B.S. degree in Mathematics. Generally offered: Fall, Spring.

**MAT 4113. Computer Mathematical Topics. (3-0) 3 Credit Hours.**

Prerequisite: MAT 1214.
Mathematical topics from algebra, Euclidean and non-Euclidean geometry, number theory, and probability and statistics will be investigated using Geometer’s Sketchpad and a variety of Web-based mathematics resources. Course will also include the application of software to the solution of a variety of geometric and algebraic problems. May not be applied toward the Mathematics Concentration of the B.S. degree in Mathematics. Generally offered: Spring, Summer.

**MAT 4123. History of Mathematics. (3-0) 3 Credit Hours.**

Prerequisites: MAT 3233 or MAT 4233, and either MAT 3123 or MAT 4263.
Selected subjects in mathematics developed through historical perspectives and biographies. May not be applied toward the Mathematics Concentration of the B.S. degree in Mathematics. (Credit cannot be earned for both UTE 3023 and MAT 4123.) Generally offered: Spring, Summer.

**MAT 4213. Real Analysis I. (3-0) 3 Credit Hours.**

Prerequisite: MAT 3213.
Continuous functions, uniform continuity; theory of differentiation; applications of the derivative to properties of functions; antiderivatives; Riemann integral; connection between differentiation and integration. Generally offered: Fall, Spring, Summer.

**MAT 4223. Real Analysis II. (3-0) 3 Credit Hours.**

Prerequisite: MAT 4213.
Lebesgue integral on the real line; n-dimensional spaces; vectors; calculus of functions of several variables; multidimensional integration. Generally offered: Fall, Spring.

**MAT 4233. Modern Abstract Algebra. (3-0) 3 Credit Hours.**

Prerequisites: MAT 2233 and MAT 3013.
Basic properties and examples of semigroups, monoids, and groups, detailed study of permutation, dihedral, and congruence groups, cyclic groups, normal subgroups, quotient groups, homomorphism, isomorphism theorems, direct products of groups, The Sylow Theorems, rings and fields and their basic properties, ideals, polynomial rings. Generally offered: Spring.

**MAT 4263. Geometry. (3-0) 3 Credit Hours.**

Prerequisite: MAT 3013.
A study of non-Euclidean geometries, including spherical geometry, hyperbolic geometry and others. Generally offered: Spring.

**MAT 4273. Topology. (3-0) 3 Credit Hours.**

Prerequisite: MAT 3213.
Set theory, including cardinal and ordinal numbers. Topological properties of the real-line and metric spaces. Generally offered: Fall.

**MAT 4303. Capstone Course for Mathematics. (3-0) 3 Credit Hours.**

Prerequisites: Consent of instructor or one each from MAT 3123 or MAT 4263, MAT 3233 or MAT 4233, and MAT 4013 or MAT 4113.
This course is for any interested mathematics major, particularly for those students who intend to pursue secondary certification in Mathematics. The goals of the course are to enable students to build connections among the mathematical areas they have studied and between undergraduate mathematics and high school mathematics, to develop their understanding of mathematics as an integrated discipline, and to strengthen their oral and written communication skills in mathematics. May not be applied toward the Mathematics Concentration of the B.S. degree in Mathematics. Generally offered: Fall, Spring.

**MAT 4353. Mathematical Foundations of Cryptography. (3-0) 3 Credit Hours.**

Prerequisite: MAT 3233 or MAT 4233 or consent of instructor.
Congruences and residue class rings, Fermat’s Little Theorem, the Euler phi-function, the Chinese Remainder Theorem; complexity; symmetric-key cryptosystems; cyclic groups, primitive roots, discrete logarithms, one-way functions; public-key cryptosystems (Diffie-Hellman key exchange, RSA, Rabin, El Gamal); digital signatures; and other groups (finite fields, elliptic curves). Generally offered: Spring.

**MAT 4803. Statistical Quality Control. (3-0) 3 Credit Hours.**

Prerequisites: MAT 1224 and STA 3003 or STA 3513.
Statistical methods are introduced in terms of problems that arise in manufacturing and their applications to the control of manufacturing processes. Topics include control charts and acceptance sampling plans. (Same as STA 4803. Credit cannot be earned for both MAT 4803 and STA 4803.).

**MAT 4913. Independent Study. (0-0) 3 Credit Hours.**

Prerequisites: Permission in writing (form available) of the instructor, the student’s advisor, the Department Chair, and the Dean of the College in which the course is offered.
Independent reading, research, discussion, and/or writing under the direction of a faculty member. May be repeated for credit, but not more than 6 semester credit hours, regardless of discipline, will apply to a bachelor’s degree.

**MAT 4953. Special Studies in Mathematics. (3-0) 3 Credit Hours.**

Prerequisite: Consent of instructor.
An organized course offering the opportunity for specialized study not normally or not often available as part of the regular course offerings. May be repeated for credit when the topics vary, but not more than 6 semester credit hours, regardless of discipline, will apply to a bachelor’s degree. Generally offered: Fall, Spring, Summer.

**MAT 4993. Honors Research. (0-0) 3 Credit Hours.**

Prerequisites: Enrollment limited to candidates for College Honors during their last two semesters; approval by the College Honors Committee.
Supervised research and preparation of an honors thesis. May be repeated once with approval.