# Department of Mathematics

## Contact Information

**Chair:**Ravi Agarwal**Phone:**361-593-3517**Email:**ravi.agarwal@tamuk.edu**Building Name:**Rhode Hall**Room Number:**217

The department offers several programs designed to give the student an insight into the structure and applications of mathematics and statistics necessary for industrial or governmental employment, teaching or pursuit of an advanced degree in mathematics and statistics.

The faculty members are committed to educating students in the scientific and engineering environment. Through mathematics courses, students will develop their logical reasoning, critical thinking, technical communication and computational skills.

The department serves students from other disciplines, students in the science, education, engineering and mathematics, as well as the community, by offering a wide range of interdisciplinary courses.

Students are allowed to register for freshman mathematic and statistic courses appropriate to their high school mathematics preparations and/or entrance examination scores as determined by the department.

## Undergraduate Certificate in SAS Programming and Data Analysis

### Admission Requirements

The certification is open to all degree-seeking undergraduate students as well as those registered as non-degree-seeking (transient) students. A student must be in good academic standing in pursuit of his or her current degree and may not be on academic probation of any kind. A student must have earned a grade of *B* or higher in a 1000-level introductory statistics course or its equivalent (must receive approval of the certificate director). The course offered at TAMU-K that meets this requirement includes STAT 1342. Students who have not taken a 1000-level statistics course or equivalent may enroll in one of two courses, STAT 4301 or STAT 4303, as a prerequisite to the certificate program. Students who have earned a grade of *B* or higher in STAT 4301 or STAT 4303 will also have that course counted toward one of the three elective courses for SAS certification, provided the instructor of these two courses also covers the corresponding SAS material appropriate for these courses.

### Application Procedure

Students apply to the certification program via an online form accessible on the department’s website. The form is automatically sent to the program director no later than four weeks after the start of the last class in the certificate sequence. A student’s standing relative to the certificate requirements will be evaluated and, if the student is qualified, he or she will be sent specific instructions on required evaluation materials to complete certification. In case the student is not qualified or is deemed to be making insufficient progress toward the certificate, he or she will be notified accordingly.

### Program of Studies

The undergraduate certificate requires 12 credit hours consisting of one 4000-level core course and three elective courses selected from the list below with a minimum of a *B* grade in each course. All elective courses are at the 4000 level and have a SAS component. Courses in the certificate program are shown below. Most of these courses will initially be taught as STAT 4390.

Code | Title | Semester Credit Hours |
---|---|---|

Required Core Course | ||

STAT 4390 | Selected Topics in Statistics | 3 |

Elective Courses (Select Three) | ||

STAT 4301 | Biostatistics | 3 |

STAT 4303 | Statistical Methods | 3 |

STAT 4390 | Selected Topics in Statistics | 3 |

Additional courses will be added as needed.

## Faculty

**Agarwal, Ravi P** Professor, Department of Mathematics; Chair; M.S., Agra University (India); Ph.D., Indian Institute of Technology (India).

**Ahangar, Reza R** Professor, Department of Mathematics; B.S., Tehran University (Iran); M.S., The Catholic University of America; Ph.D., The Catholic University of America.

**Ahmed, Aden O** Associate Professor, Department of Mathematics; B.S., Université Joseph Fourier (France); M.S., Portland State University; Ph.D., Portland State University.

**Allred, Polly** Senior Lecturer, Department of Mathematics; B.S., Utah State University; M.S., Utah State University; Ed.D., Texas A&M University-Kingsville.

**Bodjanova, Slavka** Professor, Department of Mathematics; B.S., Comenius University (Czechoslovakia); M.S., Comenius University (Czechoslovakia); Ph.D., Comenius University (Czechoslovakia).

**Conje, Ricardo** Senior Lecturer, Department of Mathematics; B.S., University of Visayas (Phillipines); M.S., University of Visayas (Phillipines); D.B.A., University of San Jose Recoletos (Phillipines).

**Hodis, Simona** Assistant Professor, Department of Mathematics; B.Sc., Universitatea Al.I.Cuza (Romania); M.Sc., McMaster University (Canada); Ph.D., University of Western Onatrio (Canada).

