Mathematics

Students will learn to analyze computational problems and develop solutions to them as algorithms. The algorithms will be implemented in Python, a modern programming language. Students will learn the fundamental principles of computer science, basic hardware and software components of a computer system, computational thinking, basic algorithms, and programming. Students will get hands-on experience in problem solving by designing, writing, testing and debugging Python programs.

Software is everywhere, including enterprise systems, mobile devices, avionics, sensors, and big data. This course focuses on Object Oriented Programming (Java) and its key concepts: object, classes, encapsulation, abstraction, polymorphism, and inheritance. In addition, topics such as generics, interfaces, threads and events/listeners complement the software development process.

Continuation of COMSC 1351: Introduction to abstract data types, records, linked lists, stacks, queues and trees and graphs; recursion; analysis of algorithms; additional sorting and searching techniques. Prerequisites: COMSC 1351

This course will introduce students into different methods, techniques, and approaches for conducting computational research applied to different disciplines such as Biology, Health Sciences, Textual Analysis, Humanities, and more.

The organization of programming languages with emphasis on language semantics; language definition, data types, and control structures of various languages. Principles of object oriented and functional programming and the translation and execution of programs. Prerequisite: COMSC 1351

Data analytics is a process that turns data into usable information for answering questions. This course will introduce the process of acquiring, managing and analyzing data. Readily available real-world data sets will be analyzed using supervised and unsupervised learning methods.

Appropriate visualizations of data are a key to revealing patterns and communicating important findings in research. This course will build on statistical and analytical thinking by emphasizing the role and use of visualizations in the analysis of data. Theories, techniques and software for managing, exploring, analyzing, displaying and communicating information about various types of data will be introduced. Visualizations will be produced using readily available real-world data sets. Prerequisites: MATH 2435, or MATH 3332, or MATH 3450, or PSYC 3433, or instructor approval.

Organization concepts and terminology of data models and the underlying data structures needed to support them. Thorough presentation of the relational database management system including an introduction to SQL programming, normalization and database design. Introduction to the programming interface to databases. Prerequisite: junior standing; COMSC 1450.

Introduction to digital logic, machine representation of data, assembly programming, processor design, memory organization, and interface communication. Prerequisite: COMSC 1351.

Presentations and discussions on current and emerging issues, topics and trends in computer science.

Practicum of on–the–job experience under the guidance of a practicing specialist in the field. This course is designed to provide opportunities for students to enhance their practical skills through application of classroom concepts and theories to real life situations. To be supervised individually by a department faculty member with the approval of the department chair.

Systematic analysis and discussion of selected topics of contemporary and current interest.

Topics of special interest chosen by the instructor. Prerequisite: COMSC 2351.

A study of concurrency, process scheduling, memory management, security and device management. Topics in syste support for parellelism, virtualization and reliability. Prerequisite: COMSC 3385

Topics include human interaction with computers, user interface design, professional ethics, sustainability, security policy, computer crime and law, and history of computing. Prerequisite:COMSC 2351

An introduction to the design and analysis of computer communication networks. Topics included application layer protocols, Internet protocols, network interfaces, local and wide area networks, wireless networks, bridging and routing, and current topics. Prerequisites: COMSC 1351

Data science is an emerging discipline whose main goal is extracting information and knowledge from datasets and using it for decision-making, answering questions, or understanding phenomena. The fundamentals of Data Science will be studied from three perspectives; 1) as a collection of disciplines: exploring the interconnections between computing, mathematics, statistics, visualization, and other domains; 2) as a process: learning the life cycle in a data science project; and 3) understanding its computational foundation. This course also addresses the potential negative impact algorithms can have on people and society.

This course is intended as a capstone. Topics include software project management, software design, reliability, verification and validation. The course includes the team development of a software system. Prerequisite: senior standing

Practicum of on–the–job experience under the guidance of a practicing specialist in the field. This course is designed to provide opportunities for students to enhance their practical skills through application of classroom concepts and theories to real life situations. To be supervised individually by a department faculty member with the approval of the department chair.

Topics of special interest chosen by the instructor. Prerequisite: COMSC 2351.

Upper-division treatment of selected topics of mutual interest to the faculty member and students. Prerequisite: Consent of Department Chair.

