# Mathematics Major

The department of mathematics and computer science provides students with courses for general knowledge and for career preparation. We stress the development of critical thinking skills, the integration of theory with practical applications and the understanding of concepts of mathematics. Mathematics courses numbered 300 or higher are typically offered once every four semesters on a rotating basis.

The major in mathematics prepares students for careers or graduate school in the mathematical sciences. We encourage mathematics majors to participate in research. The minor in mathematics supports students who are planning careers in areas that rely on applications of mathematics.

**The mathematics major requires a minimum of 40 credit hours.**

*All prerequisites must be completed prior to enrollment in the following courses. *

*A grade of C- or higher must be achieved in the 200-level courses listed below.*

**4 credit hours**

An introduction to computer science through applications such as media. A major component is programming design and development using a language such as Python or Java. A disciplined approach to problem solving methods and algorithm development will be stressed using top-down design and stepwise refinement. Topics included are syntax and semantics, input and output, control structures, modularity, data types, and object-oriented programming.* Recommended for students with previous programming experience or a strong mathematical background (math ACT score of 24 or above).*

**4 credit hours**

* It is strongly recommended that students have completed two years of high school algebra and one semester of high school trigonometry in order to be successful in this course.* A study of the fundamental principles of analytic geometry and calculus with an emphasis on differentiation.

**4 credit hours**

*Prerequisite: MATH 231 or MATH 236. It is recommended that students receive a grade of C or better in MATH 231 or MATH 236 to be successful in this course.* Continuation of Calculus I including techniques of integration and infinite series.

**4 credit hours**

*Prerequisite: MATH 232. It is recommended that students receive a grade of C or better in MATH 231 to be successful in this course.*

Functions of two variables, partial differentiation, applications of multiple integrals to areas and volumes, line and surface integrals, and vectors.

**3 credit hours**

*Prerequisite: MATH 231 or MATH 236. It is strongly recommended that students have completed MATH 232 to be successful in this course.* A careful introduction to the process of constructing mathematical arguments, covering the basic ideas of logic, sets, functions and relations. A substantial amount of time will be devoted to looking at important forms of mathematical argument such as direct proof, proof by contradiction, proof by contrapositive and proof by cases. Applications from set theory, abstract algebra or analysis may be covered at the discretion of the instructor.

**3 credit hours**

*Prerequisite: MATH 234 or CSCI 241 and CSCI 262, MATH 235.*

The elementary properties of groups, rings and fields are developed.

**3 credit hours**

*Prerequisite: MATH 233, MATH 234. It is recommended that students have completed MATH 301 in order to be successful in this course. *Real number system, set theory, continuity and differentiability.

**3 credit hours**

Modern topics in mathematics are discussed in a seminar setting. Students integrate their study of mathematics throughout their undergraduate years and explore the connections among mathematics and other courses they have pursued. Departmental assessment of the major is included. This course is designed to be a capstone experience taken during the final semester of the senior year.

**Choose three courses from at least two of the following areas (9 hrs): **

*Probability and Statistics*

**3 credit hours**

*Prerequisite: MATH 232. It is recommended that students receive a grade of C or better in MATH 232 to be successful in this course.*

This course includes an introduction to probability theory, discrete and continuous random variables, mathematical expectation and multivariate distributions.

**3 credit hours**

*Prerequisite: MATH 326. It is recommended that students receive a grade of C or better in MATH 326 to be successful in this course. *This course takes the material from MATH 326 into the applications side of statistics including functions of random variables, sampling distributions, estimations and hypothesis testing.

*Applied Math*

**3 credit hours**

*Prerequisite: MATH 231 or MATH 236, and MATH 232.*

Numerical solutions to mathematical problems are studied. Topics include approximating solutions to equations, interpolation, numerical differentiation and integrating, and numerical linear algebra.

**3 credit hours**

*Prerequisites: MATH 227 and CSCI 152*. An introductory exploration of the data science process, its uses, and its applications. Students will focus on the derivation of actionable knowledge from data using the data science pipeline. Pipeline topics include data acquisition, cleaning of data, transformation of data, analysis of data, and interpretation of data. Analysis of data includes an introduction to both statistical and machine learning techniques. Interpretation of data will include an introduction to data visualization. Additionally, the course will address the role of data science and the implications of its use in our culture, our world, and our individual lives. The course uses a problem-based approach where students will engage with other students and with the course materials.

**3 credit hours**

*Prerequisite: MATH 227 or MATH 327.* In almost any study, there is the task of predicting or explaining the behavior of a particular variable. In most cases such research is possible through the analysis of a relationship of this variable with some others. Such interactions are not pre-determined and are of a random nature. A mathematical model of such relationship becomes one of the most important tools of study. Construction, examination and use of such a model are subjects of the regression analysis.

**3 credit hours**

*Prerequisite: MATH 233, MATH 234.* A study of complex numbers, analytic functions, complex integration, residues and series.

**1-3 credit hours**

Selected Topics are courses of an experimental nature that provide students a wide variety of study opportunities and experiences. Selected Topics offer both the department and the students the opportunity to explore areas of special interest in a structured classroom setting. Selected Topics courses (course numbers 290, 390, 490) will have variable titles and vary in credit from 1-3 semester hours. Selected Topic courses may not be taken as a Directed Study offering.

*Geometry and Topology *

**3 credit hours**

*Prerequisite: MATH 234.* Foundations of Euclidian geometry from the axioms of Hilbert and an introduction to non-Euclidian geometry.

**3 credit hours**

*Prerequisite: MATH 234.* An introduction to point-set topology. Metric spaces, connectedness, completeness and compactness are some of the topics discussed.

*Computer Science *

**3 credit hours**

*Prerequisite: CSCI 351 or MATH 234.* A formal study of the mathematical basis for computer software. The following topics are included: finite automata, regular expressions, context-free languages, pushdown automata, Turing machines, decidability and computability.

**3 credit hours**

*Prerequisite: CSCI 351. * The translation of high-level languages into low-level languages is studied, including syntax definition, lexical analysis, syntax analysis and the role of the parser. Other topics include type checking, run-time environments, code generation and code optimization.

**Students may replace MATH 234 with the pair of classes CSCI 241 and CSCI 262.*