**Muzheve, Michael T** Associate Professor, Department of Mathematics; B.S., University of Zimbabwe (Zimbabwe); M.Phil., University of Zimbabwe; M.S., Texas A&M University; Ph.D., Texas A&M University.

**Ramirez, Elva** Senior Lecturer, Department of Mathematics; B.S., Texas A&M University-Kingsville; M.P.A., Texas A&M University-Kingsville.

**Sedory, Stephen A** Professor, Department of Mathematics; B.A., Luther College; M.S., Oklahoma State University; M.S., Oklahoma State University; Ph.D., Oklahoma State University.

**Singh, Sarjinder** Professor, Department of Mathematics; B.S., Punjab Agricultural Univeristy (India); M.S., Punjab Agricultural Univeristy (India); Ph.D., Punjab Agricultural Univeristy (India).

**Torres, Ramiro** Senior Lecturer, Department of Mathematics; B.S., Texas A&M University-Kingsville; M.S., Texas A&M University-Kingsville.

**Wang, Rongdong** Professor, Department of Mathematics; B.S., Peking Polytechnic University (China); M.S., Hebei Teacher's University (China); M.S., Northern Illinois University; M.S., Northern Illinois University; Ph.D., Northern Illinois University.

**Wu, Hueytzen J** Professor, Department of Mathematics; B.S., National Taiwan Normal University (Taiwan); M.S., The Ohio State University; Ph.D., University of Arkansas.

## Emeritus

**Cecil, David** Professor of Mathematics, Department of Mathematics; B.A., Tulsa University; M.S., Oklahoma State University; Ph.D., Oklahoma State University.

## Mathematics (MATH)

**MATH 0010** Basic Math Lab Coastal Bend **0 SCH** **(1)**

**MATH 0302** Developmental Algebra **3 SCH** **(3)**

The algebra skills necessary for success in college-level mathematics. Topics include real number operations, linear and quadratic equations, graphing linear and nonlinear equations, and simplifying polynomial, rational, and radical expressions. Course delivery is mainly through mathematics learning software. This course does not count toward any degree. Placement is based on analysis of student ACT/SAT, TSI, and/or placement test scores. Credit/Non-credit.

**MATH 0311** Basic Math Coastal Bend **3 SCH** **(3)**

**MATH 0314** College Algebra **0 SCH** **(0)**

**MATH 0334** Contemporary Mathematics **0 SCH** **(0)**

**MATH 1000** Math **3 SCH** **(0-3)**

**MATH 1314** College Algebra **3 SCH** **(3)**

College-level topics in algebra including functions, graphs, variation, piecewise defined functions, equations of lines, elementary curve fitting, quadratic equations and functions, systems of linear and nonlinear equations, composition of functions, inverse functions, exponential and logarithmic functions and applications related to these topics. Prerequisite: two years of high school algebra and/or appropriate scores on mathematics placement tests.

**MATH 1316** Trigonometry **3 SCH** **(3)**

**MATH 1324** Math for Bus and Econ I **3 SCH** **(3)**

A course designed for students in business administration. Selected topics from finite mathematics including: linear inequalities, vectors, matrices, linear programming and probability. Prerequisite: two years of high school algebra and/or appropriate scores on mathematics placement tests.

**MATH 1325** Math for Bus and Econ II **3 SCH** **(3)**

**MATH 1334** Contemporary Mathematics **3 SCH** **(3)**

An introduction to several contemporary applications of mathematics for the nonmajor. Emphasis is on the variety of problems which can be modeled and solved by analytic and quantitative means. Topics will vary, but may include such as: applications of graph theory to management problems; encoding and encrypting information; problems of social choice-fair division, voting systems, conflict; topics in geometry; and data analysis. Prerequisites: ALGE 0301 and/or appropriate scores on mathematics placement tests.

**MATH 1335** Contemporary Mathematic FOCUS **3 SCH** **(3-1)**

An introduction to several contemporary applications of mathematics for the nonmajor. Emphasis is on the variety of problems which can be modeled and solved by analytic and quantitative means. Topics will vary, but may include such as: applications of graph theory to management problems; encoding and encrypting informtaion; problems of social choice-fair division, voting systems, conflict; topics in geometry; and data analysis. Requires a one hour non-credit laboratory, which focuses on more extensive applications, as well as mathematics study skills and success strategies. Prerequisites: appropriate scores on mathematics placement tests. Departmental permit required.