The study of functions, and their graphs, inequalities, and linear, quadratic, piece-wise defined, rational, polynomial, exponential, and logarithmic functions.

The application of common algebraic functions, including polynomial, exponential, logarithmic, and rational, to problems in business, economics, and the social sciences are addressed. The applications include mathematics of finance, including simple and compound interest and annuities; systems of linear equations; matrices; linear programming; and probability, including expected value.

This course is an exploration of great ideas of mathematics. The course describes the nature of mathematics and provides insights into various strategies used by mathematicians in solving problems. The course emphasizes creative and effective thinking through an introductory examination of a wide variety of topics such as number theory, geometry, infinity, topology, chaos and fractals, and decision making. Prerequisite: Acceptance in the Mendenhall Summer Institute. Co-Requisite: ENGL 1311.

An integrated review course in pre–calculus algebra and trigonometry covering function concepts and symbols, rectangular coordinates, linear and quadratic functions, polynomial and rational functions, trigonometric functions, inequalities, systems of equations, complex numbers and analytic geometry.

Topics from contemporary mathematics, their development, applications and role in society. Some typical topics, to be chosen by the instructor, include graph theory, mathematical finance, critical path analysis, statistical inference, coding, game theory and symmetry. Applications are in the management, natural and social sciences.

Mathematics of finance, linear equations, inequalities and mathematical models with emphasis on applications.

An introduction to statistical reasoning focused on data collection, descriptive statistics, exploratory data analysis and simple linear regression. Other topics will include basic probability, normal distributions and fundamentals of hypothesis testing. This course is open only to students in the AAS-GENB program.

Topics covered will include numerical evaluation of logarithms and the use of methods for working with them, the interpretation and manipulation of numbers in scientific notation; trigonometric functions; the quantitative interpretation and generation of graphs; the evaluation of ratios of numbers with integer exponents; the simplification of rational expressions, and the use of percentages; estimation methods without the use of calculators; dimensional analysis; trigonometric functions. The course emphasizes creative and effective problem solving techniques in a real world context and an enhancement of mathematical skills leading to greater achievement in STEM (Science, Engineering, Technology and Mathematics) courses. Prerequisite: Acceptance in the Mendenhall Summer Institute. Co-requisite: UNIV 1201.

An integrated review course in pre–calculus algebra and trigonometry covering function concepts and symbols, rectangular coordinates, linear and quadratic functions, polynomial and rational functions, trigonometric functions, inequalities, systems of equations, complex numbers and analytic geometry.

Limits, continuity, differentiation, integration and applications of both differentiation and integration.

Transcendental functions, techniques of integration, applications of integration, parametric equations, polar coordinates, infinite sequences and series. Prerequisite: Grade of “C” or better in MATH 1431.

Provides students with the methods and logic to perform elementary statistical analysis used in clinical research including: descriptive meansures, probability, sampling, normal distribution, Student t and Chi squared distributions, estimation and hypothesis testing, analysis of variance, regression and correlation.

Basic concepts, theory, methods, and applications of ordinary differential equations. Prerequisite: MATH 1432 with a grade of "C" or better.

Provides students with the methods and logic to perform elementary statistical analysis used in clinical research including: Descriptive measures, probability, sampling, normal distribution, Student t and Chi squared distributions, estimation and hypothesis testing, analysis of variance, regression and correlation.

Vectors and the geometry of space, vector functions, partial derivatives, multiple integrals, Green’s Theorem, curl and divergence, Stokes’ Theorem, The Divergence Theorem. Prerequisite: MATH 1432 with a grade of “C” or better.

An introduction to quantitative and statistical analyses focusing on applications of algebraic and statistical methods. Topics to be covered include functions and graphs, break-even analysis, descriptive statistics, probability distributions, estimation, simple linear regression and basic hypothesis testing will be covered. This course may not be used as part of the mathematics courses required of mathematics majors.

A modern approach to the mathematics commonly taught to young children. Theoretic bases for computation and measurement are established. The geometric properties of shapes and solids are explored both visually and through computations. The basics of theoretical and empirical probability are developed using models and manipulatives. Additional topics such as problem solving algorithms, elementary logic and statistics are introduced. Prerequisites: successful completion of a University core mathematics course. Does not satisfy the University core requirements in mathematics.

