## Mathematics Curriculum

The Department of Mathematics wishes to share the beauty and usefulness

of mathematics and computer science with as many undergraduates as possible; to provide training in analytical thinking; to prepare majors for advanced work in mathematics, computer science, and related fields; and to provide the background for various kinds of employment after graduation.

The faculty adheres to the philosophy that the only way to learn mathematics is to do it. Regular written assignments enable the student and faculty to monitor the student’s progress and to verify the accuracy of the substance and style of the work.

The Department’s emphasis is on strengthening the student’s problem-solving skills.

## Computer Science Minor

The study of computer science offers students the opportunity to develop problem solving facility and helps develop skills which have broad utility in theory and application and are amongst the most sought-after by employers. The abstraction of real-world problems, the construction of algorithms to display and transform data, and the theory of computation are all central concerns of computer science. The minor in computer science can be effectively combined with any major.

Whether studied with professional goals in mind, to supplement the study of any other field, or just for interest’s sake, computer science offers a powerful way to approach many challenging problems. When combined with selected courses in mathematics and physics, the minor will help prepare the student for graduate work in computer science and related fields.

## Independent Study for Non-Majors

The Department is pleased to offer independent study courses for one semester hour each on the application of mathematics to such fields as economics and business, political science, psychology, biology, chemistry, cryptology, linguistics, and physics. These courses are intended primarily for students in other disciplines who have done well in mathematics but do not wish to take additional three-hour mathematics courses.

Interested students should contact the Department.

## Course Offerings

Below is a list of available courses offered by the mathematics department. Consult the Registrar’s Office and the College Catalog for registration information.

### MATH 1109 - Intro To Quantitative Reasoning

This course presents mathematical ideas in a real world context. Topics covered include critical thinking and problem solving, the mathematics of finance, basic statistical principles, mathematics and the arts, and the theory of voting. Credit hours: 4. (QR)

### MATH 1117 - Precal Elem Modeling I

Relations defined algebraically, graphically, and numerically. Functions, including polynomial, rational, trigonometric, exponential, and logarithmic. Applications, including modeling. Algebraic techniques and a review of basic geometric relationships. Credit hours: 4. Not open to students who have been placed into MATH 1119 or above, except by permission of the Department. (QR)

### MATH 1118 - Precal Elem Modeling Ii

Relations defined algebraically, graphically, and numerically. Functions, including polynomial, rational, trigonometric, exponential, and logarithmic. Applications, including modeling. Algebraic techniques and a review of basic geometric relationships. Credit hours: 4. Not open to students who have been placed into MATH 1119 or above, except by permission of the Department. (QR)

### MATH 1119 - Precalculus

A study of the properties of various functions, including polynomial, trigonometric, exponential, and logarithmic. Analytic geometry of conic sections. Credit hours: 4. Not open to students who have been placed into MATH 1149 or above, except by permission of the Department. (QR)

### MATH 1149 - Calculus I

Limits, continuity, and differentiation of algebraic functions of one variable. Applications to curve sketching, optimization, and rates of change. The definite integral applied to finding the area under a curve. Credit hours: 4. Prerequisite: MATH 1118 or MATH 1119 or the equivalent. (QR)

### MATH 1150 - Calculus Ii

A continuation of Mathematics 1149. Volumes and surface area of solids of revolution. Lengths of curves. The logarithm and exponential functions. Techniques of integration. Areas in polar coordinates. Improper integrals, infinite series, and power series. Credit hours: 4. Prerequisite: MATH 1149 or permission of the Department. (QR)

### MATH 2227 - Elementary Applied Statistics

An introduction to statistics, including probability, binomial distributions, normal distributions, sampling theory, testing hypotheses, chi-square tests, and linear regression. Credit hours: 4. Not open to students who have satisfactorily completed MATH 3343. A student may receive credit for two of these courses: ECON 2227, MATH 2227, POL 2231, PSYC 2227, or SOC 3395. (QR)

### MATH 2229 - Advanced Mathematical Problem Solving

In this course, students will be expected to solve and present solutions to a collection of problems gathered from various mathematics competitions. Problem solutions may involve the techniques of classical algebra, geometry, calculus, and combinatorics. Credit hours: 1. Prerequisite: permission of instructor. May be repeated for credit up to a maximum of 4 hours.

