## Mathematics Minor

### Requirements

One of the oldest academic subjects, mathematics plays an indispensable role in many fields, and new applications of mathematics are continuously being developed. A strong background in mathematics is a requirement for advancement in a large and increasing number of jobs and will give students more flexibility in choosing their careers.

### Required mathematics courses 12 hours

CODETITLECREDITS
MAT 150 Calculus I 4
MAT 205 Calculus II 4
MAT 206 Calculus III 4

### Elective mathematics courses 6 hours

Choose from:
CODETITLECREDITS
MAT 210 Mathematical Proofs 3
MAT 307 Linear Algebra 3
MAT 313 Introduction to Probability 3
MAT 314 Applied Statistics I 3
MAT 320 History of Mathematics 3
MAT 328 Differential Equations 3
MAT 340 Introduction to Number Theory 3
MAT 348 Introduction to Cryptography 3
MAT 360 Intro to Operations Research 3
MAT 361 Numerical Analysis 3
MAT 410 Foundations of Geometry 3
MAT 414 Applied Statistics II 3
MAT 434 Abstract Algebra 3
MAT 445 Introduction to Complex Analysis 3
MAT 455 Advanced Calculus I 3
MAT 456 Advanced Calculus II 3
MAT 495 Special Topics 1-5

### Courses

###### MAT 150 - Calculus I (4)

Limit processes, including the concepts of limits, continuity, differentiation, and integration of functions. Applications to physical problems will be discussed.

Prerequisite: A grade of C or better in either MAT 126 or MAT 130.

###### MAT 205 - Calculus II (4)

Applications of integration, inverse functions, the natural logarithm and exponential functions, and hyperbolic functions. Techniques of integration, sequences, series of numbers and functions, and Taylor series.

Prerequisite: A grade of C of better in MAT 150.

###### MAT 206 - Calculus III (4)

Vectors, partial derivatives, multiple integrals, line integrals, Green's Theorem, the Divergence Theorem, and Stokes Theorem. Applications to physical problems will be given.

Prerequisite: A grade of C or better in MAT 205.

###### MAT 210 - Mathematical Proofs (3)

A study of functional principles and proof techniques. Topics will include statements, consequence, proof, sufficient and necessary conditions, contraposition, induction, sets, relations, functions, cardinality, divisibility, prime numbers, congruence, Fermat's Theorem, counting principles, permutations, variations, combinations, binomial coefficients, graphs, planar and directed graphs, and graph coloring.

Prerequisite: A grade of C or better in MAT150

###### MAT 307 - Linear Algebra (3)

This course covers the fundamental concepts of vector spaces, linear transformations, systems of linear equations, and matrix algebra from a theoretical and a practical point of view. Results will be illustrated by mathematical and physical examples. Important algebraic (e.g., determinants and eigenvalues), geometric (e.g., orthogonality and the Spectral Theorem), and computational (e.g., Gauss elimination and matrix factorization) aspects will be studied.

Prerequisite: MAT 205 or permission of the Mathematics Program Director.

###### MAT 313 - Introduction to Probability (3)

This course is the first part of a two-semester sequence with MAT 314, with a focus on basic probability. It covers descriptive statistics, sample spaces and events, axioms of probability, counting techniques, conditional probability and independence, distribution of discrete and continuous random variables, joint distributions, and the central limit theorem.

Prerequisites: MAT 205

###### MAT 314 - Applied Statistics I (3)

This course is the second part of a two-semester course sequence with MAT 313, with a focus on applied statistics. It covers basic statistical concepts, graphical displays of data, sampling distribution models, hypothesis testing, and confidence intervals. A statistical software package is used.

Prerequisite: MAT 313

###### MAT 320 - History of Mathematics (3)

A survey of the history of mathematics from antiquity through modern times.

Prerequisite: MAT 205.

###### MAT 328 - Differential Equations (3)

Ordinary differential equations of first-order and first-degree, high order linear ordinary differential equations with constant coefficients, and properties of solutions.

Prerequisites: MAT 206, 307

###### MAT 340 - Introduction to Number Theory (3)

A study of properties of integer numbers. Divisibility of integers, primes and greatest common divisors, congruencies, Euclidean algorithm, Euler Phi-function, quadratic reciprocity and integer solutions to basic equations, Diophantine equations, and applications to cryptography and primality testing.

Prerequisite: MAT 210

###### MAT 348 - Introduction to Cryptography (3)

This is an introductory course in cryptography. It covers classical cryptosystems, Shannon's perfect secrecy, block ciphers and the advanced encryption standard, RSA cryptosystem and factoring integers, public-key cryptography and discrete logarithms, and linear and differential cryptanalysis.

Prerequisites: MAT 130 and MAT 140; or MAT 150; or permission of the instructor.

###### MAT 360 - Intro to Operations Research (3)

This course covers linear programming, the simplex algorithm, duality theory and sensitive analysis, network analysis, transportation, assignment, game theory, inventory theory, and queuing theory.

Prerequisites: MAT 140, or MAT 150; or permission of the instructor

###### MAT 361 - Numerical Analysis (3)

Numerical differentiation, integration, interpolation, approximation of data, approximation of functions, iterative methods of solving nonlinear equations, and numerical solutions of ordinary and partial differential equations.

Prerequisites: ITS 110 or the equivalent; MAT 206; or permission of the department chair

###### MAT 410 - Foundations of Geometry (3)

A survey of Euclidean, non-Euclidean, and other geometries. The emphasis will be on formal axiomatic systems.

Prerequisite: MAT 150, 210; or permission of the instructor

###### MAT 414 - Applied Statistics II (3)

This course covers statistical techniques with applications to the type of problems encountered in real-world situations. These topics include categorical data analysis, simple linear regression, multiple regression, and analysis of variance. A statistical software package is used.

Prerequisite: A grade of B or above in MAT 314; or permission of the instructor.

###### MAT 434 - Abstract Algebra (3)

An axiomatic treatment of groups, rings, and fields that bridges the gap between concrete examples and abstraction of concepts to general cases.

Prerequisite: MAT 206, 210, 307, or permission of the the Mathematics Program Director.

###### MAT 445 - Introduction to Complex Analysis (3)

This is an introductory course in complex analysis. The algebra of complex numbers, analytic functions, contour integration, Cauchy integral formula, theory of residues and poles, and Taylor and Laurent series.

Prerequisite: MAT 206 and MAT 210, or permission of the instructor

###### MAT 455 - Advanced Calculus I (3)

This course is the first part of a two-semester course sequence with MAT 456. This course covers a theoretical approach to calculus of functions of one and several variables. Limits, continuity, differentiability, Reimann integrability, sequences, series, and contour integration.

Prerequisites: MAT 206, 210, 307

###### MAT 456 - Advanced Calculus II (3)

This course is the second part of a two-semester course sequence with MAT 455. This course covers a theoretical approach to calculus of functions of one and several variables. Limits, continuity, differentiability, Reimann integrability, sequences, series, and contour integration.

Prerequisite: MAT 455

###### MAT 495 - Special Topics (1-5)

Special topics in the discipline, designed primarily for seniors who are majors or minors. Students may enroll in 495 Special Topics multiple times, as long as the topics differ.

Prerequisite: Permission of the department chair