Junior division treatment of selected topics of mutual interest to the faculty member and students. Prerequisite: Department Consent.

Junior division treatment of selected topics of mutual interest to the faculty member and students. Prerequisite: Department Consent.

Basic concepts of statistics with emphasis on statistical inference. Sampling and experimentation, descriptive statistics, confidence intervals, probability, two–sample hypothesis tests for means and proportions, Chi–squared tests, linear and multiple regressions, analysis of variance. Not open to students with credit in MATH 2434 or 3430. This course may not be used as part of the upper–division mathematics courses required of mathematics majors.

Matrices, inverses, linear systems, determinants, eigenvalues, eigenvectors, vector spaces, linear transformations, inner product spaces, Fourier series and orthogonal bases. Prerequisite: MATH 1432.

An elementary introduction to the mathematical theory of probability for students of mathematics, engineering and the sciences (including the social sciences and management science). Topics include combinatorial analysis, axioms of probability, conditional probability and independence, and random variables. Prerequisite: MATH 1432.

A study of the foundations of Euclidean geometry; non–Euclidean geometry. Prerequisite: Successful completion of a University core mathematics course.

Numerical algorithms as applied to differential and integral calculus; stability and convergence of methods with error estimates. Prerequisites: COMSC 1450 and MATH 1431.

Continuation of Math 2343. Power series solutions of differential equations and Bessel functions, Fourier series and transforms, matrices, systems of differential equations, introduction to generalized functions. Recommended for students interested in applications of mathematics and engineering. Prerequisite: MATH 2343.

Evolution of mathematics from earliest to modern times. Major tends in mathematical thought, the interplay of mathematical and technological innovations, and the contributions of great mathematicians. Appropriate for prospective and in–service teachers. Prerequisite: Successful completion of a University core mathematics course.

Analysis topics chosen at the discretion of the instructor from logic, set theory, combinatorics, and graph theory. Methods of enumerative combinatorics: sum, product, and division rules, bijective and recursive techniques, inclusion and exclusion, generating functions, and the finite difference calculus. Advanced topics to be selected from the theory of partitions, Polya theory, designs, and codes, graphs and trees with applications including games of complete information. Combinatorial existence theorems, Ramsey’s theorem. Prerequisite: MATH 1431.

Data analytics is a process that turns data into usable information for answering questions. This course will introduce the process of acquiring, managing and analyzing data. Readily available real-world data sets will be analyzed using supervised and unsupervised learning methods. Prerequisite: MATH 2435, MATH 3332, MATH 3450 or PSYC 3433.

Appropriate visualizations of data are a key to revealing patterns and communicating important findings in research. This course will build on statistical and analytical thinking by emphasizing the role and use of visualizations in the analysis of data. Theories, techniques and software for managing, exploring, analyzing, displaying and communicating information about various types of data will be introduced. Visualizations will be produced using readily available real-world data sets. Prerequisites: MATH 2435, or MATH 3332, or MATH 3450, or PSYC 3433, or instructor approval.

Junior division treatment of selected topics of mutual interest to the faculty member and students. Prerequisite: Department Consent.

Basic concepts leading to advanced applications in biostatistics. Topics include study design, data collection, descriptive statistics, probability and probability distributions, confidence intervals, hypothesis testing, power of statistical tests, and simple regression with an emphasis on applications in the biomedical sciences and biomedical research. Data will be analyzed using statistical software packages. Students may be required to register for MATH 1050 for this course.

Junior division treatment of selected topics of mutual interest to the faculty member and students. Prerequisite: Department Consent.

Student research on a selected problem in the field pursued under the guidance of an assigned member of the faculty. Prerequisite: consent of chair.

Upper–division treatment of selected topics of mutual interest to the faculty member and students. Prerequisite: consent of chair.

Student research on a selected problem in the field pursued under the guidance of an assigned member of the faculty. Prerequisite: consent of chair.

Upper–division treatment of selected topics of mutual interest to the faculty member and students. Prerequisite: consent of chair.

Introduction to concepts and methods basic to real analysis. Topics such as the real number system, sequences, continuity, uniform continuity, differentiation, infinite series and integration. Prerequisite: Math 2341.

