Undergraduate Mathematics (MATH) Course Listings

MATH 1300, ELEMENTARY ALGEBRA

Fall, Spring, Summer

A course in elementary algebra designed for the student with a background in numerical skills.  Students have the opportunity to prepare for intermediate algebra and other mathematics coursework recommended in education, fine arts, the humanities or social sciences.  Topics include basic operations on real numbers, elementary geometry, introduction to algebra, linear equations and graphs, linear equations with applications, exponent properties, systems of linear equations in two unknowns, polynomials and factoring methods. This course may not be used to satisfy any general university graduation requirements. This course does not count toward a student's hours for graduation or in the determination of hours attempted or earned.  
THIS COURSE MAY NOT BE USED TO SATISFY ANY GENERAL UNIVERSITY GRADUATION REQUIREMENTS.

Student Learning Outcomes: After completing this course students will be able to

1. Demonstrate knowledge and understanding of the real numbers, the basic operations and their properties, basic operations with algebraic expressions, order of operations, and be able to translate algebraic expressions into English phrases, and from English phrases into algebraic expressions.
2. Demonstrate knowledge and understanding of combining like terms, use the addition-subtraction property, the multiplication-division property of equalities and inequalities and several combinations of these properties to solve linear equations and inequalities. Use of ratios, proportion and percent in problem solving.
3. Demonstrate knowledge and understanding of the formulas (geometric and others) which can be used to transform word problems into equations, and solving application problems involving geometry, motion, and mixture.
4. Demonstrate knowledge and understanding of Cartesian coordinate system, graphing linear equations, the slope of the line and solve the system of two linear equations in two variables.
5. Demonstrate knowledge and understanding of the properties of exponents, use of scientific notation, and addition, subtraction, multiplication, and division of polynomials.
6. Demonstrate knowledge and understanding of factoring by the distributive property, by grouping, factoring the difference of two squares, factoring of trinomials, solving quadratic equations using factoring method and application problem solving.

MATH 1334, INTERMEDIATE ALGEBRA

Fall, Spring, Summer

A course in algebra designed to prepare the student for College Algebra or the equivalent. Topics include factors of polynomials; rational expressions; radical expressions; an introduction to complex numbers; quadratic equations; rational equations, radical equations and elementary inequalities. 

Prerequisite: MATH 1300 with a grade of C or better, ACT math score 17 or better, or THEA math score 230 or better, or ACCUPLACER Elementary Algebra part score 82 or better. 
This course may not be used to satisfy any general university graduation requirements. This course does not count toward a student's hours for graduation or in the determination of hours attempted or earned. 

Student Learning Outcomes: After completing this course students will be able to

1. Demonstrate knowledge and understanding of factoring quadratic expressions by using a variety of methods.
2. Demonstrate knowledge and understanding of simplifying rational expressions involving the basic operations of rational expressions and complex fractions, solve rational equations, and solve application problems containing rational expressions.
3. Demonstrate knowledge and understanding of applying the laws of radicals to perform addition, subtraction, multiplication, and division of expressions involving radicals, solve the equations containing one radical and two radicals.
4. Demonstrate knowledge and understanding of complex numbers and perform the basic operations involving complex numbers, solve quadratic equations by technique of completing the square, by quadratic formula and solving application problems.
5. Demonstrate knowledge and understanding of the properties and techniques for solving simple and compound inequalities, and solving problems involving inequalities.

MATH 1340, COLLEGE ALGEBRA

Fall, Spring, Summer

Topics include nonlinear and absolute value inequalities, functions, complex numbers, polynomial and rational functions, exponential and logarithmic functions, systems of linear and nonlinear equations, and matrices.

Prerequisite: MATH 1334 with a grade of C or better, or ACT math score 20 or better, or THEA math score 260 or better, or ACCUPLACER College Level Mathematics part score 70 or better .

MATH 1340 Texas State Board Educator Certification (SBEC) Mathematics Standards (linked PDF file)

Student Learning Outcomes: After completing this course students will be able to

1. Demonstrate knowledge and understanding of the mathematical characterization of relationships (functions, equations, and inequalities included) and how mathematics provides structures for critical thinking, disciplined inquiry and the formulation of discoveries and applications to real-world situations.
2. Demonstrate knowledge and understanding of the mathematical concept of function, the essentials regarding their domains, correspondences, and ranges; and how to perform addition, subtraction multiplication, division, composition, and inversion of functions which are basic operations in the algebra of functions.
3. Demonstrate facility with multiple representations of algebraic relationships by coordinating the use of formulas, graphs, tables, verbal descriptions, and appropriate technology, noting interconnections and providing translations between these different modes of representation.
4. Demonstrate knowledge and understanding of relationships expressed through systems of equations and inequalities, and an assortment of functions - linear and nonlinear, absolute value, greatest integer, exponential, logarithmic, polynomial, and rational - which are essential for mathematical modeling and problem solving in real-world situations,
5. Demonstrate an understanding of complex numbers and how they extend the real number system to provide roots for certain types of equations, and that they constitute the highest order characterization for the concept of number with the system of complex numbers including within it all of the other subsystems of numbers - real, rational, integers, whole numbers and natural numbers.
6. Demonstrate an understanding of the strengths and limitations of mathematically expressed models (e.g., simple and compound interest, law of gravity).
7. Demonstrate an appreciation of the contributions of mathematics to exceptional accomplishments in the sciences and humanities.

