## Mathematics Courses

MATH135. Mathematical Modeling of Finan

A mathematical investigation of elementary personal finance. Students will make use of the mathematics of sequences, series, linear and exponential functions, and regression modeling to investigate financial concepts such as simple interest, compound interest, annuities, and consumer loans, Additional topics may include stocks and bonds; the geometric simplex method; basic probability, Markov chains, and game theory. Emphasis will be placed on applications that help individuals plan for personal financial success. Computer software such as Microsoft Excel will be used throughout. FQRC, WI. 3 credits.

MATH155. Overview Statistical Reasoning

An introductory statistics course focusing on the interpretation of quantitative information in statistical reports.  This course is designed to give students an overview of the tools and foundations of statistical reasoning and how this form of logical argumentation is used in society to solve problems and make decisions. Topics include the summarization and visualization of qualitative & quantitative data in 1 & 2 dimensions, measures of center, spread & association, exploratory data analysis, the framework of the null hypothesis statistical test, estimation with confidence intervals, and measures of effect. Emphasis is on the development of statistical thinking, the critical analysis of when statistical reasoning is appropriate in authentic scenarios, and the interpretation of statistical results. FQRC. WI. 3 credits.

MATH164. Precalculus

A study of polynomial, rational, exponential, logarithmic, and trigonometric functions; conic sections; and their applications in order to prepare students for calculus. FQRC, WI. 4 credits.

MATH171. Statistical Decision Making

An elementary statistics course designed to give students a working knowledge of the ideas and tools of practical statistics and their usefulness in problem solving and decision making. topics include graphical displays of data, measures of central tendency and variability, sampling distributions, and confidence intervals and hypothesis testing for means and proportions. Additional topics may include elementary probability concepts, correlation and regression, or Chi Square analysis. Special emphasis is placed upon the proper use and interpretation of statistics in real life situations. 3 credits. FQRC, WI.

MATH175. Discrete Mathematics

An introduction to subjects in discrete mathematics including elementary set theory, logic, counting, probability and graph theory. 2 credits.

MATH1QR. Math QR Transfer Pillar

Math QR Pillar Course

MATH1XX. Math Elective

MATH261. Differen and Int Calculus I

The first semester of an introduction to the calculus of algebraic and transcendental functions, including limits, continuity, derivatives and antiderivatives, methods of differentiation, and applications of the derivative. Prerequisite: MATH 164 with a C- or better. 4 credits.

MATH262. Differen and Int Calculus II

A continuation of calculus topics, including techniques of integration, applications of integration, sequences, power series, and Taylor series. Prerequisite: MATH 261 with a C- or better. 4 credits.

MATH275. Prob & Bayesian Stats I

The Bayesian framework for data analysis is carefully examined with an emphasis on model likelihoods and prior and posterior distributions.  Simple probability models (binomial and normal distributions) will be examined with an emphasis on marginal and conditional probability and Bayes’ Theorem.  Topics include conjugate and non-informative priors; single- and multi-parameter models; and Bayesian computation methods: Markov-chain Monte-Carlo simulation and Gibbs sampler.  Frequentist and Bayesian approaches to hypothesis testing and statistical inference are compared.  This course is the first of a two-course sequence and requires some coding using appropriate statistical software. Pre-requisites: MATH 171 and MATH 175, both with grade of C- or higher. 3 credits.

MATH280. Linear Algebra

A basic study of vector spaces, linear transformations, and their relationships to matric algebra. Also included are determinants, eigenvalues, and eigenvectors. Prerequisite: MATH 261. 3 credits.

MATH292. Internship in Mathematics

An on-the-job learning experience designed to apply the principles of mathematics. 1-3 credits.

MATH295. Special Topics Mathematics

Selected topics in mathematics. The topics may vary from semester to semester. May be repeated for credit when topics change. 1-3 credits.

MATH2QR. Math QR Transfer Pillar

Math QR Pillar Course

MATH2XX. Math Elective

MATH300. Proofs and Number Theory

Mathematical proof techniques through the lens of introductory number theory. Topics include relations, mathematical induction, recursion, divisibility, prime numbers, and congruences. Prerequisite: MATH 175 and MATH 262 both with grades of C- or better. It is also strongly recommended that a student have a C- or better this course before proceeding with future MATH coursework. 3 credits.

MATH301. Applied Statistics

Topics include one-way and two-way analysis of variance, correlation and linear regression, multiple linear regression, and nonparametric tests. The emphasis will be on practical applications of these techniques and the use of computer software. Prerequisites: MATH 171 with a grade of C- or better, and either FHBS. 3 credits. PQRC, WI.

MATH304. Mathematics History

An introduction to the history of mathematics, concentrating on the period from the early Egyptians through the 17th century. The study of mathematics is Egyptian, Mesopotamian, Greek, Chinese, Indian, Islamic, and European cultures will include number and number systems, algebra, geometry, pre-calculus, probability, statistics, discrete mathematics, and calculus. Prerequisites: FQRC, FHCI, MATH 261. 3 credits. PQRC, SI.

