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 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 Bachelor of Science 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 1203Academic Inquiry and Scholarship3

Communication (6 semester credit hours)

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

WRC 1013Freshman Composition I (Q)3
WRC 1023Freshman 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 1023College Algebra with Applications3
MAT 1033Algebra with Calculus for Business3
MAT 1043Introduction to Mathematics3
MAT 1073Algebra for Scientists and Engineers3
MAT 1093Precalculus3
MAT 1193Calculus for the Biosciences3
MAT 1214Calculus I4
STA 1053Basic Statistics3

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 2033Introduction to Biological Anthropology3
AST 1013Introduction to Astronomy3
AST 1033Exploration of the Solar System3
BIO 1233Contemporary Biology I3
BIO 1243Contemporary Biology II3
BIO 1404Biosciences I4
BIO 1414Biosciences II4
ES 1113Environmental Botany3
ES 1123Environmental Zoology3
ES 1213Environmental Geology3
ES 2013Introduction to Environmental Science I3
ES 2023Introduction to Environmental Science II3
GEO 1013The Third Planet3
GEO 1123Life Through Time3
GRG 2613Physical Geography3
PHY 1013Universes3
PHY 1943Physics for Scientists and Engineers I3
PHY 1963Physics for Scientists and Engineers II3

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 2013Introduction to African American Studies3
AAS 2113African American Culture, Leadership and Social Issues3
ANT 2063Language, Thought, and Culture3
ARA 1014Elementary Arabic I4
ARC 1113Introduction to the Built Environment3
ARC 1413Architecture and Culture3
CHN 1014Elementary Chinese I4
CLA 2013Introduction to Ancient Greece3
CLA 2023Introduction to Ancient Rome3
CLA 2323Classical Mythology3
CSH 1103Literary Masterpieces of Western Culture I3
CSH 1113Literary Masterpieces of Western Culture II3
CSH 1213Topics in World Cultures3
CSH 2113The Foreign Film3
ENG 2013Introduction to Literature3
ENG 2213Literary Criticism and Analysis3
ENG 2383Multiethnic Literatures of the United States3
ENG 2423Literature of Texas and the Southwest3
FRN 1014Elementary French I4
FRN 2333French Literature in English Translation3
GER 1014Elementary German I4
GER 2333German Literature in English Translation3
GLA 1013U.S. in the Global Arena3
GRG 1023World Regional Geography3
GRK 1114Introductory Classical Greek I4
HIS 2123Introduction to World Civilization to the Fifteenth Century3
HIS 2133Introduction to World Civilization since the Fifteenth Century3
HIS 2533Introduction to Latin American Civilization3
HIS 2543Introduction to Islamic Civilization3
HIS 2553Introduction to East Asian Civilization3
HIS 2573Introduction to African Civilization3
HIS 2583Introduction to South Asian Civilization3
HUM 2093World Religions3
ITL 1014Elementary Italian I4
ITL 2333Italian Literature in English Translation3
JPN 1014Elementary Japanese I4
LAT 1114Introductory Latin I4
MAS 2013Introduction to Chicano(a) Studies3
PHI 1043Critical Thinking3
PHI 2023Introduction to Ancient Philosophy3
PHI 2033Introduction to Early Modern Philosophy3
PHI 2123Contemporary Moral Issues3
RUS 1014Elementary Russian I4
RUS 2333Russian Literature in English Translation3
SPN 1014Elementary Spanish I4
SPN 2333Hispanic Literature in English Translation3
WS 2013Introduction to Women’s Studies3
WS 2023Introduction to LGBTQ Studies3

Creative Arts (3 semester credit hours)

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

AHC 1113Survey of Art and Architecture from Prehistoric Times to 13503
AHC 1123Survey of Art and Architecture in Europe and the New World from 1350 to 17503
AHC 1133Survey of Modern Art3
ARC 1214Design I4
ARC 1513Great Buildings and Cities of the World3
ART 1103Introduction to Visual Arts3
ART 1143Art for Non-Art Majors3
CLA 2033Introduction to Classical Literature3
DAN 2003Introduction to Dance3
ENG 1113Introduction to Creative Literary Arts3
HUM 2023Introduction to the Humanities I3
HUM 2033Introduction to the Humanities II3
HUM 2053History of Film3
MAS 2023Latino Cultural Expressions3
MUS 2243World Music in Society3
MUS 2623Fundamentals of Music for the Non-Music Major3
MUS 2633American Roots Music3
MUS 2663History and Styles of Jazz3
MUS 2673History and Styles of Rock3
MUS 2683Masterpieces of Music3
MUS 2693The Music of Latin America and the Caribbean3
MUS 2743Music and Film3
PHI 2073Philosophy of Art3