MATH 1341, BUSINESS ALGEBRA

Fall, Spring, Summer

This course is designed for students who plan to major within the College of Business Administration. Topics include inequalities, quadratic functions, logarithmic and exponential functions, sequences and series, mathematics of finance, systems of linear equations, matrices, and an introduction to linear programming. Use of electronic calculators and microcomputers is emphasized to perform numerical computations.

Prerequisite: MATH 1334 with a grade of C or better, ACT math score of 20 or better, or THEA math score of 260 or better, or ACCUPLACER College Level Mathematics part score 70 or better.

Student Learning Outcomes: After completing this course students will be able to

1. Solve simple linear and absolute value inequalities and apply this skill to real-world problems.
2. Understand the concepts of function, inverse function, and graph of a function; distinguish the different classes of functions, such as linear, nonlinear, quadratic, polynomial, and rational; recognize symmetries in the graphs of functions; and apply simple transformations to functions.
3. Solve simple linear and nonlinear systems and apply this skill to real-world problems.
4. Solve exponential and logarithmic equations and understand their relevance to the solution of real-world problems, such as those involving compound interest and general growth and decay.
5. Solve basic time-value-of-money problems.
6. Understand the concept of a matrix, operations on matrices, their application to solving systems of linear equations, and their application to real-world problems.
7. Solve simple linear optimization (linear programming) problems and apply this skill to real-world problems.
8. Utilize technology where appropriate to accomplish the learning outcomes described above.

MATH 1342, BUSINESS CALCULUS

Fall, Spring, Summer

This course is designed for students who plan to major within the College of Business Administration. Topics include differential calculus with business applications, multivariable calculus including optimization techniques and applications, and an introduction to integral calculus.

Prerequisite: MATH 1341 or MATH 1340 with a grade of C or better, or ACCUPLACER College Level Mathematics part score 80 or better.

Student Learning Outcomes: After completing this course students will be able to

1. Compute limits of algebraic functions graphically, numerically, and algebraically.
2. Compute the derivative of basic algebraic, exponential, and logarithmic functions using derivative rules and implicit differentiation.
3. Interpret the derivative graphically and as a rate of change in business applications.
4. Use limits and derivatives to construct, analyze, and interpret the graph of a function.
5. Use derivatives to analyze and solve applied optimization problems.
6. Compute indefinite and definite integrals of functions using anti-derivative rules and the Fundamental Theorem of Calculus.
7. Represent area as a definite integral and interpret the result in business applications.
8. Compute and interpret partial derivatives of functions of more than one variable.

MATH 1348, CONTEMPORARY MATHEMATICS

Fall, Spring, Summer

Topics include Real World Problem Solving and Critical Thinking; Mathematical Logic; Graphs and Graphical Representations; Statistics and Probability; Voting and Apportionment Methods; Financial Mathematics. This course is designed to meet the THECB Exemplary Educational Objectives and to satisfy the core requirement in mathematics. 

Prerequisite: MATH 1334 with a grade of C or better, or ACT math score 20 or better, or THEA math score 260 or better, or ACCUPLACER College Level Mathematics part score 70 or better .

Student Learning Outcomes: After completing this course students will be able to

1. Understand and be able to solve graph theoretical problems with applications to real life problems.
2. Solve simple linear optimization (linear programming) problems.
3. Represent given statistical data through tables and pictures.
4. Have the basic ideas of central tendencies and dispersions and be able to use calculators to calculate them.
5. Understand how different voting systems work and what their limitations are.
6. Be able to solve problems in information science using binary numbers, cryptology and mathematical logic.
7. Understand the concept of golden ratio, and identify different types of symmetry,patterns and fractals.
8. Evaluate interest and loan amounts numerically, and use spreadsheets to model mortgages.

MATH 1389, CONTEMPORARY MATHEMATICS - HONORS
(honors equivalent of MATH 1348)

Fall, Spring, Summer

Topics include Real World Problem Solving and Critical Thinking; Mathematical Logic; Graphs and Graphical Representations; Statistics and Probability; Voting and Apportionment Methods; Financial Mathematics. This course is designed to meet the THECB Exemplary Educational Objectives and to satisfy the core requirement in mathematics. 

Prerequisite: MATH 1334 with a grade of C or better, or ACT math score 20 or better, or THEA math score 260 or better, or ACCUPLACER College Level Mathematics part score 70 or better .

Student Learning Outcomes: After completing this course students will be able to

1. Understand and be able to solve graph theoretical problems with applications to real life problems.
2. Solve simple linear optimization (linear programming) problems.
3. Represent given statistical data through tables and pictures.
4. Have the basic ideas of central tendencies and dispersions and be able to use calculators to calculate them.
5. Understand how different voting systems work and what their limitations are.
6. Be able to solve problems in information science using binary numbers, cryptology and mathematical logic.
7. Understand the concept of golden ratio, and identify different types of symmetry,patterns and fractals.
8. Evaluate interest and loan amounts numerically, and use spreadsheets to model mortgages.

MATH 1450, PRECALCULUS WITH TRIGONOMETRY

Fall, Spring, Summer

Topics include trigonometric functions, applications, graphs, equations, and identities; inverse trigonometric functions; vectors; sequences and series; the Binomial Theorem; conic sections; and parametric and polar equations. 

Credit Restrictions: A student may use MATH 1450 to replace a grade received in MATH 1357; however, one may not receive credit for both MATH 1357 and MATH 1450. 

Prerequisite: MATH 1340 or its equivalent with a grade of C or better, or ACCUPLACER College Level Mathematics part score 80 or better, or appropriate high school background and placement scores.