### MATH 2232 - Introduction To Data Science

Data science is an interdisciplinary field incorporating statistical techniques with algorithms to collect and to process large data sets, in order to extract meaning and make decisions. Students will explore the collection and filtering of data, machine learning algorithms, and methods for drawing conclusions. Identical with DSCI 2232. Credit hours: 4. Prerequisite: ECON 2227 or EVST 2205 or MATH 2227 or MATH 3343 or POL 2231 or PSYC 2227 or SOC 3395.

### MATH 2234 - Techniques Of Mathematical Proof

An introduction to formal mathematical proof. Topics include logical inference, statements involving quantifiers, indirect proof, and mathematical induction. We investigate proofs in a variety of disciplines but with a particular focus on set theory, combinatorics, and graph theory. Credit hours: 4. Prerequisite: MATH 1149.

### MATH 2236 - Discrete Math And Graph Theory

Discrete mathematics focuses on structures where the parts are distinct and separated, as contrasted with the continuous structures studied in calculus. This course has a particular focus on graphs and networks.. We will consider paths and cycles, coloring, planar graphs, and trees. We also consider algorithms to find shortest paths, minimum spanning trees, and maximum flows. Credit hours: 4. Prerequisite: MATH 1149 or CSCI 1151.

### MATH 2241 - Linear Algebra

Systems of linear equations, vector spaces and subspaces, bases and dimension, linear transformations, eigenvalues and eigenvectors, and inner product spaces. Credit hours: 4. Prerequisite: MATH 1149 or permission of the Department.

### MATH 2250 - Calculus Iii

An introduction to vector calculus. Differential and integral calculus of more than one variable. Vector fields, including Green's, Stokes', and the Divergence Theorems. Credit hours: 4. Prerequisite: MATH 1150 and either MATH 2241 or PHYS 1115 or permission of the Department.

### MATH 2273 - Math One Time Only

Credit hours: 4. One time only.

### MATH 2286 - Math One Time Only

One time only.

### MATH 2286S - One Time Only Summer

One time only summer.

### MATH 3320 - Introductory Topology

An introduction to point-set geometry, including topological spaces, metric spaces, homotopy, the Urysohn lemma, and Tychonoff's theorem. Students explore topology as the underpinning of modern geometry. Credit hours: 4. Prerequisite: MATH 2241 or permission of the Department.

### MATH 3331 - Differential Equations

First order linear and non-linear equations, second and higher order linear equations, series solutions, Laplace transforms, and systems of linear differential equations. Applications, primarily to mechanics and population dynamics. Credit hours: 4. Prerequisite: MATH 1150 and 2241 or the course may be taken concurrently with MATH 2241 by permission of the Department.

### MATH 3337 - Number Theory

Properties of the integers. Unique factorizations, congruences and modular arithmetic. Diophantine equations, prime numbers, quadratic reciprocity, and integer functions. Applications to cryptology. Credit hours: 4. Prerequisite: MATH 1150 and MATH 2234 or permission of the Department.

### MATH 3343 - Mathematical Statistics

Probability. Discrete and continuous probability distributions. Sampling and the Central Limit Theorem. Confidence intervals, hypothesis testing, linear regression, and non-parametric tests. Credit hours: 4. Prerequisite: MATH 2250.

### MATH 3353 - Mathematical Modeling

The construction and analysis of mathematical models to solve problems in the physical and social sciences. Dynamical systems are emphasized with a particular concentration on linear and non-linear discrete dynamical systems. Topics may include dimensional analysis, stability, chaos, and fractals. Credit hours: 4. Prerequisite: MATH 1150 and 2241.

