## Undergraduate MATH Courses

**Note: For courses that are part of the core curriculum, click the course title for a sample syllabus and SLOs that you need to include in your syllabus. The definitive UTRGV course listing, which includes course description and prerequisites, is available via ASSIST.**

**MATH 0290 - Intermediate Algebra**

A study of the real number system, equations, inequalities and its applications, graphs of equations and inequalities, exponents and polynomials, factoring and its applications, rational expressions and its applications, systems of linear equations and inequalities, roots and radicals, quadratic equations. This course may not be used to satisfy any University core curriculum requirements. Co/Prerequisites: None

**MATH 0310 - Elementary Algebra**

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 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 University core curriculum requirements. Co/Prerequisites: TSI Assessment score 336-349 and with NEEDS IMPROVEMENT or LIMITED PROFICIENT in Elementary Algebra

**MATH 0320 - Intermediate Algebra**

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. This course may not be used to satisfy any University core curriculum requirements. Co/Prerequisites: TSI Assessment score 336-349 and with PROFICIENT in Elementary Algebra or PROFICIENT in Intermediate Algebra or MATH 0310 with minimum grade RC.

**MATH 0330 - Pre-Statistics and Probability**

This course is a Developmental Mathematics option for students in majors and degree programs which do not require College Algebra (MATH 1340, MATH 1440). The course aims to provide students with the mathematical background necessary for success in Elementary Statistical Methods and Introduction to Biostatistics. Topics covered will include: Operations and Numbers, Rounding and Percentages, Fractions, Square Roots, Summations, Linear Equations and Graphs, Descriptive Statistics and Charts, Introductory Probability. This course may not be used to satisfy any University core curriculum requirements. Co/Prerequisites: TSI Assessment score 336-349 and a major which does not require College Algebra

**MATH 1314 - College Algebra**

Topics include polynomial functions, rational functions, exponential functions, logarithmic functions, and matrices. Applications of these topics will be emphasized. Prerequisites: College Ready TSI status in Mathematics.

**MATH 1324 - Math for Business & Soc Sci**

Topics include functions (polynomial, rational, exponential, logarithmic) to problems in business and economics. Applications include financial mathematics, matrices, and linear programming. Prerequisites: College Ready TSI status in Mathematics.

**MATH 1325 - Calculus for Business & Soc Sc**

Topics include limits, differentiation, optimization, graphing, and integration. Applications related to business and economics will be emphasized. Prerequisites: MATH 1314, MATH 1414, or MATH 1324 with a grade of 'C' or better or passing the College Algebra Exemption test administered by the Department of Mathematics.

**MATH 1332 - Contemporary Mathematics**

Topics include voting methods, apportionment methods, financial mathematics, mathematical logic, graph theory, statistics, and probability with an emphasis on problem solving and critical thinking. Prerequisites: College Ready TSI status in Mathematics.

**MATH 1333 - Math for Art & Music**

This course explores the common foundations of mathematics, art and music. Topics from art include symmetry and the mathematics of dance; tessellations and tilings; fractals, origami; perspective and proportion; 3-dimensional printing. Topics from music include quantification of pitch, harmony, and musical scales; key signatures and equivalence relations; octaves and modular arithmetic; rhythm and the Euclidean algorithm; musical intervals and logarithms; tone and trigonometry; timbre and harmonic analysis. Co/Prerequisites: College Ready TSI status in Mathematics.

**MATH 1342 - Elementary Statistical Methods**

This course provides an elementary overview of the nature and uses of descriptive statistics, inferential statistics, and probability. Topics include statistical graphs, measures of central tendency and dispersion, linear regression, empirical and theoretical concepts of probability, the Central Limit Theorem, interval estimation, and hypothesis testing. Prerequisites: College Ready TSI status in Mathematics.

**MATH 1343 - Intro to Biostatistics**

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. Prerequisites: College Ready TSI status in Mathematics.

**MATH 1350 - Fund of Mathematics I**

This course is designed for students seeking teacher certification from early childhood through eighth grade. Topics includes sets, numeration systems, and the development of special number sets (whole, integers, rationals, and real) with an emphasis on problem solving and the use of manipulatives. Prerequisites: MATH 1314 or MATH 1414 with a grade of 'C' or better.

