- The Department of Computer and Mathematical Sciences
- Major in Mathematics (BA)
- Major in Math and Computer Science for Secondary School Teachers
- Major in Math and Computer Science for Secondary School Teachers (BA)
- Minor in Mathematics
- Minor in Math and Computer Science for Elementary School Teachers
- Math Course Descriptions

## Major in Mathematics (BA)

The Bachelor of Arts in Mathematics comprises the same curriculum of Mathematics courses as for the Bachelor of Science degree. However, Bachelor of Arts candidates will select an academic minor in a field other than science.

## Minor in Mathematics

Students desiring a minor in mathematics are required to complete at least 29 hours in mathematics courses consisting of 23 hours of required courses and at least six hours of mathematics electives.

**Required courses: 23 credit hours**

MATH 1510 Calculus 1 (4)

MATH 1520 Calculus 2 (4)

MATH 2530 Calculus 3 (4)

MATH 3170 Discrete Mathematics (4)

MATH 3200 Linear Algebra (3)

MATH 4300 Math Problem Solving (4)

Electives: 6 credit hours

Choose two 3000- or 4000-level math electives.

**Minor Total: 29 credit hours**

## Major in Math and Computer Science for Secondary School Teachers

This major requires a core of courses from mathematics and computer science. Graduates of the program will be equipped to teach both mathematics and computer science in secondary schools. The purpose of the major is to provide secondary school teachers in training with a fundamentally strong background in mathematics and computer science. This will create a greater pool of talent in math and computer science education from which middle and high school teachers can be drawn. The program has been designed to emphasize the fundamental understanding of both mathematics and computer science.

The objectives of the math and computer science major are to:

• Provide secondary teachers in training a program that will adequately prepare and encourage them to teach the expected mathematics and computing courses to students in middle and high school math and computer science programs.

• Train math teachers to develop each of the competencies required by the State Board of Education for licensure in math education.

• Broaden the scope of mathematics and computing to secondary school teachers in training, allowing them to develop methods in which to relay the content material to their students so that the students can fully understand what is being taught.

• Provide secondary teachers in training with the background so they can assume responsibility for managing the computing facilities at their school.

**Prerequisite courses: 8 credit hours**

MATH 1220 College Algebra (3*)

MATH 1250 PreCalculus (5)

**Applies to University proficiency requirement.*

## Minor in Math and Computer Science for Elementary School Teachers

The purpose of this minor is to provide elementary school teachers in training with a fundamentally strong background in mathematics and computer science. The objectives of the math and computer science minor are to:

- Provide elementary teachers in training a program that will adequately prepare and encourage them to teach the fundamental concepts of mathematics and computing to students at the elementary level.
- Broaden the scope of mathematics and computing to elementary school teachers in training, allowing them to develop methods in which to relay the content material to their students so that the students can fully understand what is being taught.
- Provide elementary teachers in training with the background so they can assume responsibility for managing the computing facilities at their school.

**Prerequisites: 9 credit hours**

MATH 1009 Math for the Elementary Teacher (3)

MATH 1116 Math for the Elementary Teacher II (3)

BCIS 1110 Living with Computers (3)

**Required courses: 17 credit hour**s

MATH 1220 College Algebra (3)

MATH 1250 PreCalculus (5)

CS 1440 Introduction to Computer Science (3)

CS 1450 Introduction to Object-Oriented Programming (3)

CS 2450 Advanced Computer Programming (3)

**Electives: 12 credit hours**

Choose two courses from the following:

MATH 3170 Discrete Mathematics (3)

MATH 3450 Mathematical Statistics 1 (3)

MATH 4060 College Geometry (3)

Any 3000- or 4000-level math course approved by adviser

Choose three courses from the following:

CS 3250 Computer Hardware Install and Maintenance (1)

CS 3260 Computer Software Installation (1)

CS 3270 Hands-on UNIX (1)

CS 3320 Advanced Internet (1)

Any 3000- or 4000-level computer science course approved by adviser

Choose one course from the following:

CS 4560 Internet Services (3)

CS 4570 Computer Networks (3)

CS 4630 Web Programming (3)

**Minor Total: 27 credit hours**

## Mathematics (MATH), Courses in

**MATH 1009. Mathematics for the Elementary Teacher (3); 2, 2 Fa, Sp**

Course offers an in-depth look at the representations of rational numbers, including base-ten and decimal numbers, integers, fractions, arithmetic operations on these sets and number properties using student activities and investigations. Problem solving is emphasized throughout.