### MATH 3360 - Abstract Algebra

Groups, rings, integral domains. Homomorphisms and isomorphisms. Elementary number theory. The fields of rational, real, and complex numbers. Credit hours: 4. Prerequisite: MATH 2234 and MATH 2241 or permission of the Department.

### MATH 3388 - Math One Time Only

Credit hours: 4. One time only.

### MATH 3390 - Independent Study

### MATH 4426 - Complex Variables

The complex number system. Limits, continuity, and differentiability of functions of a single complex variable. Contour integration and Cauchy's Theorem. The calculus of residues. Conformal mapping. Credit hours: 4. Prerequisite: MATH 2250.

### MATH 4443 - Introduction To Analysis

A rigorous study of limits, continuity, differentiation, and integration of functions of a real variable. Credit hours: 4. Prerequisite: MATH 2234 and MATH 2250 or permission of the Department.

### MATH 4490 - Independent Study

### MATH 4492 - Professional Devel Sem

Students will explore how the skills they have accumulated over the course of their degree may be applied both to solve problems in the real world and to extend the limits of human knowledge. They will select a research advisor and a research topic in mathematics and begin directed readings. Credit hours: 1. Prerequisite: MATH 3360.

### MATH 4494 - Senior Seminar

Students will conduct research on a particular question in mathematics or computer science under the direction of a research advisor. Students will draw on skills they have accumulated over their undergraduate careers as well as see familiar topics presented in a new light. Work will culminate in a research paper and a presentation in front of faculty and peers. Identical with CSCI 4494. Credit hours: 4. Prerequisite: MATH 4492 or CSCI 4492.

### MATH 4497H - Honors In The Major

### MATH 4498H - Honors In The Major

### CSCI 1151 - Computer Programming I

An introduction to computers and computer programming. Emphasis will be placed on problem-solving with examples and exercises from social, natural, and mathematical sciences. Techniques of flowcharting and structured programming, development of algorithms, and types of computer hardware will also be discussed. Intended for students with no previous programming experience. Credit hours: 3. A student may not receive credit for this course after taking CSCI 1156 or its equivalent.

### CSCI 1151L - Computer Programming I Lab

Hands-on application of the topics studied in CSCI 1151. Credit hours: 1. Prerequisite or Corequisite: CSCI 1151 or the equivalent.

### CSCI 1156 - Computer Programming Ii

A continuation of Computer Science 1151. Emphasis on top-down programming using methods. Topics include user-defined classes and advanced data types, arrays, recursion, algorithms for sorting and searching, exception handling, advanced GUIs and graphics, and embedding Java applets into HTML documents. Credit hours: 4. Prerequisite: CSCI 1151 or the equivalent.

### CSCI 1156L - Computer Programming Ii Lab

Hands-on application of the topics studied in CSCI 1156. Credit hours: 1. Prerequisite or Corequisite: CSCI 1156 or the equivalent.

### CSCI 2225 - Matlab & Labview

This course covers beginning and intermediate programing in the Matlab and Labview computer languages. Students will learn the basics of computer programming as well as the specifics of programing in Matlab and Labview including data input/output, code structuring, coding best practices and limitations, data acquisition and beginning GUI development. This course is project based with projects taken from real world computing problems. Credit hours: 4. Prerequisite: MATH 1149.

### CSCI 2252 - Data Structures

Students will study abstract data types and their implementation. Arrays, lists, stacks, queues, trees, heaps, hash tables, maps, and graphs are considered. Fundamental algorithms including list manipulation, sorting, graph searches and tree traversals are also covered. Credit hours: 4. Prerequisite: CSCI 1156 or the equivalent.