Student Learning Outcomes: After completing this course students will be able to

1. Demonstrate an understanding and skill in the use of trigonometric functions, formulas, and fundamental identities.
2. Demonstrate knowledge of the exact values of certain trigonometric functions for particular angles in degrees and radians.
3. Demonstrate an understanding and be able to solve right triangle and non right triangle problems using trigonometric functions.
4. Graph and name the graph of a circular function.
5. Demonstrate an understanding and be able to solve trigonometric equations using the basic trigonometric identities.
6. Demonstrate an understanding of sequences and series, in general, and in particular the geometric sequences and series.
7. Demonstrate an understanding of the basic shapes in analytic geometry (in rectangular coordinates and polar coordinates): lines, parabolas, ellipses, hyperbolas, and conics.

MATH 1460, CALCULUS 1

Fall, Spring, Summer
Honors equivalent:  MATH 1487 
Credit Credit Restrictions: Credit may be received for only one of MATH 1460 and MATH 1487. 

Topics include limits, the derivative and its applications, antiderivatives, definite integrals, and the derivatives and integrals of transcendental functions. [Sample Syllabus] 

Prerequisite: MATH 1450 with a grade of C or better, or ACCUPLACER College Level Mathematics part score 100 or better, or appropriate high school background and placement scores.

Student Learning Outcomes: After completing this course students will be able to

1. Understand limits and be able to evaluate them numerically, graphically, and symbolically.
2. Understand derivatives and be able to evaluate them numerically, graphically, and symbolically.
3. Understand definite and indefinite integrals and be able to evaluate them numerically, graphically, and symbolically.
4. Use the ideas of limits, derivatives, and integrals to solve applied problems. In particular, you will become skilled in using these ideas to solve related rate problems, optimization problems, curve sketching problems, and area problems and in identifying and modeling the physical situations in which these ideas are useful.
5. Use graphing calculators and/or computer programs to evaluate limits, derivatives, and integrals.

MATH 1470, CALCULUS 2

Fall, Spring, Summer
Honors equivalent:  MATH 1488 
Credit Restrictions:  Credit may be received for only one of MATH 1470 and MATH 1488. 

Topics include derivatives and integrals of transcendental functions, methods of integration, parameterized curves, integration in polar coordinates, and infinite sequences and series. [Sample Syllabus] 

Prerequisite: MATH 1460 with a grade of C or better, or appropriate high school background and placement scores.

Student Learning Outcomes: After completing this course students will

1. Correctly apply the standard methods of integration, including substitution, integration by parts, trigonometric identities, trigonometric substitution, and partial fraction decomposition.
2. Approximate definite integrals using the Riemann sums, trapezoid rule, Simpson's rule, and series techniques.
3. Properly define and evaluate improper integrals and apply the Comparison Test to determine whether they converge or diverge.
4. Apply integration to compute areas, volumes, work, average values of functions, arc lengths, surface areas, hydrostatic pressures and forces, centers of mass, and moments.
5. Define curves parametrically and in polar coordinates, and perform the standard calculus computations on parametric and polar curves, such as derivatives, integrals, areas, arc lengths, and surface areas.
6. Understand the concepts of sequence, series, limits of sequences and series, convergence and divergence of sequences and series, and absolute and conditional convergence of series.
7. Compute power, Taylor, and Maclaurin polynomials and series for a function, and apply these ideas to problems in mathematics, science, and engineering.

MATH 1487, CALCULUS 1 - HONORS
(honors equivalent of MATH 1460)

Credit Restrictions:  A student may receive credit for only one of MATH 1460 and MATH 1487. 

Topics of derivatives, definite integrals, limits are studied taking examples from algebraic and transcendental functions.  Emphasis is placed on calculus as a discipline and calculus as a tool in modeling.

Prerequisite: MATH 1450 with a grade of C or better, or ACCUPLACER College Level Mathematics part score 100 or better, or appropriate high school background and placement scores, together with admissions to the honors program or consent of instructor.

Student Learning Outcomes: After completing this course students will be able to

1. Understand limits and be able to evaluate them numerically, graphically, and symbolically.
2. Understand derivatives and be able to evaluate them numerically, graphically, and symbolically.
3. Understand definite and indefinite integrals and be able to evaluate them numerically, graphically, and symbolically.
4. Use the ideas of limits, derivatives, and integrals to solve applied problems. In particular, you will become skilled in using these ideas to solve related rate problems, optimization problems, curve sketching problems, and area problems and in identifying and modeling the physical situations in which these ideas are useful.
5. Use graphing calculators and/or computer programs to evaluate limits, derivatives, and integrals.

MATH 1488, CALCULUS 2--HONORS
(honors equivalent of MATH 1470)

Credit Restrictions:  Credit may be received for only one of MATH 1470 and MATH 1488. 

Topics include methods and applications of integration, alternative coordinate systems, parameterizations, infinite sequences and series.  Topics are viewed as useful tools and are studied in the context of calculus as a discipline.

Prerequisite: MATH 1487 or  MATH 1487 with a grade of C or better, or appropriate high school background and placement scores, together with admissions to the honors program or consent of instructor.