**MATH 1348** Analytic Geometry **3 SCH** **(0-3)**

**MATH 1350** Fundamentals of Mathematics I **3 SCH** **(3)**

Problems from number theory, number systems, systems of operations and proportional reasoning. Requires approaching problems from multiple perspectives, drawing connections among those perspectives and strengthening flexibility and fluency in mathematical thinking and communicating. Not applicable for credit in the physical sciences or engineering. Prerequisite: MATH 1314 or higher.

**MATH 1351** Fundamentals of Mathematics II **3 SCH** **(3)**

Problems from probability, statistics, measurement, geometry and spatial thinking. Requires approaching problems from multiple perspectives, drawing connections among those perspectives and strengthening flexibility and fluency in mathematical thinking and communicating. Not applicable for credit in the physical sciences or engineering. Prerequisite: MATH 1350.

**MATH 2305** Math. Methods in Biomedicine **3 SCH** **(3)**

**MATH 2314** Calculus II **3 SCH** **(3)**

This course is a continuation of MATH 2313. Differentiation and integration of logarithmic, exponential and trigonometric functions. Techniques of integration. Applications of the integral to problems such as volumes of revolution, work, arc length and fluid pressure. Prerequisite: MATH 2313.

**MATH 2413** Calculus I **4 SCH** **(3-0)**

Limits and continuity. Definition of the derivative of a function and techniques of differentiation. Derivatives of various functions, to include rational, exponential, logarithmic, trigonometric and their inverses. Maximizing or minimizing a function, curve sketching, and rate of change problems; L'Hospital's rule. Introduction to integration, the Fundamental Theorem of Calculus, applications to areas; introduction to numerical integration. Prerequisite: MATH 1348.

**MATH 2414** Calculus II **4 SCH** **(3-0)**

Continuation of MATH 2413. Integration of logarithmic, exponential, and trigonometric functions. Techniques of integration. Applications of the integral to problems involving volumes, work, arc length, and fluid pressure. Infinite sequences and series, power series expansion of function. Calculus with parametric curves, and polar coordinates. Prerequisite: MATH 2413.

**MATH 3315** Calculus III **3 SCH** **(3)**

**MATH 3320** Differential Equations **3 SCH** **(3)**

The ordinary differential equations of physics, chemistry and engineering; methods for their solution and the properties of their solution. Introduction to partial differential equations. Prerequisite: MATH 2314. Laboratory fee, $5.

Fee: $5.00

**MATH 3325** Intro Mathematical Proofs (WI) **3 SCH** **(3)**

Principles and techniques of discovering and writing correct mathematical proofs. Independently prove theorems from various areas in mathematics, which may include topics from logic, the structure of the real number system, number theory, geometry and algebra. Prerequisite: MATH 2313.

**MATH 3340** Linear Algebra with Appl **3 SCH** **(3)**

Systems of linear equations, matrices and determinants, vector spaces, subspaces, bases and dimension, linear transformations and their representations by matrices, orthogonality, eigenvectors, and diagonalization. Problem solving using difference equations. Prerequisite: MATH 2413.

**MATH 3352** Applied Fundamentals of Math **3 SCH** **(3)**

Applied projects in selected areas of mathematics, such as number systems, systems of operations, proportional reasoning, probability, statistics, measurement, and geometry. Emphasis on understanding pedagogical content for pre-service teachers in mathematics. Planning, implementing and assessing mathematics activities during a two-week summer camp for area youth. Prerequisite: MATH 2413.

**MATH 3360** Modern Geometry **3 SCH** **(3)**

Historical review of set theory logic and applications in Euclidean Geometry, Hilbert's approach and revision of Euclid's postulates, rewriting of Euclid's fifth postulate, Axiomatic approach to modern Geometry, Foundations of non-Euclidean geometry. Prerequisite: MATH 3325.

**MATH 3370** Discrete Mathematics **3 SCH** **(3)**

This course covers many topics in mathematics which are important in computer science. Some of these topics are sets, relations, functions, algorithms, graphs, monoids, lattices, Boolean algebras and graphs. Prerequisite: 3 semester hours of advanced mathematics. Laboratory fee, $5.