Continuation of Math 4331 covering such topics as uniform convergence and functions of several variables. Strongly recommended for students planning to enter graduate school or secondary teaching and those interested in applied mathematics. Prerequisite: MATH 4331.

The basics of point–set topology. Open and closed sets, limit points, topological spaces, countability, compactness, connectedness, metrics and metric topologies. Prerequisite: MATH 2431 and MATH 3334

Calculus of a function of a complex variable. Prerequisite: MATH 2431

Fundamental algebraic systems including groups, rings and fields. The structure of a system as a set with its operations and relationships between systems. Prerequisite: MATH 3360.

Direct products, Sylow theory, ideals, extensions of rings, factorization of ring elements, modules, and Galois theory. Prerequisite: MATH 4338.

Continuation of Math 2341. Linear transformations and similarity, eigenvalues and diagonalization, complex vector spaces, unitary and self–adjoing matrices, Spectral Theorem, Jordon canonical form. Selected topics in linear programming, convexity, numerical methods, and functional analysis. Prerequisites: MATH 3334.

Mathematical formulation of physical laws. Existence and uniqueness for Cauchy and Dirichlet problems; classification of equations; potential–theoretic methods; other topics at the discretion of the instructor. Recommended for students interested in applications of mathematics and engineering. Prerequisite: MATH 2343.

This course provides an introduction to developing mathematics models from real world situations through discussion of a series of examples, and hands-on exercises and projects that make use of a range of continuous and discrete mathematical tools.

Application and extension of Biostatistics I with a focus on advanced statistical concepts which recur in biomedical research literature; multiple regression, logistic regression and survival analysis. Other topics may include time series analysis and clinical trials. Practival experience with the widely used statistical research software package R. Emphasis on realistic data typically encountered in applications of biostatistics.

The student will work with faculty supervision and undertake a research project. The project will culminate in a tangible product such as a paper, a presentation or a research poster.

Advanced methods and/or applications of material learned in statistics courses. May be repeated for credit.

Student research on a selected problem in the field pursued under the guidance of an assigned member of the faculty. Prerequisite: consent of chair.

Upper–division treatment of selected topics of mutual interest to the faculty member and students. Prerequisite: consent of chair.

Student research on a selected problem in the field pursued under the guidance of an assigned member of the faculty. Prerequisite: consent of chair.

Upper–division treatment of selected topics of mutual interest to the faculty member and students. Prerequisite: consent of chair.

An introduction to programming and using Python, a modern programming language used in data science. Computational will be emphasized through solving problems by writing and testing and debugging programs.

Fundamental statistical concepts used in data science, including types of data, the collection of data, summarizing data, estimation and an introduction to hypothesis testing.

Data analytics is a process that turns data into usable information for answering questions. This course will introduce the process of acquiring, managing and analyzing data. Readily available real-world data sets will be analyzed using supervised and unsupervised learning methods.

Appropriate visualizations of data are a key to revealing patterns and communicating important findings in research. This course will build on statistical and analytical thinking by emphasizing the role and use of visualizations in the analysis of data. Theories, techniques and software for managing, exploring, analyzing, displaying and communicating information about various types of data will be introduced. Visualizations will be produced using readily available real-world data sets.

Organization concepts and terminology of data models and the underlying data structures needed to support them. Presentation of the relational database management system including an introduction to SQL programming, normalization and database design. Introduction to the programming interface to databases.

Fundamentals of the research process including formulating questions to assess data needs, determining how to collect and manage the necessary data, and putting results in the correct context.

The analysis of data using linear and non-linear regression models, including techniques for building models and diagnostics for assessing models.

An examination of algorithmic bias, legal and privacy issues about data that arise in the phases of a data science project and how data is related to social issues. Case studies from various disciplines will be used to explore these issues.

The tools and techniques of managing and analyzing big data will be covered. Students learn how to use cloud services and data mining techniques for analyzing big data.

An overview of the key concepts of machine learning through practical examples and applications. Programming projects will be used for learning techniques, for interpreting results and understanding scaling up from thousands of records to millions/billions.

Hands-on experience as a part of a data science team covering all phases of a data science project, with a focus on the design and data collection phases.

A continuation of the hands-on experience, with a focus on the analytics phase. Teams will present their results to the stakeholders.