Student Learning Outcomes: After completing this course students will

1. Correctly apply the standard methods of integration, including substitution, integration by parts, trigonometric identities, trigonometric substitution, and partial fraction decomposition.
2. Approximate definite integrals using the Riemann sums, trapezoid rule, Simpson's rule, and series techniques.
3. Properly define and evaluate improper integrals and apply the Comparison Test to determine whether they converge or diverge.
4. Apply integration to compute areas, volumes, work, average values of functions, arc lengths, surface areas, hydrostatic pressures and forces, centers of mass, and moments.
5. Define curves parametrically and in polar coordinates, and perform the standard calculus computations on parametric and polar curves, such as derivatives, integrals, areas, arc lengths, and surface areas.
6. Understand the concepts of sequence, series, limits of sequences and series, convergence and divergence of sequences and series, and absolute and conditional convergence of series.
7. Compute power, Taylor, and Maclaurin polynomials and series for a function, and apply these ideas to problems in mathematics, science, and engineering.

MATH 2330, SURVEY OF ELEMENTARY STATISTICS

Fall, Spring, Summer
Equivalent course:  STAT 2330.  Honors equivalent:  MATH 2387 
Credit Restrictions:  Credit may be received for only one of MATH 2330, STAT 2330, and MATH 2387.  

Prerequisite: MATH 1334 with a grade of C or better, ACT math score of 20 or better, or THEA math score of 260 or better, or ACCUPLACER College Level Mathematics part score 70 or better.

Student Learning Outcomes: After completing this course students will be able to

1. Have the basic ideas regarding what is the difference between a population and a sample, and will be able to identify which is a representative sample and which is not.
2. Understand the difference between Statistics and Probability.
3. Represent given data through tables or pictures.
4. Have the basic ideas of central tendencies and dispersions and be able to use calculators to calculate them.
5. Get some heuristic ideas while looking at univariate and bivariate data and be able to draw conclusions on the required parameters.
6. Calculate probabilities for binomial and normal probability distributions and use binomial and normal probability tables.
7. Calculate confidence intervals and do testing of hypotheses using Normal table and t table for p-values and critical values.

MATH 2335, Introduction to Biostatistics

Fall, Spring, Summer
Equivalent course: STAT 2335. Honors equivalent: MATH 2388
Credit Restrictions:  Credit may be received for only one of MATH 2335, STAT 2335, and MATH 2388.

Topics include introduction to biostatistics; biological and health studies and designs; probability and statistical inferences; one- and two-sample inferences for means and proportions; one-way ANOVA and nonparametric procedures.

Prerequisite: MATH 1334 with a grade of “C” or better or satisfactory score on ACT or placement exam.

Student Learning Outcomes: After completing this course students will be able to

1. understand statistical concepts and procedures such as probability distributions, hypothesis tests, nonparametric models, and analysis of variance.
2.  identify procedures appropriate (and inappropriate) to a given situation.
3.  carry out appropriate statistical procedures.
4.  interpret results from those statistical methods and communicate with other people.
5.  recognize the limitations of specific statistical methods.

MATH 2346, MATHEMATICS FOR ELECTRICAL ENGINEERS

This course covers the essentials of matrix theory, discrete mathematics, and numerical methods needed for majors in Electrical Engineering.  Topics include Gauss-Jordan elimination, matrix algebra, determinants, graphs, trees, combinatorics, root finding algorithms, numerical differentiation, numerical integration, and numerical matrix methods.

Prerequisite:  CSCI 1380 with a grade of C or better.
Corequisite:  MATH 1470.

Student Learning Outcomes: After completing this course students will be able to

1. Perform the basic operations of matrix algebra.
2. Solve a system of linear equations using Gauss-Jordan elimination, including augmented matrices and elementary row operations.
3. Compute matrix inverses when they exist and solve linear systems using matrix inverses where applicable.
4. Compute determinants of square matrices using the definition, elementary row operations, and cofactor expansion, know the basic properties of determinants, and solve linear systems using Cramer's rule where applicable.
5. Compute eigenvalues and eigenvectors of a square matrix and apply them to problems in engineering, mathematics, and science.
6. Know graph terminology, graph connectivity, Euler and Hamilton paths, planar graphs, and some of the major problems of graph theory, such as shortest path problems (solved by Dijkstra's algorithm) and coloring problems.
7. Understand trees, traversals of trees, sorting, and minimal spanning trees (Prim's and Kruskal's algorithms).
8. Perform counting and discrete probability calculations using basic counting principles, permutations, and combinations.
9. Find roots of functions using the bisection, fixed-point, secant, and Newton's methods.
10. Approximate derivatives of functions using finite differences.
11. Approximate integrals using midpoint, trapezoid, and Simpson's rules; Gaussian quadrature; and adaptive methods.
12. Approximate the basic functions, such as sin x, cos x, and e^x, using Taylor series.

MATH 2387, PROBABILITY & STATISTICS-HONORS STUDIES
(honors equivalent of MATH/STAT 2330)

Credit Restrictions:  Credit may be received for only one of MATH 2330, STAT 2330, and MATH 2387.  

An enriched introductory probability and statistics course with topics chosen from descriptive statistics, probability, and inferential statistics.  Special emphasis will be given to problem solving using statistical calculators and software.


Prerequisite:  Admission to Honors Studies or by permission, and either ACT math score of 20 or better, TASP math of 260 or better, or MATH 1334 with a grade of C or better.

MATH 2388 INTRODUCTION TO BIOSTATISTICS - HONORS
(honors equivalent of MATH 2335 / STAT 2335)

Fall, Spring, Summer
Credit Restrictions: Credit may be received for only one of MATH 2335, STAT 2335, and MATH 2388.

Topics include introduction to biostatistics; biological and health studies and designs; probability and statistical inferences; one- and two-sample inferences for means and proportions; one-way ANOVA and nonparametric procedures.

Prerequisite: MATH 1334 with a grade of “C” or better or satisfactory score on ACT or placement exam.