MATH307. Intro to Math Game Theory

An introduction to mathematical game theory and its applications. Students will use mathematical game theory to model and analyze the strategic and dynamic decision-making processes involved in competitive and cooperative situations. Mathematical topics to be covered include two-person zero-sum games, two-person non-zero-sum games, backwards induction, mixed strategy games, Nash equilibria and N-person games. Emphasis will be placed on application to areas in the natural and social sciences throughout the semester.

MATH308. Math and Elections

A study of mathematical applications in elections, voting, and politics and how they can help solve problems in politics and government.  Topics include the structure of American government and elections, voting methods, apportionment, and Arrow’s Theorem. Pre-requisite: Completion of the FQRC Pillar. 3 Credits. PQRC. WI.

MATH309. Numeration Systems

Examines various numberation systems past and present, computational algorithms, basic sets of operations, elementary number theory, concepts of rational numbers, and proportional reasoning in a problem-solving environment through student investigations and hands-on activities. 3 credits.

MATH310. Probability, Stats and Program

Examines probability, descriptive statistics, graphical representations and simple computer programming in a problem-solving environment through student investigations and hands-on activities. This course will require the use of a scientific calculator and computer. Prerequisite: MATH 309. 3 credits.

MATH313. Geometry and Reasoning

Examines properties of and relationships between geometric figures, measurement, concepts of perimeter area, and volume of two- and three-dimensional figures, transformations and coordinate geometry, constructions, the Pythagorean Theorem and trigonometric ratios, and geometric reasoning both deductive and inductive in a problem-solving environment through student investigations and hands-on activities. Prerequisite: MATH 309. 3 credits.

MATH313. Geometry and Reasoning

A basic study of polygons, polyhedra, measurement, transformational geometry, coordinate geometry, descriptive statistics, graphical methods and empirical and theoretical probabilities and their uses. 3 credits.

MATH320. International Studies Math His

The study of the mathematics of a particular culture with a focus on the historical relevance of the culture's mathematical results and its impact on later cultures. Course will provide a short-term immersion in the country (at additional cost) where the relevant mathematical developments took place. Prerequisites: FQRC, FHCI, MATH 261. 3 credits. PQRC, SI.

MATH331. Survey Instr Design & Analy

An introduction to the creation of a questionnaire instrument and the statistical tools used to analyze the resulting data.  While the study of survey research methods is a broad and widely encompassing domain that intersects with many disciplines, this course serves as a good preview of the key themes for this methodology.  By the end of this course, students will have the basic skills necessary to design, implement, and critically assess the quality of a survey instrument and resulting data and proposed conclusions.  Principal topics include the creation and evaluation of survey items, assessment of impacts of mode of administration, concepts of validity and reliability, introduction to basic principles of latent variable measurement theory, and the presentation of results from survey data.  The course has a strong pragmatic focus, culminating in the creation, administration, and analysis of a collaboratively designed survey tool. Pre-requisite: MATH 171 with grade of C- or better. PQRC. WI. 3 credits.

A study of Euclidean geometry from a more advanced viewpoint. The methods and techniques of synthetic axiomatic geometry will be stressed through a study of logic and formal proof, applied to Euclidean and non-Euclidean geometries. Prerequisite: MATH 300. 3 credits. Offered fall of odd numbered years.

MATH342. Introduction to Modern Algebra

An introduction to general algebraic structures, the course includes topics of groups, rings, fields, and relevant algebraic mappings. Prerequisite: MATH 300. 3 credits.

MATH350. Ethical Issues Math CmSc

Consideration of ethical implications of mathematics and computer science in society. Overview of ethical theory; case studies of situations illustrating ethical dilemmas. A knowledge of calculus and algorithms will be assumed. 3 credit.

MATH357. Interscts: World of Art & Math

In this course students will explore key intersections between art and mathematics in human culture. Ranging from antiquity to present times, students will connect and articulate informed perspectives on how mathematics can inspire art, as well as reflect upon the beauty of mathematics. Students will build upon content learned in the Aesthetic Expression and Quantitative Reasoning Pillars to both identify and execute artistic and mathematical expression as it directly relates to presented concepts. An emphasis will be on drawing parallels between different cultures and historical periods while investigating art and mathematics from a global perspective. Pre-requisites: Completion of FAES and FQRC. PAES. AA. 3 credits.

MATH361. Multivariable Calculus

Advanced topics in calculus will include curves and planes in three dimensions as well as differentiation and integration of multi-variable functions. Prerequisites: MATH 262 with a C- or better. 4 credits.

MATH362. Differential Equations

A study of ordinary differential equations of the first and second order, to include basic graphical, numerical, and analytic solution techniques, series solutions, eigenvalues and eigenvectors, and some applications to physics. Prerequisite: MATH 262 with a C- or better. 3 credits.