**MATH 1351 - Fund of Mathematics II**

This course is designed for students seeking teacher certification from early childhood through eighth grade. Topics include probability, statistics, geometry, and measurement with an emphasis on problem solving and the use of manipulatives. Prerequisites: MATH 1350 with a grade of 'C' or better.

**MATH 1387 - Elem Statistical Methods HON**

This course provides an elementary overview of the nature and uses of descriptive statistics, inferential statistics, and probability. Topics include statistical graphs, measures of central tendency and dispersion, linear regression, empirical and theoretical concepts of probability, the Central Limit Theorem, interval estimation, and hypothesis testing. Prerequisites: College Ready TSI status in Mathematics and admission to the honors program

**MATH 1388 - Intro to Biostatistics HON**

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. Prerequisites: College Ready TSI status in mathematics and admission to the honors program

**MATH 1414 - College Algebra**

Topics include polynomial functions, rational functions, exponential functions, logarithmic functions, and matrices. Applications of these topics will be emphasized. Prerequisites: College Ready TSI status in Mathematics.

**MATH 2305 - Discrete Mathematics**

This course addresses mathematical topics readily used in computer science, including logic, mathematical proof, counting techniques, functions and relations, an introduction to computability, and the Church-Turing thesis. Prerequisites: MATH 2413 (or MATH 2487) with a grade of 'C' or better.

**MATH 2318 - Linear Algebra**

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. Prerequisites: MATH 2413 (or MATH 2487) with a grade of 'C' or better.

**MATH 2321 - Diff Equations & Linear Alg**

This course emphasizes solution techniques. Topics include differential equations, vector spaces, linear transformation, matrix/vector algebra, eigenvectors, Laplace Transform and systems of equations. Prerequisites: MATH 2414 (or MATH 2488) with a grade of 'C' or better.

**MATH 2346 - Math for EE & CE**

This course covers the essentials of matrix theory, graph theory, numerical methods, and introduction to proofs needed for majors in Electrical and Computer Engineering. Topics include Gauss-Jordan elimination, matrix algebra, determinants, graphs, trees, root finding algorithms, numerical differentiation, numerical integration, numerical matrix methods, propositional and predicate logic, and formal logic proofs. Prerequisites: CSCI 1380 (or CSCI 1387) or CMPE 1170/1370 (or CMPE 1378/1178) with a grade of 'C' or better, and MATH 2413 (or MATH 2487) with a grade of 'C' or better.

**MATH 2412 - Precalculus**

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. Prerequisites: MATH 1314 or MATH 1414 with a grade of 'C' or better; or passing the College Algebra Exemption Test administered by the Department of Mathematics.

**MATH 2413 - Calculus I**

Topics include limits, derivatives, antiderivatives, and definite integrals of algebraic and transcendental functions. Applications of these topics will be emphasized. Prerequisites: MATH 2412 with a grade of 'C' or better; or passing the Precalculus Exemption Test administered by the Department of Mathematics.

**MATH 2414 - Calculus II**

Topics include methods of integration, applications of definite integrals, parameterized curves, integration in polar coordinates, and infinite sequences and series. Prerequisites: MATH 2413 (or MATH 2487) with a grade of 'C' or better.

**MATH 2415 - Calculus III**

Topics include functions of several variables, partial derivatives, multiple integrals, Lagrange multipliers, and vector calculus including the Divergence Theorem and Stoke's Theorem. Prerequisites: MATH 2414 (or MATH 2488) with a grade of 'C' or better.

**MATH 2487 - Calculus I HON**

Topics include limits, derivatives, antiderivatives, and definite integrals of algebraic and transcendental functions. Applications of these topics will be emphasized. Prerequisites: MATH 2412 with a grade of C or better and admission to the honors program

**MATH 2488 - Calculus II HON**

Topics include methods of integration, applications of definite integrals, parameterized curves, integration in polar coordinates, and infinite sequences and series. Prerequisites: MATH 2413 (or MATH 2487) with a grade of C or better and admission to the honors program

**MATH 3326 - Hist of Mathematics**

This course is a study of the historical development of ideas that shape modern mathematical thinking. Emphasis is placed on mathematical development and solving problems. ] Prerequisites: MATH 2414 (or MATH 2488) with a grade of 'C' or better.