Student Learning Outcomes: After completing this course students will be able to

1. understand statistical concepts and procedures such as probability distributions, hypothesis tests, nonparametric models, and analysis of variance.
2.  identify procedures appropriate (and inappropriate) to a given situation.
3.  carry out appropriate statistical procedures.
4.  interpret results from those statistical methods and communicate with other people.
5.  recognize the limitations of specific statistical methods.

MATH 2401, CALCULUS 3

Fall, Spring, Summer 

Topics include calculus of several variables,partial derivatives, multiple integrals, and vector calculus including the Divergence Theorem and Stoke's Theorem. [Sample Syllabus]

Prerequisite: MATH 1470 with a grade of C or better.

Student Learning Outcomes: After completing this course students will be able to

1. Understand vectors in Euclidean N-space, operations involving vectors, and their application to applied problems;
2. Understand vector functions, operations with them (including differentiation and integration), and their application to motion in space;
3. Understand real functions of several variables, operations with them (including differentiation and integration), optimization of multivariable functions, and their application to physical problems;
4. Compute multiple integrals in Cartesian, polar, cylindrical, and spherical coordinates, and apply multiple integrals to physical problems;
5. Understand line and surface integrals, master the theorems of Green, Stokes, and Gauss (Divergence), and the Fundamental Theorem of Line integrals, and apply line and surface integrals to physical problems;
6. Apply computer and graphing calculator technology to gain insight into the topics discussed in class and to aid in performing computations.

MATH 3303, HISTORY OF MATHEMATICS

Fall, Spring, Summer

This course is a study of the historical development of ideas that shape modern mathematical thinking. Although mathematicians are studied, emphasis is placed on mathematical development.

Prerequisite: MATH 1470.

Student Learning Outcomes: After completing this course students will be able to

1. Demonstrate an understanding of the number systems and symbols of Egyptian, Greek, and Babylonian.
2. Demonstrate an understanding of Mathematics in Early Civilizations.
3. Demonstrate an understanding of Greek mathematics and the three ancient problems of antiquity.
4. Demonstrate an understanding of the development of the Alexandrian School and Euclid’s contributions.
5. Demonstrate an understanding of the mathematical contributions of Arabic, Chinese, and Indian scholars.
6. Demonstrate an understanding of the work of Fibonacci.
7. Demonstrate an understanding of the Italian Renaissance of mathematicians.
8. Demonstrate an understanding of the mechanical world of Descartes, Newton and Leibniz.
9. Demonstrate an understanding of the number theory developed by Fermat, Euler, and Gauss.
10. Demonstrate an understanding of the outline the mathematical accomplishments in the 19th and 20th centuries.

MATH 3311
THE ORGANIZATION STRUCTURES AND PROCESSES OF MATHEMATICS

Fall, Spring, Summer 

This course examines the content and organization of logical, axiomatic, and algorithmic structures and the corresponding networks of concepts, principles, and skills in the field of mathematics. It includes the analysis, justification, and application of such mathematical processes as those for proofs, algorithms, problem solving, and applications of mathematics (content and method) up through integral calculus.

Prerequisite: MATH 1470.

Student Learning Outcomes: After completing this course students will be able to

1. Demonstrate an understanding of selected areas of mathematics as hypothetico-deductive systems with their respective set-theoretic, logical, and axiomatic STRUCTURES at levels suitable for professional quality teaching of the State of Texas secondary school mathematics curriculum [TEA, TEKS] in Texas [SBEC, TExES].
2. Demonstrate understanding and skill in the use of Representation, Reasoning, Communication, Proof, Problem Solving, and Application PROCESSES in the teaching, learning, and uses of mathematics and the assessment of the learning of mathematics. [See NCTM Curriculum and Evaluation Standards, 2000.]
3. Demonstrate understanding and skill in uses of mathematics to understand mathematical structures and processes for the purposes of teaching and learning mathematics, and assessing the learning of mathematics, in relation to #1 and #2 above.

MATH 3328, INTRODUCTION TO MATHEMATICAL PROOF

Fall, Spring, Summer

This course is intended to prepare the student for advanced mathematics courses that require the writing of proofs. It reviews the elementary proof methods and the logical structure underlying them.  It examines the formal definitions and basic properties of the mathematical structures that one encounters when constructing proofs, and it recounts famous theorems concerning these structures that every mathematician needs to know. Students are expected to construct, independently, non-routine mathematical proofs and to present their work in written form. Substantial written work is required.

Prerequisites:  MATH 1460 with a grade of C or better.

Student Learning Outcomes: After completing this course students will

1. Understand the logical structure of mathematical proofs and associated constructs, such as logical statements, conditional statements, and quantified statements.
2. Master the basic techniques and strategies used in mathematical proofs, such as direct proof of conditional and quantified statements, proof by contrapositive, proof by contraction, proof by exhaustion, uniqueness proofs, and mathematical induction.
3. Master the basic techniques used to disprove false conjectures.
4. Write mathematical arguments, such as proofs, in clear, precise, and correct English.
5. Master rudimentary mathematical typesetting.
6. Understand and use correctly mathematical structures and tools such as sets, relations, orders, functions, and cardinality, as well as often used formulas and inequalities.
7. Develop an expanding vocabulary of mathematical terminology and the ability to use it fluently and correctly.
8. Become acquainted with famous mathematical ideas, theorems, arguments, proofs, and formulas that every mathematician should know.