MATH372. Mathematical Prob & Stats I

A study of mathematical probability and statistics, including probability, discrete and continuous distributions, bivariate distributions, distributions of functions of random variables, and select topics in statistical estimation and tests of statistical hypotheses. Prerequisite: MATH 171, MATH 175, and either CMSC 140 or CMSC 160. Prerequisite/Corequisite: MATH 361. 3 credits.

MATH373. Exper Design & Stat Analysis

An introduction to experimental and quasi-experimental designs intended for causal inference.  In this course, students will learn how to effectively design an experiment in such a way that the statistical analysis objectively, substantively, and validly answers a given research question (given the contextual constraints of the physical or social environment).  They will also learn the statistical tools necessary to analyze the resulting data to reach their conclusions.  Statistical analysis techniques for balanced and unbalanced designs are introduced, including 1-way ANOVA, 2- and 3-way ANOVA with fixed, random, & mixed effects, hierarchically nested designs, repeated measures ANOVA, ANCOVA, and a brief introduction to general linear models and multilevel modeling.  Additional topics may include sample size estimation, power, multiple comparison protocols, MANOVA, non-parametric analyses, and response surface methods. Pre-requisite: MATH 301 with grade of C- or better. 3 credits.

MATH375. Prob & Bayesian Stats II

Bayesian statistical modeling and inference for data analysis is examined with an emphasis on model likelihoods and prior and posterior distributions.  Common models for both univariate and multivariate data based on binomial, beta, gamma, exponential and normal distributions will be examined.  Topics include model fit assessment and comparison; single- and multi-parameter models; and Bayesian computation methods: Markov-chain Monte-Carlo simulation, Gibbs sampler, and the Metropolis-Hastings algorithm.  Additional topics may include theory of conjugate priors and missing data imputation techniques.  This course is the second of a two-course sequence and requires coding using appropriate statistical software. Pre-requisites: MATH 262 and MATH 275 with a grade of C- or higher; and CMSC 140 or CMSC 160. 3 credits.

MATH390. Directed Study in Mathematics

Individualized study; recommended only when material cannot be studied through existing course offerings. Must have permission of department chair. 1-3 credits. May be repeated when topics change; no more than 6 credits.

MATH392. Internship in Mathematics

An on-the-job learning experience designed to apply the principles of mathematics. 1-3 credits.

MATH395. Special Topics In Mathematics

Selected topics in mathematics. The topics may vary from semester to semester. May be repeated for credit when topics change. 1-3 credits.

MATH420. Graph Theory

An introduction to topics in graph theory, focusing on analysis of specific applications and proofs of important theorems in the discipline. Topics include graphs, paths, and cycles; directed graphs, trees, and applications of graph theory in real world contexts. Preprequisites: CMSC 160 and either MATH 300 or CMSC 208. 3 credits.

MATH430. Tch Math Middle School

A study of current practices in middle-school mathematics teaching with emphasis on principles, techniques, and materials. Required for those planning to teach middle school mathematics. Prerequisite: MATH 309 or MAED 209. 3 credits.

MATH461. Senior Seminar in Math

A capstone course for the mathematics major focused on mathematical modeling. Students will bring to bear a variety of mathematical approaches to model real-world phenomena. Prerequisite: MATH 171, MATH 280, MATH 300, MATH 361, and senior status. 2 credits.

A theoretical approach to the real numbers and the calculus, including the study of the topology of the real numbers, sequences, limits, continuity, differentials, and derivatives. Prerequisite: MATH 300, MATH 361. 3 credits.

MATH472. Mathematical Prob & Stat II

Continued discussion of mathematical probability and statistics includes additional discrete and continuous distributions, multivariate distributions, moment-generating functions, and a theoretical approach to statistical estimation and tests of statistical hypotheses. Prerequisite: MATH 372. 3 credits.

MATH481. Complex Variables

An introduction to the fundamental concepts of complex analysis, including the complex plane, holomorphic functions, the exponential function, Cauchy Integral formula, Taylor series, Laurent series, the notion of residue, and applications in physics. Prerequisite: MATH 361. 3 credits.

MATH490. Directed Study in Mathematics

Individualized study; recommended only when material cannot be studied through existing course offerings. Must have permission of department chair. 1-3 credits. May be repeated for no more than 6 credits.

MATH492. Internship in Mathematics

A semester-long, on-the-job learning experience designed to apply the principles of mathematics. 1-18 credits.

Selected topics in mathematics that require a student to have a firm grasp of proof techniques. The topics may vary from semester to semester. May be repeated for credit when topics change. Pre-requisite MATH 300. 1-3 credits.

MATH498. Senior Thesis in Mathematics

Students conduct an in-depth project in mathematics under the direction of a faculty member and the Longwood Senior Thesis Committee. May be repeated as 499. 3 credits.

MATH499. Senior Thesis in Mathematics

Students conduct an in-depth project in mathematics under the direction of a faculty member and the Longwood Senior Thesis Committee. 3 credits.

MATH4XX. Math elective

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