**MATH 3332 - Applied Statistics II**

This course is a continuation of MATH 3337 and includes special designs, analysis of variance and covariance, multiple comparisons, and coding. Prerequisites: MATH 3331 with a grade of 'C' or better.

**MATH 3341 - Diff Equations**

This course studies first-order and linear second-order differential equations, Laplace transforms, power series solutions, and first order linear systems. Applications of these topics will be emphasized. Prerequisites: MATH 2414 (or MATH 2488) with a grade of 'C' or better.

**MATH 3343 - Intro to Math Software**

This course involves using mathematical software such as Mathematica, Maple and MATLAB as an investigative tool for solving mathematical problems. Prerequisites: MATH 2414 (or MATH 2488) and MATH 2318 with a grade of 'C' or better.

**MATH 3345 - Linear Optimization**

The course covers basic theory of linear priming, an introduction to the simplex method path-following interior-point methods, and applications of linear programming. Examples will be presented through visualization and computational methods. Prerequisites: MATH 2318 with a grade of 'C' or better.

**MATH 3347 - Elementary Cryptology**

Topics include elementary ciphers, public key ciphers, and error-correcting codes. Prerequisites: MATH 2318 with a grade of 'C' or better.

**MATH 3349 - Numerical Methods**

This course studies the numerical solutions to various problems occurring in engineering, the sciences, and mathematics. These problems include finding solutions to nonlinear equations, solutions to linear and nonlinear systems of equations, interpolation of data, approximation of functions, numerical integration, and solutions to differential equations. It also studies the influence of data representation and computer architecture on the choice and development of algorithms. Prerequisites: MATH 2414 (or MATH 2488) and MATH 3343, each with a grade of 'C' or better.

**MATH 3350 - Intro to Math Proof**

This course will prepare the student for advanced mathematics courses that require the writing of proofs. It reviews various 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 should know. Students are expected to construct non-routine mathematical proofs independently and to present their work in written form clearly and precisely. Substantial written work is required. Prerequisites: MATH 2318 with a grade of 'C' or better.

**MATH 3352 - Modern Geometry I**

Topics include Euclidean geometry, analytic geometry, transformation geometry, and a brief introduction to non-Euclidean geometries. Prerequisites: MATH 2318 with a grade of 'C' or better.

**MATH 3361 - Applied Discrete Mathematics**

Topics include applications of recurrence relations, advanced combinatorics, relations, graph theory, Boolean algebra, and modeling computation. Prerequisites: MATH 2318 with a grade of 'C' or better.

**MATH 3363 - Modern Algebra I**

This course provides a rigorous introduction to algebraic structures. Topics are to be taken from groups, rings, and fields. Prerequisites: MATH 2318 and MATH 3350, each with a grade of 'C' or better.

**MATH 3365 - Number Theory**

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 2318 and MATH 3350, each with a grade of 'C' or better.

**MATH 3372 - Real Analysis I**

This course presents a rigorous introduction to the elements of real analysis. Topics include sequences, series, limits, continuity, and derivatives. Prerequisites: MATH 2414 (or MATH 2488) and MATH 3350, each with a grade of 'C' or better.

**MATH 3382 - Actuarial Probability Models**

Probability tools used in quantitative risk management are introduced. The course covers material included in the Society of Actuaries' Exam P. Prerequisites: MATH 2414 (or MATH 2488) with a grade of 'C' or better.

**MATH 3383 - Actuarial Stat Estimates**

Statistical tools used for the construction and evaluation of actuarial models are covered in this course. The course covers material included in the Society of Actuaries' Exam C. Prerequisites: MATH 3382 with a grade of 'C' or better.

**MATH 3385 - Theory of Interest**

The theory of interest will be developed. Emphasis is placed on topics included in the financial mathematics portion of the Society of Actuaries' Financial Mathematics exam. Prerequisites: MATH 2414 (or MATH 2488) with a grade of 'C' or better.

**MATH 3386 - Actuarial Financial Math**

Financial mathematics is applied to areas of financial economics important in actuarial applications. Emphasis is placed on topics included in the financial economics portion of the Society of Actuaries' Financial Mathematics exam. Prerequisites: MATH 2414 (or MATH 2488) and MATH 3385, each with a grade of 'C' or better.