Fee: $5.00

**MATH 3371** Prob Solving with Computers **3 SCH** **(3)**

Brief historical overview of computing and computers; strategies for solving problems by computers; programming in a higher level language. Students will be exposed to problem solving using technology, graphing calculator, and computer algebra system. Prerequisite: MATH 2413.

**MATH 3372** Mathematical Biology **3 SCH** **(3)**

Formulating biological problems as problems in mathematics. Modeling population growth, inter-species dependency, the spread of infectious diseases, biochemical enzyme reactions, and the oscillations of biological systems. How models are initially formulated and subsequently refined. Prerequisite: MATH 1325 or MATH 2413, and BIOL 136 and BIOL 1307.

**MATH 3373** Mathematical Physiology **3 SCH** **(3)**

Mathematical models to describe the physiology of human organs and their associated systems. Includes circulatory, respiratory, renal, endocrine, and gastrointestinal systems. Models for adequacy in capturing features of the systems and in predicting pathologies. Prerequisites: MATH 1325 or MATH 2413, and BIOL 1306 and BIOL 1307.

**MATH 3390** Selected Topics in Math **3 SCH** **(3)**

Different topics will be covered at varying times. May be repeated for credit with consent of the instructor. Prerequisite: 3 semester hours of advanced mathematics.

**MATH 3415** Calculus III **4 SCH** **(3-0)**

Continuation of MATH 2414. Vectop operations in 2 and 3 dimensions, lines, planes; vector functions, space curves, partial derivatives, curvature; multivariable calculus, optimization, Lagrange multipliers; multiple integral; vector fields, theorems of Green, Gauss and Stokes. Prerequisite: MATH 2414.

Fee: $5.00

**MATH 4320** Advanced Calculus **3 SCH** **(3)**

Partial differentiation, Lagrange multipliers, Leibnitz’s rule, multiple integrals, vector analysis, infinite series, uniform convergence and Fourier series.

**MATH 4321** Real Variables **3 SCH** **(3)**

The real number system, its structure and properties. Properties of real functions and sequences, including uniform continuity and the Cauchy criterion. Introduction to the theory of sets. Theory and application of the derivative. Introductory concepts of function spaces, norms and metrics. Prerequisite: 6 semester hours of advanced mathematics, including MATH 3325.

**MATH 4340** Modern Algebra **3 SCH** **(3)**

Properties of the Integers: divisibility, prime factorization and congruences. Integral domains, rings and fields. Groups, permutations and cosets. A historical development of these topics is included. Prerequisite: MATH 3325.

**MATH 4341** Linear Alg and Matrix Theory **3 SCH** **(3)**

Vector spaces and their linear subspaces. Representation of linear transformations by matrices. Normal forms, eigenvalues, special transformations and applications. Prerequisite: 6 semester hours of advanced mathematics. Laboratory fee, $5.

Fee: $5.00

**MATH 4342** Algebraic Structures **3 SCH** **(3)**

An intensive axiomatic study of groups, rings, polynomial rings, fields and modules, along with their principal substructures. Emphasis on classification and structure theorems. Prerequisite: 6 hours of advanced mathematics or consent from instructor.

**MATH 4351** Mathematical Theory of Games **3 SCH** **(3)**

Introduction to game theory. Topics include: combinatorial and strategic games, backward induction, payoffs, cooperative and non-cooperative games, mixed strategies, equilibria, repeated games and finite automata, common knowledge and incomplete information, the prisoner's dilemma. Selected applications to economics, biology, computer science, and political science. Prerequisite: MATH 3340 or consent of instructor.

**MATH 4370** Vector Analysis **3 SCH** **(3)**

**MATH 4371** Laplace Transformation **3 SCH** **(3)**

An introduction to the theory of the Laplace Transformation. Applications to the solution of ordinary and partial differential equations, integral equations, difference equations and integro-differential equations. An introduction to other types of integral transformations. Prerequisites: MATH 3315 and MATH 3320.