Prerequisite: MATH 1000 with a minimum grade of C, or ACT score of 17 or above. Previous NMHU MATH 115.

**MATH 1116. Mathematics for the Elementary Teachers II (3); 2, 2 Fa, Sp**

Algebra from the viewpoint of the elementary curriculum with emphasis on proportional and linear relationships. Additional topics include: number theory, ratio, percent, probability and statistics. Student activities, investigations and problem solving are emphasized throughout.

Prerequisite: MATH 1009 with a minimum grade of C. Previous NMHU MATH 130.

**MATH 1215. Intermediate Algebra (3); Fa, Sp**

A study of linear equations and inequalities in one variable with applications, integer and rational exponents, the equation of the line, polynomials and rational expressions. Previous NMHU MATH 120.

**MATH 1220. College Algebra (3); Fa, Sp**

The study of equations, functions and graphs, reviewing linear and quadratic functions, and concentrating on polynomial, rational, exponential and logarithmic functions. Emphasizes algebraic problem solving skills and graphical representation of functions.

Prerequisite: MATH 1215 with a minimum grade of C, or ACT score of 23 or above. Previous NMHU MATH 140.

**MATH 1250. Trigonometry & Pre-Calculus (5); 4, 2 Fa, Sp**

Trigonometry & Pre-Calculus includes the study of functions in general with emphasis on the elementary functions: algebraic, exponential, logarithmic, trigonometric and inverse trigonometric functions. Topics include rates of change, limits, systems of equations, conic sections, sequences and series, trigonometric equations and identities, complex number, vectors, and applications. Previous NMHU MATH 160.

Prerequisites: MATH 1220 a grade of C or better.

**MATH 1350. Introduction to Statistics (3); Fa, Sp**

This course discusses the fundamentals of descriptive and inferential statistics. Students will gain introductions to topics such as descriptive statistics, probability and basic probability models used in statistics, sampling and statistical inference, and techniques for the visual presentation of numerical data. These concepts will be illustrated by examples from a variety of fields. Previous NMHU MATH 145.

**MATH 1430. Applications of Calculus 1 (3); Fa, Sp**

An algebraic and graphical study of derivatives and integrals, with an emphasis on applications to business, social science, economics and the sciences.

Prerequisite: MATH 1220 with a minimum grade of C. Previous NMHU MATH 155.

**MATH 1440. Applications of Calculus 2 (3); Fa, Sp**

A continuation of MATH 1430. Topics include partial derivatives, max and min problems, Lagrange multipliers, brief trigonometry, techniques of integration, differential equations and probability. Prerequisite: MATH 1430 with a minimum grade of C. Previous NMHU MATH 205.

**MATH 1510. Calculus 1 (4); 4, 2 Fa, Sp**

Introduces the intuitive, numerical and theoretical concepts of limits, continuity, differentiation and integration. Includes the study of extrema, curve sketching, and applications involving algebraic, exponential, logarithmic and trigonometric functions. Designed for mathematics, science and engineering majors. Prerequisite: MATH 1250 with a grade of C or better. Previous NMHU MATH 211.

**MATH 1520. Calculus 2 (4); Fa, Sp**

A continuation of MATH 1510 Calculus 1. Topics include numerical methods of integration, integration techniques, L’Hôpital’s rule, improper integrals, applications of integration, sequences, and series. Prerequisite: MATH 1510 with a C or better. Previous NMHU MATH 252.

**MATH 2350-4350. Selected Topic in Mathematics (1-4 VC); Fa, Sp**

Course in a topic or topics in Mathematics. May be repeated with change of content. Previous NMHU MATH 235-435.

**MATH 2530. Calculus 3 (4); Fa, Sp**

A study of differential and integral calculus or functions of several variables. Topics include partial derivatives, tangent planes, the chain rule, the gradient, extremes of functions of two variables, Lagrange multipliers, double integration in rectangular and polar coordinates, triple integration in rectangular, cylindrical, and spherical coordinates. Prerequisite: MATH 1440 with a C or better. Previous NMHU MATH 273.