MATH 3333, MATHEMATICS IN A COMPUTER ENVIRONMENT

Fall, Spring, Summer

This course studies mathematics that can be developed and explored in an environment that includes the computer as the primary investigative tool.

Prerequisites:  MATH 1470 with a grade of C or better.

MATH 3337, APPLIED STATISTICS 1

Fall, Spring, Summer
Equivalent course:   STAT 3337 
Credit Restrictions:  Credit may be received for only one of MATH 3337 and STAT 3337. 

Prerequisite: Junior standing and either MATH 1340 or MATH 1341. It is highly recommended that the student have some knowledge of statistics such as offered in MATH 2330 or STAT 2330.

Student Learning Outcomes: After completing this course students will

1. Have the basic ideas regarding what is the difference between a population and a sample. be able to identify which is a representative sample and which is not.
2. Be able to understand the difference between Statistics and Probability.
3. Be able to represent given data through tables or pictures.
4. Have the basic ideas of central tendencies and dispersions and will be able to use calculators to calculate them.
5. Be able to get some heuristic ideas while looking at univariate and bivariate data and should be able to draw conclusions on the required parameters.
6. Be able to calculate probabilities, moments etc. for various probability distributions (discrete or continuous).
7. Be able draw inferences related to studies involving one, two or more than two population means.
8. Be able to draw inferences related to population variances.
9. Be able to construct ANOVA tables and should have some basic ideas in experimental design.
10. Have some basic ideas of correlation and linear regression.

MATH 3338, APPLIED STATISTICS 2

Fall, Spring, Summer

This course is a continuation of MATH 3337 and includes special designs, multiple comparisons, analysis of variance and covariance, multiple regression, and coding.

Prerequisite: MATH 3337 or STAT 3337.

Student Learning Outcomes: After completing this course students will

1. Have basic ideas of simple and multiple linear regression;
2. Be able to obtain least square estimates of simple and multiple linear regression coefficients numerically for given the data;
3. Be able to use software packages to obtain the best line of fit for simple and multiple linear regressions;
4. Be able to select the appropriate number of variables for multiple linear regression;
5. Be able to formulate models and check the validity of assumptions in selected models.
6. Be able to construct ANOVAs for important designs in design of experiments problems.
7. Have the basic idea of basic factorial designs;
8. Be able to do ANCOVA when covariates are present;
9. Be able to do ANOVA for random and mixed effects models;
10. Be able to handle situations and use appropriate techniques for doing ANOVA for missing data;

MATH 3345, APPLIED LINEAR ALGEBRA

Fall, Spring, Summer

Topics include systems of linear equations, matrices and their algebraic properties, determinants, vectors, Euclidean n-space, linear transformations and their matrix representations, vector spaces, eigenvalues and eigenvectors, and applications to the sciences and business. Use of mathematical technology will be incorporated throughout the course.

Prerequisite: MATH 1460 with a grade of C or better.

Student Learning Outcomes: After completing this course students will be able to

1. Solve linear systems using matrices and Gaussian elimination, understand the different types of solutions that are possible, and use these ideas in applied problems.
2. Perform the common operations of matrix algebra and use them to solve applied problems.
3. Compute the determinant of a square matrix and understand its properties.
4. Understand the ideas of linear independence, spanning set, basis, change of basis of a linear transformation, rank of a matrix, vector space, subspace, and their application to applied problems.
5. Understand eigenvectors and eigenvalues, how they characterize the action of some linear transformations, and how to use them to solve applied problems.
6. (Optional) Use the ideas of inner products, orthogonality, and projections to determine least-squares solutions to a linear system and perform Gram-Schmidt orthogonalization on a set of vectors.

MATH 3349, DIFFERENTIAL EQUATIONS

Fall, Spring, Summer 

This course contains a study of ordinary differential equations and applications. [Sample Syllabus]


Prerequisite: MATH 1470 with a grade of C or better.

Student Learning Outcomes: After completing this course students will

1. Understand what differential equations are, how they arise, why they are useful, and what they can tell us about the situations they model;
2. Be able to use correct differential equations terminology, such as the terms linear, nonlinear, order, explicit solution, implicit solution, ordinary differential equation, partial differential equation, existence of solutions, uniqueness of solutions, etc.;
3. Be able to solve first order differential equations by the standard methods of separation of variables, integrating factors, exact methods, substitutions, and transformations or show that solutions do not exist;
4. Be able to solve certain types of linear differential equations of order greater than one;
5. Be able to model applied problems in terms of differential equations and use the equations to obtain useful information about the problems;
6. Be able to use Laplace transform and series solution methods to obtain solutions and other useful information about the differential equations to which these methods apply;
7. Be able to use technology to solve differential equations or to obtain other useful information about the problems that they model.

MATH 3355, LINEAR PROGRAMMING 

Fall, Spring, Summer

This course covers basic theory of linear programming, an introduction to the simplex method, path-following methods, and applications of linear programming. Programming will be done in MATLAB. [Sample Syllabus]

Prerequisite: MATH 2345 with a grade of C or better.

Student Learning Outcomes: After completing this course students will

1. Be able to apply the Jordan exchange as part of the simplex method to solve linear programs
2. Be able to solve linear programs using the simplex method and interior-point methods
3. Be able to solve linear programs via the primal or dual method
4. Be able to model problems as linear programs
5. Be able to understand applications of linear programming

MATH 3368, NUMERICAL METHODS

Fall, Spring, Summer
Equivalent course:  CSCI 3350

This course includes interpolation, numerical integration, numerical solutions to differential equations, and a study of numerical solutions to systems of equations.