**MATH 3399 - Special Topics in Math**

This course covers special undergraduate topics in mathematics which are not taught elsewhere in the department. This course may be repeated for credit when topic is different. Prerequisites: Departmental approval.

**MATH 4192 - Math Problem Solving**

This course is intended as a chance for mathematics majors to enhance their skills in mathematical problem solving. Students will learn how to use different techniques to tackle different types of problems ranging from the Calculus to advanced level math courses. In addition to learning problem solving techniques, students will be encouraged to discuss the best methods for solving problems efficiently. This course is highly recommended for math majors who are planning to apply for graduate school. Prerequisites: MATH 2414 (or MATH 2488), MATH 2318, and 9 advanced hours of MATH, all with grades of 'C' or better.

**MATH 4342 - Complex Variables**

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. Prerequisites: MATH 2415 with a grade of 'C' or better.

**MATH 4344 - Boundary Value Problems**

This course is an introduction to elementary partial differential equations, with applications to physics and engineering. Heat conduction, diffusion processes, wave phenomenon, and potential theory are explored by means of Fourier analysis. Prerequisites: MATH 3341 or MATH 2321 with a grade of 'C' or better.

**MATH 4346 - Integral Transforms**

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 application to mathematical analysis, differential equations and linear systems. Prerequisites: MATH 2415 and either MATH 3341 or MATH 2321, both with a grade of 'C' or better.

**MATH 4352 - Modern Geometry II**

Topics include a complete overview of Hilbert's axioms (connection, order, parallels, congruence, continuity), convex geometry (convex hull, extreme points, linear programming), and projective geometry (collineation, coordination, the Main Theorem, affine spaces). Prerequisites: MATH 3352 with a grade of 'C' or better.

**MATH 4355 - Topology**

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 2414 (or MATH 2488) and MATH 3350, each with a grade of 'C' or better.

**MATH 4357 - Algebraic Geometry**

This course is a first introduction to the ideas behind Algebraic Geometry: Nullstellensatz, the definition of varieties, and mappings between them. To Illustrate key ideas and motivate theorems, this course focuses its attention on concrete examples, often making use of mathematical software for visualization. Additionally, students will learn about computational techniques and how to use them. Prerequisites: MATH 3350 with a grade of 'C' or better.

**MATH 4359 - Diff Geometry**

Starting with multi-variable calculus, this course will develop the theme of invariants attached to the geometry of curves and surfaces. The various notations of curvature of surfaces are related to curvature and torsion of curves. The contrast between local and global phenomena is also emphasized. Topics will include Gauss' "Theorema Egregium" and the Gauss-Bonnett Theorem. Visualization of ideas with mathematical software will be regularly present. Prerequisites: MATH 2415 with a grade of 'C' or better.

**MATH 4364 - Modern Algebra II**

This course is a continuation of MATH 3363. Topics include groups, rings, and fields, with applications to geometric constructability and solvability by radicals. Prerequisites: MATH 3363 with a grade of 'C' or better.

**MATH 4367 - Adv Linear Algebra**

This is a proof-based course of linear algebra topics chosen from vector spaces, linear transformations, determinants, matrices, equivalence relations, canonical forms, inner product spaces, linear functional, and applications. Prerequisites: MATH 2318 and MATH 3350, each with a grade of 'C' or better.

**MATH 4373 - Real Analysis II**

This course is a continuation of MATH 3372. Topics include Riemann integration of a single-variable function; continuity, differentiation and integration of multivariable functions; the mean value theorem; the implicit and inverse function theorems; Green's theorem; and the convergence of sequences and series of functions. Prerequisites: MATH 3372 with a grade of 'C' or better.

**MATH 4390 - Math Project**

Students will complete a major mathematical project and will communicate its results in oral and written form. Students will also take comprehensive test from the Mathematics core courses. Prerequisites: Credit for or concurrent enrollment in MATH 2415, STAT 3337, MATH 3341, MATH 3352, MATH 3363, MATH 3372.

**MATH 4391 - Research Experience in Math**

This course is designed to give students experience in research not normally covered within standard courses. Research projects will vary according to student interest and faculty availability. Students will complete a major mathematical research project communicating its results both in oral and written forms to the department faculty and students. Prerequisites: 12 advanced hours of MATH with grades of 'C' or better, and departmental approval.