**MATH 2900-4900. Independent Study (1-4 VC); Fa, Sp**

Independent study arranged with an instructor. Prerequisite: Permission of instructor. Previous NMHU MATH 290-490.

**MATH 3010. Introduction to Mathematical Proofs (3); Fa, Sp**

An introduction to reading and writing Mathematical proofs. Techniques of proof writing (constructive, contradiction, contrapositive, etc.) will be emphasized over a wide variety of settings (number theory, set theory, introductory analysis, e.g.). Prerequisite: MATH 1440 with a minimum grade of C or permission of instructor. Previous NMHU MATH 301.

**MATH 3170. Discrete Mathematics (4); Fa, Sp**

An algorithm-based treatment of sets, matrices, functions, graphs, and relations along with a study of modular arithmetic, enumeration, induction, recursion, algorithm efficiency, Boolean algebra, tees, and graphs. Prerequisite: MATH 1220 or MATH 1250 with a grade of C or better. Previous NMHU MATH 317.

**MATH 3200. Linear Algebra (3); Fa, Sp**

An introduction to solutions of linear systems of equations, properties of matrices, nonsingular matrices, determinants, eigenvalues and eigenvectors, similar matrices and Euclidean vector spaces. Prerequisite: MATH 1510 with a minimum grade of C. Previous NMHU MATH 320.

**MATH 3250. Applied Ordinary Differential Equations (3); Fa, Sp**

An introduction to ordinary differential equations. Topics include linear and separable first-order equations, linear second-order equations with constant coefficients, applications of first-order and second-order equations, and Laplace transform methods. Prerequisite: MATH 1440 with a minimum grade of C. Previous NMHU MATH 325.

**MATH 3450. Mathematical Statistics 1 (3); Fa, Sp**

A calculus-based introductory course in statistics including probability, discrete and continuous distributions, confidence intervals, p-values and the analysis of decision rules. Prerequisite: MATH 1440 or MATH 1510 with a minimum grade of C. Previous NMHU MATH 345.

**MATH 4010. Discrete Chaos and Fractals (3); Fa, Sp**

An introduction to fractal geometry and discrete dynamics in one dimension. Topics include stability of one-dimensional maps, periodic points, bifurcations, period three orbits, Sharkovsky’s theorem, Schwarzian derivative, chaos in one dimension, metric spaces, transitivity, conjugacy, fractals, fractal dimension, Julia and Mandelbrot sets. Prerequisites: MATH 3170 and MATH 2530 with a minimum grade of C, or permission of instructor. Previous NMHU MATH 401.

**MATH 4020. Discrete Dynamical Systems and Chaos (3); Fa, Sp**

A continuation of MATH 401 in higher dimensions. Topics include discrete linear dynamical systems, orbits, stability, spectral decomposition theorem, affine systems, nonlinear dynamical systems, bounded invariance, global stability of fixed points, sinks, repellers and saddles, bifurcation, attractors, Li- Yorke chaos, and more on fractal dimension. Prerequisites: MATH 3200 and MATH 4010 with a minimum grade of “C”. Previous NMHU MATH 402.

**MATH 4040. Introduction to Numerical Analysis (3); Fa, Sp**

An introduction to numerical methods for determining the roots of nonlinear equations, numerical interpolation and integration, and numerical methods for approximating solutions to ordinary differential equations. Prerequisites: MATH 3200 and MATH 3250 with a minimum grade of C. Previous NMHU MATH 404.

**MATH 4060. College Geometry (4); 3, 2 Fa, Sp**

A rigorous treatment of the elements of Euclidean geometry. Prerequisite: MATH 3170 with a grade of C or better. Previous NMHU MATH 406.

**MATH 4070. Mathematical Models (3); Fa, Sp**

An overview of model construction with many different examples. The course includes differential equations, Markov chains, linear programming, zero sum games, graphs, and queues. Prerequisites: MATH 3200 and MATH 3250 with a minimum grade of C. Previous NMHU MATH 407.

**MATH 4100. Optimization Techniques (3); Fa, Sp**

The study of unconstrained and constrained optimization computational algorithms, including both linear and nonlinear methods. Prerequisite: MATH 3200 and MATH 2530 with a minimum grade of C. Previous NMHU MATH 410.

