# Undergraduate MATH Courses

*A sample syllabus with SLO language is available for the following UTRGV Core courses.*

**MATH 1314 - ****College Algebra **

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

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

MATH 1332 - **Contemporary Mathematics**

MATH 1342 - **Elementary Statistical Methods**

MATH 1343 - **Intro to Biostatistics**

MATH 1387 - **Elem Statistical Methods HON**

MATH 1388 - **Intro to Biostatistics HON**

MATH 1414 - **College Algebra 1414**

MATH 2412 - **Precalculus**

MATH 2413 - **Calculus I**

MATH 2487 - **Calculus I HON**

**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 - Prep for College Algebra NCBO**

This course is a non-course based option for students to satisfy their mathematics requirements for entry into College Algebra (MATH 1314 or 1414). This course will target students in the upper range of scores on the TSI Assessment and will allow students to proceed faster.

**MATH 0314 - Pre College Algebra Co Req**

The major objective of this course is to prepare student to demonstrate college readiness in mathematics and apply basic mathematical tools for the solution of real-world problems. The mathematical topics introduced and discussed in this course are designed to prepare students for successful completion of College Algebra and Algebra intensive mathematics courses. Students should be in a degree plan or program that requires algebra intensive courses: MATH 1314, 1414, 1324; or Calculus based courses: MATH 1325, 2412, 2413.

**MATH 0320 - Pre College Algebra Jumpstart**

The major objective of this course is to prepare students to demonstrate college readiness in mathematics and apply basic mathematical tools for the solution of real-world problems. The mathematical topics introduced and discussed in this course are designed to prepare students for successful completion of College Algebra and Algebra intensive mathematics courses. This course is part of the summer Jumpstart program and will only be offered in summer sessions. Students should be in a degree plan or program that requires algebra intensive courses: MATH 1314, 1414, 1324; or Calculus based courses: MATH 1325, 2412, or 2413. 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 Jumpstart**

The major objective of this course is to prepare students to pass Statistics with the ability to apply basic mathematical tools for the solution of real-world problems. The mathematical topics introduced and discussed in this course are: numbers, algebraic expressions, linear equations, lines in the coordinate plane, descriptive statistics, and counting and probability. This is a Jumpstart course that runs only in the Summer sessions. Students should be in a degree plan that requires or can use Statistics courses: MATH 1342 or 1343. Prerequisites: TSI Assessment score 336-349 and a major which does not require College Algebra.

**MATH 0332 - Pre Math for Lib Arts Co Req**

The major objective of this course is to prepare students to pass the Mathematics for Liberal Arts course with the ability to apply basic mathematical tools for the solution of real-world problems. The mathematical topics introduced and discussed in this course are: set operations, simple logic, numbers, percentages, simple finance, counting, descriptive statistics, and probability. Students should be in a degree plan that requires or may use Mathematics for Liberal Arts (MATH 1332) and related courses.

**MATH 0340 - Pre Math for Liberal Arts Jump**

The major objective of this course is to prepare students to pass the Mathematics for Liberal Arts course with the ability to apply basic mathematical tools for the solution of real-world problems. The mathematical topics introduced and discussed in this course are: set operations, simple logic, numbers, percentages, simple finance, counting, descriptive statistics, and probability. This is a Jumpstart course that only runs in the Summer sessions. Students should be in a degree plan that requires or may use Mathematics for Liberal Arts (MATH 1332) and related courses.

**MATH 0342 - Pre Statistics Co Req**

The major objective of this course is to prepare students to pass MATH 1342 Elementary Statistical Methods with the ability to apply basic mathematical tools for the solution of real-world problems. The mathematical topics introduced and discussed in this course are: set operations, simple logic...

**MATH 1314 - College Algebra**

Topics include polynomial functions, rational functions, exponential functions, logarithmic functions, and matrices. Applications of these topics will be emphasized. Prerequisites: TSI exemption in Math, or College Ready TSI status in Math, or Satisfactory grade in Developmental Math course.

**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.

**MATH 1332 - Math for Liberal Arts**

Intended for Non STEM (Science, Technology, Engineering and Mathematics) majors. Topics include introductory treatments of sets and logic, financial mathematics, probability and statistics with appropriate applications. Number sense, proportional reasoning, estimation, technology, and communication should be embedded throughout the course. Additional topics may be covered. 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: TSI exemption in Math, or College Ready TSI status in Math, or Satisfactory grade in Developmental Math course.

**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: TSI exemption in Math, or College Ready TSI status in Math, or Satisfactory grade in Developmental Math course.

**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: Minimum grade of C in one of the following: MATH 1314, MATH 1414, MATH 2412, or MATH 2413.

**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 1414 - College Algebra**

Topics include polynomial functions, rational functions, exponential functions, logarithmic functions, and matrices. Applications of these topics will be emphasized. Prerequisites: TSI exemption in Math, or College Ready TSI status in Math, or Satisfactory grade in Developmental Math course.

**MATH 2146 - Math Practicum for EE and CE**

This course is additional practicum to MATH 2346. It covers practice on the topics covered by MATH 2346: matrix operations, inversion, determinants, graph theory, root finding algorithms, numerical differentiation, numerical integration, numerical matrix methods, and practice of complex number operations, conversion between polar and rectangular forms, solving of real and complex linear equations by Cramer's rule, Gauss-Jordan elimination and inverse matrix ways. The course will involve the application problems for majors in Electrical and Computer Engineering. Co-requisite: Math 2346.

**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 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 3300 - Internship in Mathematics**

This course is designed to give students an opportunity to gain practical experience in the mathematics career field by working with a participating employing firm or organization. The student will be supervised by a faculty member acting as a liaison between the University and the employing organization to ensure compliance with specific learning and experience requirements. The employment can be either pair or unpaid, and normally would include practical experience spread over one academic term or summer. May be repeated once. A maximum of three hours of credit from MATH 3300 can be used toward the Mathematics major. For summer research in academia see MATH 4391. Prerequisites: Junior Standing and a minimum of 18 hours of Mathematics, Statistics, Math Education (MATH/STAT/MATE) completed/ Approval by both the department and employer providing the practicum/internship experience.

**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: STAT 3301 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 3449 - Mech Engineering Analysis I**

The course prepares engineering students to be able to solve problems in the following topics in engineering applications: complex numbers and calculus of complex functions; matrix and vector algebra, linear systems of equations and matrix eigenvalue problems; vector differential and integral calculus, including integral theorems; unconstrained and constrained optimization, including linear and quadratic programming. Prerequisites: A grade of 'C' or better in MATH 2414 (or MATH 2488) and credit/registration in MECE 2350.

**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: Pre- or co-requisite in MATH 2415, STAT 3337, MATH 3341, MATH 3352, MATH 3363, MATH 3372.

**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.