Prerequisite: MATH 1460, and CSCI 1380 or CSCI 2325 or consent of instructor.

Student Learning Outcomes: After completing this course students will be able to

1. Understand the Taylor Series and Taylor's theorem, and understand the influence of data representation and computer architecture on the choice and development of algorithms.
2. Locate the roots of equations by using the bisection method, the secant method, and the Newton's method.
3. Do polynomial interpolation, write Matlab programs to solve simple interpolation problems.
4. Estimate derivatives and Richardson extrapolation by using the first- and the second- derivative formulas.
5. Write Matlab programs to numerical approximate the definite integrals by using the basic algorithms including Trapezoid Rule, an Adaptive Simpson's Scheme, and the Gaussian Quadrature Formulas.
6. Solve the systems of linear equations by using the Gaussian elimination method and the Gaussian elimination with scaled partial pivoting method.
7. Understand the special type of linear systems including tridiagonal systems, diagonal dominance systems and pentadiagonal systems. Be able to solve the special type of linear systems by using special techniques including the LU factorization.
8. Solve the linear system by using some iterative methods.
9. Understand the concept of approximating functions. Be able to approximate the functions by using the spline functions from the first degree splines to the cubic splines.
10. Solve the initial value problems of ordinary differential equations by using the Taylor series methods and the Runge-Kutta methods.

MATH 3373, DISCRETE STRUCTURES

Fall, Spring, Summer

This course is an introduction to discrete mathematics, studying enumeration, lattices, graphs, and other topics in combinatorics.  Particular emphasis is given to those structures applicable in computer science. [Sample Syllabus]

Prerequisite: MATH 1460 or MATH 1342, and CSCI 1380.

Student Learning Outcomes: After completing this course students will be able to

1. Apply formal methods of symbolic propositional and predicate logic.
2. Describe how formal tools of symbolic logic are used to model algorithms and real life situations.
3. Know how to use formal logic proofs and logical reasoning to solve problems.
4. Understand various proof techniques and determine which type of proof is best for a given problem
5. Understand basics of number theory and matrices and their application to algorithms
6. Relate the ideas of mathematical induction to recursion
7. Understand the basic terminology of and perform basic operations associated with functions, relations, and sets.
8. Relate practical examples to the appropriate set, function, or relation model, and interpret the associated operations and terminology in context.
9. Understand basic counting principles, such as the pigeonhole principle, and their applications.
10. Compute permutations and combinations of a set and interpret the meaning in application problems.
11. Calculate probabilities of events and expectations of random variables, and be able to differentiate between dependent and independent events.
12. Differentiate between types of structures used in models of computations and their applications.

MATH 4302, NUMBER THEORY

Fall, Spring, Summer
Topics include the binomial theorem, divisibility, the extended Euclidean algorithm, Diophantine equations, primes, congruences, Euler's theorem, multiplicative functions, the Fibonacci sequence, Pythagorean triples, continued fractions, and applications to cryptology.

Prerequisites:  MATH 3345 with a grade of C or better.

Student Learning Outcomes: After completing this course students will be able to

1. Understand basic number theoretic concepts such as primes, divisibility, and congruences and apply these basic number theoretic concepts to more advanced topics such as Diophantine equations, multiplicative functions, continued fractions, and Pythagorean triples;
2. Construct rigorous elementary proofs involving basic number theoretic concepts;
3. Read and understand proofs involving basic number theoretic concepts and advanced topics;
4. Give examples and counterexamples involving basic number theoretic concepts and advanced topics;
5. Make connections of number theoretic concepts to other areas of mathematics;
6. Apply number theoretic methods to problems in cryptology; and
7. Write mathematics in a precise, effective, and understandable way.

MATH 4304, MODERN GEOMETRIES

Fall, Spring, Summer
Credit restriction: A student may not receive credit for both MATH 3304 and MATH 4304.

This course studies Euclidean and non-Euclidean geometries focusing on axiomatic systems.  Note:  A student may not receive credit for both MATH 3304 and MATH 4304.

Prerequisites:  MATH 3345 with a grade of C or better.

Student Learning Outcomes: After completing this course students will be able to

1. Demonstrate an understanding of the historical development of geometry from its Euclidean foundations on through the formulation of hyperbolic and elliptical non-Euclidean geometries.
2. Demonstrate an understanding of the axiomatic foundations of various geometries and skill in formulating conjectures, proving theorems, disproving non-theorems, and solving problems in these geometries.
3. Demonstrate an understanding and skill in comparing and contrasting geometries - finite, non-finite, L1, L2, affine, projective, elliptic, hyperbolic, parabolic, and such.
4. Demonstrate an understanding and skill in proving theorems and solving problems in two and three-dimensional Euclidean geometry whether through synthetic, vector, matrix, and/or transformational approaches.
5. Demonstrate an understanding and skill with Cabri Geometry II, Geometer's Sketchpad, Maple and other software as it relates to different approaches and the study of different geometries.

MATH 4317, COMPLEX ANALYSIS

Fall, Spring, Summer

This course is an introduction to the theory of functions of a complex variable with basic techniques and some applications. Topics include complex numbers and the extended complex plane, elementary functions of a complex variable, differentiation, conformal mappings, contour integration, Cauchy's theorem, Cauchy's formula, Taylor and Laurent series, and residue theory.

Prerequisite: MATH 2401.