### CSCI 2256 - Algorithms

Students will study techniques for designing and analyzing algorithms. The design techniques including divide-and-conquer, dynamic programming, greediness and probabilistic approaches will be covered. An analysis of best/average/worst case complexity in both time and space will be covered. Credit hours: 4. Prerequisite or Corequisite: MATH 2236 or the equivalent.

### CSCI 2290 - Independent Study

### CSCI 3326 - Computer Architecture And Assembly Lang

Introduction to internal computer architecture including the instruction cycle, parts of the CPU, memory hierarchy including caching, pipelining, exception handling, and issues of multiprocessing. Implementation of assembly language programs using sample architectures. Principles of translating high-level languages. Credit hours: 3. Pre- or co-requisites: CSCI 2251 and MATH 1149 or equivalent.

### CSCI 3328 - Computer Networks

Introduction to the design and analysis of computer networks. Topics include application layer protocols, Internet protocols, network interfaces, local and wide area networks, wireless networks, bridging and routing. Credit hours: 4. Prerequisites: CSCI 1156 and MATH 2236.

### CSCI 3336 - Operating Systems

Design and implementation of operating systems. Mutual exclusion, concurrency, deadlock, process scheduling, memory management, and files systems. Credit hours: 4. Prerequisite CSCI 1156.

### CSCI 3344 - Computer Graphics

Techniques for the display of graphical information. 2D and 3D geometry and transformations. Interactive graphics, shading, hidden surface elimination, perspective, and depth. Modeling and realism. Credit hours: 4. Prerequisites: CSCI 2256 and MATH 2241.

### CSCI 3346 - Software Development

This course provides an in-depth study of steps in the software-development process: user requirements, specifications, design, implementation, testing, maintenance, documentation, and management. Students will develop the facility to apply the general principles to new problems. Credit hours: 4. Prerequisite CSCI 2251.

### CSCI 3364 - Game Development

Design and development of interactive games. Principles of game development will be illustrated with 2D games, while students with the appropriate graphics background may develop 3D games. This is a hands-on course. Credit hours: 4. Prerequisite: CSCI 2256.

### CSCI 3366 - Computer Security

Introduction to the field of computer security as it relates to other areas of information technology. Topics include security threats, hardening systems, securing networks, and cryptography. Credit hours: 4. Prerequisites: CSCI 1156 and MATH 3337.

### CSCI 3386 - Csci One Time Only

Credit hours: 4. One-time only.

### CSCI 4490 - Independent Study

### CSCI 4492 - Professional Dev Sem

Students will explore how the skills they have accumulated over the course of their degree may be applied both to solve problems in the real world and to extend the limits of human knowledge. They will select a research advisor and a research topic in computer science and begin directed readings. Credit hours:1. Prerequisite: CSCI 2251.

### DSCI 2232 - Intro To Data Science

Data science is an interdisciplinary field incorporating statistical techniques with algorithms to collect and to process large data sets, in order to extract meaning and make decisions. Students will explore the collection and filtering of data, machine learning algorithms, and methods for drawing conclusions. Credit hours: 4. Prerequisite: ECON 2227 or EVST 2205 or MATH 2227 or MATH 3343 or POL 2231 or PSYC 2227 or SOC 3395. Identical with MATH 2232.

### DSCI 2233 - Machine Learning

A broad introduction to machine learning and statistical pattern recognition. Unsupervised and supervised learning algorithms including dimensionality reduction (PCA and variants), clustering (simple clustering, agglomerative and non-agglomerative), probabilistic models, neural networks, and support vector machines. Credit hours: 4. Prerequisite: ECON 2227 or EVST 2205 or MATH 2227 or MATH 3343 or POL 2231 or PSYC 2227 or SOC 3395.

### DSCI 4495 - Data Science Seminar

The seminar requires students to explore the areas of their personal interest in data science in order to inform their choice of research topics, graduate school, and employment. Students will review the major ideas in data science and will prepare for the rigorous data science-related job interview. Credit hours: 1.