**MATH 4372** Math for Physics and Eng I **3 SCH** **(3)**

**MATH 4373** Application of Matrix Methods **3 SCH** **(3)**

**MATH 4374** Numerical Analysis **3 SCH** **(3)**

The mathematical formation of the concepts in numerical analysis. These concepts include the theory of errors, roots of equations, interpolation, linear systems of equations, numerical differentiation and integration and solutions of ordinary differential equations. Prerequisites: MATH 3315 and MATH 3320.

**MATH 4390** Selected Topics in Mathematics **3 SCH** **(3)**

Different topics will be covered at varying times. May be repeated for credit with consent of instructor. Prerequisite: 3 semester hours of advanced mathematics.

**MATH 4399** Capstone Experience in Math **3 SCH** **(3)**

Designed to integrate mathematical standards and skills of mathematics majors. Students will demonstrate their ability to organize and synthesize mathematical knowledge; and design, implement, and present an advanced project in mathematics or mathematics education. Prerequisite: Senior standing in mathematics.

## Statistics (STAT)

**STAT 1342** Elementary Statistics **3 SCH** **(3)**

**STAT 2342** Statistical Analytics **3 SCH** **(3)**

Foundation course in statistical analysis, with emphasis on methods and interpretation of results, review of probability and common distributions, sampling distributions of mean, proportion, and variance; Central Limit Theorem; hypothesis testing, confidence interval, power of a test, sample-size calculation, contingency tables, chi-squared test, and introduction to ANOVA. Prerequisites: STAT 1342 or equivalent.

**STAT 3331** Intro to Nonparametric Stats **3 SCH** **(3)**

The basic foundation for nonparametric statistical methods. Focus on methods and interpretation of the results. Measure of scales (nominal, ration, and interval) and overview of analyzing data having these scales of measurements using nonparametric methods. Emphasis on one-and-two sample tests of locations using standard nonparametric methods. Prerequisites: STAT 1342 or equivalent.

**STAT 3332** Intro. to Data Analysis/SAS **3 SCH** **(3)**

Statistical computing using SAS (Statistical Analysis Software). Covers all of the objectives tested on the SAS Certification Exam (Base). Topics include importing and exporting raw data files, creating and modifying SAS data sets, identifying and correcting data syntax, programming logic errors, and some common PROCs. Prepares students to take the basic SAS certification exam conducted by the SAS institute. Prerequisite: STAT 1342 or equivalent.

**STAT 3344** Regression and Expt. Design **3 SCH** **(3)**

Basic methods of regression and fundamental principles and techniques in designing experiments. Introduction to correlation, regression, multiple regression, and ANOVA; diagnostics of regression models; and model selection (forward selection, backward elimination, and stepwise selection). Statistical principles in the design and analysis of industrial experiments. Prerequisite: STAT 1342 or equivalent.

**STAT 4301** Biostatistics **3 SCH** **(3)**

For students in biology, health sciences, human sciences, and wildlife science. Descriptive and inferential statistics, basic probability concepts, probability distributions, estimation, hypothesis testing, correlation, simple linear regression, principles of epidemiology, statistical vs. clinical significance, and quasi-statistical methods. Prerequisite: Math 1314.

Fee: $5.00

**STAT 4303** Statistical Methods **3 SCH** **(3)**

Calculus-based probability, discrete and continuous random variables, joint distributions, sampling distributions, the central limit theorem, descriptive statistics, interval estimates, hypothesis tests, ANOVA, correlation, and simple regression. Prerequisite: Math 2414.

Fee: $5.00

**STAT 4350** Probability **3 SCH** **(3)**

Sample spaces, combinatorics, independence, conditional probability and Bayes' rule. Discrete and continuous probability distributions, Chebychev's inequality and limit theorems. Prerequisite: MATH 3315.

**STAT 4351** Math Theory of Statistics **3 SCH** **(3)**

Sampling distributions, estimation properties and methods, testing hypothesis, power of tests and likelihood ratios. Prerequisites: STAT 4350 or the equivalent and 3 semester hours of advanced mathematics.

**STAT 4390** Selected Topics in Statistics **3 SCH** **(3)**

Topics in statistics not adequately covered in regular courses. This course may be repeated for credit as topic changes. Prerequisite: 3 semester hours of advanced mathematics or statistics.