Student Learning Outcomes: After completing this course students will

1. Work with complex numbers and functions of a complex variable, such as i^i, cos(i), e^i, and log(i);
2. Understand the ideas of continuity, analyticity (differentiability), and the multivalued nature of (some) functions of a complex variable;
3. Understand the theory of analytic functions, including Liouville's Theorem, Maximum Modulus Theorem, Cauchy's Theorem, Cauchy's Integral formula, path independence and the Fundamental Theorem of Calculus for analytic functions, Taylor's Theorem, Laurent's Theorem, and the Residue Theorem;
4. Apply residue theory to evaluate integrals and series that could not be evaluated with the methods of MATH 1470;
5. Analyze the mappings, such as conformal mappings, of complex-valued functions of a complex variable;
6. Apply the theory of analytic functions to problems in science and engineering.

MATH 4318, BOUNDARY VALUE PROBLEMS

Fall, Spring, Summer

This course is an introduction to elementary partial differential equations, with applications to physics and engineering.  Heat conduction, diffusion processes, wave phenomena, potential theory are explored by means of Fourier analysis.

Prerequisite: MATH 3349.

MATH 4319, INTEGRAL TRANSFORMS

Fall, Spring, Summer

This course is an introduction to transform analysis based on the theory of Fourier and Laplace integrals.  Topics include contour integration, inverse formulas, convolution methods, with applications to mathematical analysis, differential equations, and linear systems.

Prerequisites:  MATH 2401 and MATH 3349.

MATH 4329, ELEMENTARY CRYPTOLOGY

Fall, Spring, Summer

Topics include elementary ciphers, error-control codes, public key ciphers, and pseudo-random number generators.

Prerequisites:  MATH 3345 with a grade of C or better.

MATH 4339, PROBABILITY AND STATISTICS

Fall, Spring, Summer

Topics include probability, random variables, discrete and continuous probability distributions, expectations, moments and moment generating functions, distribution of functions of random variables, limiting distributions. [Sample Syllabus]

Prerequisite: MATH 1470 with a grade of C or better.

Student Learning Outcomes: After completing this course students will be able to

1. Have the basic ideas regarding what is the difference between a population and a sample and will be able to identify which is a representative sample and which is not.
2. Understand the difference between Statistics and Probability.
3. Write down the sample space for given experiments and compute probabilities and conditional probabilities using the appropriate formulas (addition rule, multiplication rule etc.)
4. Understand the basic difference between discrete and continuous probability distributions and will understand the concepts of probability mass function in the discrete cas and the probability density function in the continuous case.
5. Expectations and variances for various probability distributions (discrete or continuous).
6. Know the important discrete probability distributions and their important properties and will be able to calculate the expectations and variances for these distributions.
7. Know the important continuous probability distributions and their important properties and be able to calculate the expectations and variances for these distributions.
8. Calculate the probability density functions for functions of continuous random variables - both in the univariate and bivariate scenario.
9. Calculate moments and moment generating functions for important discrete and continuous probability distributions.

MATH 4351, MODERN ALGEBRA

Fall, Spring, Summer 

This course provides an introduction to algebraic structures. Topics to be taken from groups, rings, and fields.

Prerequisites:  MATH 3328 and MATH 3345, both with a grade of C or better.

Student Learning Outcomes: After completing this course students will be able to

1. Understand the intellectual structure of algebra and its major theorems, definitions, axioms, and problems;
2. Understand the definitions, axioms, and major theorems underlying the algebraic structures of groups, rings, and fields;
3. Apply the concepts of groups, rings, and fields to solve problems in which their use is fundamental to obtaining and understanding the solution;
4. Understand what constitutes a valid proof of results in modern algebra and learn how to create such proofs;
5. Write mathematics in a precise, effective, and understandable way.

MATH 4357, REAL ANALYSIS

Fall, Spring, Summer 

This course presents a rigorous introduction to the elements of real analysis. Topics include sequences, series, functions, limits, continuity, and derivatives.

Prerequisites:  MATH 1470 and MATH 3328, both with a grade of C or better.

Student Learning Outcomes: After completing this course students will be able to

1. Understand the intellectual structure of differential calculus and its major theorems, definitions, axioms, and problems;
2. Understand the definitions, axioms, and major theorems underlying the terms sequence, series, limit, continuity, derivative, and convergence as these concepts relate to real numbers and real-valued functions of a real variable;
3. Apply the concepts of sequence, series, limit, continuity, derivative, and convergence to solve problems in which their use is fundamental to obtaining and understanding the solution;
4. Understand what constitutes a valid proof of results in real analysis and learn how to create such proofs;
5. Write mathematics in a precise, effective, and understandable way.

MATH 4360, TOPOLOGY

Fall, Spring, Summer 

This course presents a rigorous introduction to the elements of topology. Topics include a study of metric spaces, separation axioms, topological spaces, and topological properties of point sets and mappings.

Prerequisites:  MATH 1470 and MATH 3328, both with a grade of C or better.

MATH 4364, SPECIAL PROBLEMS IN MATHEMATICS

Fall, Spring, Summer

This course covers special undergraduate topics in mathematics which are not taught elsewhere in the department. May be repeated for credit.

Prerequisite: Consent of instructor.

MATH 4379, SPECIAL PROBLEMS IN APPLIED MATHEMATICS

Fall, Spring, Summer

This course covers special undergraduate topics in applied mathematics which are not taught elsewhere in the department. May be repeated for credit when topic is different. 

Prerequisite: Consent of instructor.

MATH 4390, MATHEMATICS PROJECT

Fall, Spring, Summer

Students will complete a major mathematical project communicating its results in oral and written form.

Prerequisites:  12 advanced MATH hours with grades of C or better, and consent of instructor.