**MATH 4150. Introduction to Cryptography (3); Fa, Sp**

An introductory course on the Mathematics of cryptography. Topics include column transposition, monoalphabetic and polyalphabetic ciphers, the one-time pad, and the Hill cipher. Prerequisite: MATH 3170 with a grade of C or better. Previous NMHU MATH 415.

**MATH 4170. Mathematical Statistics 2 (3); Fa, Sp**

A continuation of MATH 3450 covering the topics of contingency tables, multiple regression, analysis of variance, and other special topics in Mathematical Statistics. Prerequisite: MATH 3450 with a minimum grade of C. Previous NMHU MATH 417.

**MATH 4190. Modern Methods of Cryptography (3); Fa, Sp**

A study of modern methods of cryptography and their applications. Topics include the data encryption standard, the RSA public key cryptosystem, and digital signatures. Prerequisite: MATH 3170-4150 with a grade of C or better. Previous NMHU MATH 419.

**MATH 4210. Applied Abstract Algebra (3); Fa, Sp**

An introduction to abstract algebra and its applications to error-correction codes, cryptography, polynomial algorithms and fast Fourier transforms. Prerequisites: MATH 3170 and MATH 3200. Previous NMHU MATH 421.

**MATH 4250. Introduction to Real Analysis (3); Fa, Sp**

This course gives students a solid background in theoretical undergraduate analysis with the theory and deeper understanding of calculus stressed. Students are introduced to proofs that motivate them toward clear thought and understanding of limits, continuity, differentiation, and series. This provides a rigorous training in Mathematical thinking. Prerequisites: MATH 3010, MATH 3200, and MATH 2530 with a minimum grade of C. Previous NMHU MATH 425.

**MATH 4260. Introduction to Complex Variable (3); Fa, S**p

An introduction to the properties of analytic functions. Topics include mappings, limits, continuity, differentiation, Cauchy-Riemann equations, harmonic functions, multi-valued functions and branch points, definite integrals and the Cauchy-Goursat theorem, Cauchy integral formula, maximum modulus theorem, Liouville’s theorem, fundamental theorem of algebra, Taylor and Laurent series, residues and poles. Prerequisite: MATH 4250 with a minimum grade of C. Previous NMHU MATH 426.

**MATH 4300. Mathematical Problem Solving (4); 3, 2 Fa, Sp**

A study of problem-solving techniques and the applications of such techniques to challenging problems in Mathematics. In addition, students will be required to demonstrate mastery of the fundamentals of undergraduate Mathematics by passing a series of examinations on college algebra, trigonometry, calculus, and linear algebra. Prerequisites: MATH 2530 and MATH 3200 with a grade of C or better. Previous NMHU MATH 430.

**MATH 4440. Matrix Theory with Applications (3); Fa, Sp**

A study of advanced topics in linear algebra and the theory of matrices with emphasis on computer-based applications. Similarity, characteristic and minimal polynomials, diagonalizable matrices and symmetric matrices, Jordan canonical form, vector and matrix norms, spectral radius, stable matrices, functions of matrices, non-negative matrices and Perron- Frobenius theory, differential equations, stability, location of eigenvalues, Rayleigh quotient and Gersgorin’s theorem. Prerequisites: MATH 3170, MATH 3200, and MATH 3250 with a minimum grade of C. Previous NMHU MATH 444.

**MATH 4500. Seminar in Mathematics (1-4 VC); Fa, Sp**

Seminar course in a topic or topics in mathematics. Previous NMHU MATH 450.

**MATH 4600. Applied Multivariate Statistics 1 (3); Fa, Sp**

Introductory matrix analysis for statistics, multivariate distributions, multiple regression, multiple analysis of variance and covariance, principal component analysis, and canonical correlations. Prerequisite: MATH 3200 with a minimum grade of C. Previous NMHU MATH 460.

**MATH 4610. Applied Multivariate Statistics 2 (3); Fa, Sp**

A continuation of MATH 4600, including discriminant analysis, factor analysis, categorical techniques, distance concepts, and cluster analysis. Prerequisite: MATH 4600 with a minimum grade of C. Previous NMHU MATH 461.

**MATH 4990. Independent Research (1 – 4 VC); Fa, Sp**

Individual research arranged with an instructor. Prerequisite: Permission of instructor. Previous NMHU MATH 499.

This major is under the College of Arts and Sciences