American History (6 semester credit hours)

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

HIS 1043United States History: Pre-Columbus to Civil War Era3
HIS 1053United States History: Civil War Era to Present3
HIS 2053Texas History3

Government-Political Science (6 semester credit hours)

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

POL 1013Introduction to American Politics3
and one of the following two courses:
POL 1133Texas Politics and Society3
POL 1213Civil Rights in Texas and America3

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 2043Approaches to American Culture3
ANT 1013Introduction to Anthropology3
ANT 2043Introduction to Archaeology3
ANT 2053Introduction to Cultural Anthropology3
BBL 2003Language, Culture, and Society3
BBL 2243Globalizing the Local: Bilingual Families, Communities, and Schools3
BIO 1033Drugs and Society3
CRJ 1113The American Criminal Justice System3
ECO 2003Economic Principles and Issues3
ECO 2013Introductory Macroeconomics3
ECO 2023Introductory Microeconomics3
EGR 1343The Impact of Modern Technologies on Society3
GRG 1013Fundamentals of Geography3
GRG 2623Human Geography3
HTH 2413Introduction to Community and Public Health3
HTH 2513Personal Health3
IDS 2113Society and Social Issues3
PSY 1013Introduction to Psychology3
SOC 1013Introduction to Sociology3
SOC 2013Social Problems3
SOC 2023Social Context of Drug Use3

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 competent area requirement, for a total of 3 semester credit hours:

COM 2113Public Speaking3
CS 1173Data Analysis and Visualization3
EGR 1403Technical Communication3
ENG 2413Technical Writing3
PAD 1113Public Administration in American Society3
PHI 2043Introductory Logic3
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 Bachelor of Science 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 1214Calculus I
MAT 1224Calculus II

Mathematics Degree Requirements

All candidates for the Bachelor of Science 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 1214Calculus I (The student who is not prepared to begin MAT 1214 must take MAT 1093 Precalculus.)4
MAT 1224Calculus II4
MAT 2214Calculus III4
MAT 2233Linear Algebra3
MAT 3013Foundations of Mathematics3
MAT 3213Foundations of Analysis3
MAT 4213Real Analysis I3
Total Credit Hours24

In addition, a candidate for the Bachelor of Science 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 courses21
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 advisor9
D. Electives
Select 24 or 25 semester credit hours of electives24-25
Total Credit Hours58

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. Computer Science
CS 1063Introduction to Computer Programming I3
or CS 2073 Computer Programming with Engineering Applications
B. Mathematics and/or Statistics
1. Mathematics
MAT 3103Data Analysis and Interpretation3
MAT 3123Fundamentals of Geometry3
or MAT 4263 Geometry
MAT 3233Modern Algebra3
or MAT 4233 Modern Abstract Algebra
MAT 4013Graphing Calculator Topics3
MAT 4113Computer Mathematical Topics3
MAT 4303Capstone Course for Mathematics3
2. Approved upper-division course in mathematics3
C. Required academic foundations
COM 1043Introduction to Communication3
D. 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 Hours57

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
FallCredit Hours
AIS 1203Academic Inquiry and Scholarship (core) 3
MAT 1214Calculus I (core and major) 4
WRC 1013Freshman Composition I (Q) (core) 3
American History core 3
Life & Physical Sciences core 3
Spring
MAT 1224Calculus II 4
WRC 1023Freshman Composition II (Q) (core) 3
Life & Physical Sciences core 3
Select one of the following: 3-4
CS 1063Introduction to Computer Programming I
CS 1713
CS 1711
Introduction to Computer Programming II
CS 2073Computer Programming with Engineering Applications
Second Year
Fall
MAT 2214Calculus III 4
MAT 2233Linear Algebra 3
Government-Political Science core 3
Free elective 3
Free elective 3
Spring
MAT 3013Foundations of Mathematics 3
STA 3003Applied Statistics 3
Creative Arts core 3
Government-Political Science core 3
Free elective 3
Third Year
Fall
MAT 3613Differential Equations I 3
STA 3513Probability and Statistics 3
Social & Behavioral Sciences core 3
Upper-division MAT or STA elective 3
Free elective 3
Spring
MAT 3213Foundations of Analysis 3
MAT 4233Modern Abstract Algebra 3
Component Area Option core 3
Free elective 3
Upper-division MAT or STA elective 3
Fourth Year
Fall
MAT 3633Numerical Analysis 3
MAT 4213Real Analysis I 3
MAT 4273Topology 3
Free elective 3
Upper-division Free elective 3
Spring
MAT 4223Real Analysis II 3
Free elective 12-3
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
FallCredit Hours
AIS 1203Academic Inquiry and Scholarship (core) 3
COM 1043Introduction to Communication 3
MAT 1214Calculus I (core and major) 4
WRC 1013Freshman Composition I (Q) (core) 3
Life & Physical Sciences core 3
Spring
CS 1063 or 2073Introduction to Computer Programming I (or Computer Programming with Engineering Applications) 3
MAT 1224Calculus II 4
WRC 1023Freshman Composition II (Q) (core) 3
Free elective 3
Life & Physical Sciences core 3
Second Year
Fall
MAT 2214Calculus III 4
MAT 2233Linear Algebra 3
Free elective 3
American History core 3
Spring
MAT 3013Foundations of Mathematics 3
MAT 3103Data Analysis and Interpretation 3
POL 1133 or 1213Texas Politics and Society (core) 3
Free elective 3
Free elective 3
Third Year
Fall
MAT 4013Graphing Calculator Topics 3
MAT 3123 or 4263Fundamentals of Geometry (or Geometry) 3
POL 1013Introduction to American Politics (core) 3
Free elective 3
Social & Behavioral Sciences core 3
Spring
MAT 3213Foundations of Analysis 3
MAT 3233 or 4233Modern 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 4213Real Analysis I 3
MAT 4303Capstone Course for Mathematics 3
Free elective 3
Free elective 3
Upper-division MAT elective (not MAT 3253) 3
Spring
MAT 4113Computer 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
FallCredit Hours
AIS 1203Academic Inquiry and Scholarship (core) 3
COM 1043Introduction to Communication 3
GEM 1011GEEMS Mathematics/Science I 1
MAT 1214Calculus I (core and major) 4
WRC 1013Freshman Composition I (Q) (core) 3
Life & Physical Sciences core 3
Spring
CS 1063 or 2073Introduction to Computer Programming I (or Computer Programming with Engineering Applications) 3
GEM 1021GEEMS Mathematics/Science II 1
MAT 1224Calculus II 4
WRC 1023Freshman Composition II (Q) (core) 3
Life & Physical Sciences core 3
Second Year
Fall
EDU 2103Social Foundations for Education in a Diverse U.S. Society 13
GEM 1031GEEMS Mathematics/Science III 1
MAT 2214Calculus III 4
MAT 3013Foundations of Mathematics 3
American History core 3
Spring
EDP 3203Learning and Development in the Secondary School Adolescent 3
MAT 2233Linear Algebra 3
MAT 3103Data Analysis and Interpretation 3
Creative Arts core 3
Summer
POL 1013Introduction to American Politics (core) 3
Language, Philosophy & Culture core 3
Third Year
Fall
BBL 3403Cultural and Linguistic Equity for Schooling 13
MAT 3123 or 4263Fundamentals of Geometry (or Geometry) 3
MAT 3233 or 4233Modern Algebra (or Modern Abstract Algebra) 3
POL 1133 or 1213Texas Politics and Society (core) 3
Social & Behavioral Sciences core 3
Spring
MAT 3213Foundations of Analysis 3
MAT 4013Graphing Calculator Topics 3
SPE 3603Introduction to Special Education 13
Upper-division MAT elective (not MAT 3253) 3
Component Area Option core 3
Summer
MAT 4113Computer Mathematical Topics 3
American History core 3
Fourth Year
Fall
C&I 4203Models of Teaching in the Content Areas of the Secondary School 3
EDP 4203Assessment and Evaluation 3
MAT 4213Real Analysis I 3
MAT 4303Capstone Course for Mathematics 3
RDG 3773Reading and Writing Across the Disciplines–Secondary 3
Spring
C&I 4646Clinical Teaching: Grades 8–12 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 1214Calculus I4
MAT 1224Calculus II4
MAT 2214Calculus III (Computer Science majors substitute CS 3333) 13-4
or CS 3333 Mathematical Foundations of Computer Science
MAT 2233Linear Algebra3
MAT 3613Differential Equations I 23
B. Approved upper-division mathematics electives
Select a minimum of 6 semester credit hours of approved upper-division mathematics electives6-7
Total Credit Hours24
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 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 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. 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 4253. Number Theory. (3-0) 3 Credit Hours.

Prerequisite: MAT 3233 or MAT 4233. The theory of primes, congruences, and related subjects.

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 4313. Applied Combinatorics. (3-0) 3 Credit Hours.

Prerequisite: MAT 1224. Permutations, combinations, arrangements, selections, distributions, generating functions, inclusion-exclusion principle.

MAT 4323. Applied Graph Theory. (3-0) 3 Credit Hours.

Prerequisite: MAT 1224. Isomorphism, planarity, computer representation of graphs, covering circuits and graph colorings, Euler and Hamiltonian graphs, trees and searching network algorithms (shortest paths, connectivity, traveling salesman, network flow, matching, sorting, etc.).

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.