## Scholarships

$40,000 Scholarships are available in mathematics and statistics with CPaMS Scholars

This course provides a review for students whose mathematical skills are weak and need to improve their abilities prior to taking MA109 (Precalculus) or ST110 (Introduction to Statistical Methods and data Analysis). Sets, polynomials, algebra of fractions, linear equations, inequalities of one variable, exponents, radicals, complex numbers, graphing equations, inequalities of two variables, systems of equations, and other selected topics.

Note: No college credit is earned by taking this course.

Can you figure out the following message? DOO DUH ZHOFRPH? This message is an example of a cipher. There are a wide variety of different schemes for creating ciphers; in fact, one of the earliest known methods was used by Julius Caesar. The course will focus on those schemes that have a mathematical basis. We will begin with Caesar's method and end with a scheme currently used for security on the Internet. The mathematics used will be elementary and will be developed in the course.

"This sentence is false." Does this statement make any sense?

Why is 1 not a prime number?

These questions, and even more interesting ones, will be answered as we examine reasoning and logic (inductive and deductive) in a mathematical setting. We will also look at the nature of numbers, including types of numbers and differences among kinds of numbers. We will examine the uses of numbers in real world applications such as interest, installment buying, amortization, etc. We will also look at the fascinating world of probability. For example, how many people have to be in a room so that the chances of two of them having the same birthday not counting the year are 50-50?

The philosopher Proclus described mathematics as "the invisible form of the soul." In this course, you will experience mathematics in ways that you never thought possible. We will discover the power and beauty of mathematics by exploring some very intriguing ideas. Simultaneously, we will learn effective strategies for thinking and making decisions in our everyday lives. Some of the topics we will examine are: the beauty of numbers (What does the number of spirals on a pineapple have to do with rabbits?), infinity (Are some infinities larger than others?), modular arithmetic (On what day of the week will your birthday fall in 2057?), and financial management (How much do you need to save each month if you want to have $5000 saved up when you graduate?).

**Prerequisites:** The only prerequisites for this course are an open and curious mind and the willingness to put aside any preconceived prejudices or dislikes for mathematics.

This course surveys the development of mathematical ideas throughout history. We will discuss and analyze mathematical concepts, critical thinking and problem solving from a historical point of view. Topics include the historical development of numbers, calculations, geometry, algebra, and the concept of infinity in various civilizations with specific emphasis on developments in Europe, Egypt, Mesopotamia, Greece, India, and China. We will also connect the history of mathematics to other fields such as the natural and applied sciences, social sciences and business.

**Prerequisite:** The focus of this course will be to fulfill the core mathematics requirement of the students. Thus it will serve the needs of a wide range of students. The prerequisite will be an interest in mathematics and exposure to algebra and plane geometry.

This is the course for students intending to take Applied Calculus (MA 151) or Calculus I (MA 251), which will allow review of several fundamental elements necessary for Calculus. These reviews include factoring, exponents and radicals; equations and inequalities; functions and relations including algebraic, exponential, logarithmic and trigonometric functions.

**Prerequisites:** 56 or better on Math Placement Test or math SAT of 560 score or better or math ACT score of 24 or better.

This course does not fulfill the mathematics core requirement. It is offered Fall and Spring Semesters.

An introductory statistics course requiring no calculus. Statistical methods are motivated through real data sets. Topics include graphical summaries of data, measures of central tendency and dispersion, chi-squared tests, regression model fitting, normal distributions, and sampling.

**Prerequisite:** MA004 or a score of 56 or better on Part I of the Math Placement Test or a math SAT score of 560 or better or a math ACT score of 24 or better or any other MA100-level course.

Offered Fall and Spring semesters.

A one semester calculus that stresses applications in business and social sciences. Every concept is considered graphically, numerically, algebraically and verbally. Graphing calculators are used to help students learn to the think mathematically. This is a terminal course so if you plan on taking more mathematics and/or minoring in mathematics or statistics, you should take MA 251 instead.

**Prerequisite:** MA 109 or a score of 48 or better on Part II of the Math Placement Test.

Offered Fall and Spring semesters.

A non-calculus-based course covering descriptive statistics, regression model fitting, probability, normal, binomial, and sampling distributions, estimation, and hypothesis testing.

ST210 is not open to students who have already taken ST265, ST/EG381, PY292, or EC220.

**Prerequisite:** MA109 or a score of 48 or better on Part II of the Math Placement Test or one year of high school calculus.

Definition, interpretation, and applications of the derivative and definition and interpretation of the integral are studied.

**Prerequisite:** MA 109 or 56 or better on Part II of the Math Placement Test

Offered Fall and Spring semesters.

A continuation of Calculus I. Techniques and applications of integration, parametric equations, polar coordinates, sequences and series will be studied.

**Prerequisite:** MA 251

Offered Fall and Spring semesters

A non-calculus-based course covering descriptive statistics, regression model fitting, probability, distributions, estimation, and hypothesis testing. Applications are geared toward research and data analysis in biology and medicine.

ST265 is not open to students who have already taken ST210, ST/EG381, PY292, or EC220.

**Prerequisite:** MA109 or a score of 48 or better on Part II of the Math Placement Test or one year of high school calculus.

This course is intended mainly for Biology majors. It is offered only in the Spring Semester.

Boolean algebra, combinatorics, inductive and deductive proofs, graphs, functions and reflections, recurrence.

**Prerequisite:** CS201, MA109 or a score of 56 or better on Part II of the Math Placement Test or one year of high school calculus.

This course is limited to Computer Science Majors and Minors and is also listed as CS 295. It is offered only in the Fall Semester.

In your video games, what makes Mario jump over the barrel? Linear Algebra! In the airline industry, what technique helps to optimize the scheduling process? Linear Algebra! In the economic world, what technique helps to minimize costs? Linear Algebra! It is the "bread and butter" of mathematics as much as calculus is. In high school, you saw linear algebra. Remember the old "two equations, two unknowns" problems? That was linear algebra. But in the real world, there are 3,000 equations and 5,000 unknowns! That is LINEAR ALGEBRA!!

**Prerequisite:** MA 252.

This course is required for the major and is usually taken in the sophomore year. It is only offered in the Spring Semester.

The basics of MATLAB programming are covered through the investigation of various mathematical topics, including functions, conditional statements, loops, and plotting.

**Prerequisites:** CS201.

**Pre/Corequisite:** MA301

This is an introductory course in ordinary differential equations (ODEs) and their application in modeling physical phenomena. In particular, the following topics are covered: first and second order ODEs, separable ODEs, existence and uniqueness of solutions, and numerical solutions (using software such as MATLAB). Modeling plays a crucial role in the course, as do applications to other disciplines.

**Prerequisite:** MA 351 or MA252 and written permission of the instructor.

This course is only offered in the Spring Semester.

This course is a continuation of MA 252 and covers multivariable calculus. Topics covered: vectors and their geometry, parametric curves, functions of several variables, partial derivatives, multiple integrals, and the course climaxes with the big theorems, namely the divergence theorem, Stokes' theorem and Green's theorem.

**Prerequisite:** MA 252.

This course is required for the major and is usually taken in the sophomore year. It is offered only in the Fall Semester.

A laboratory course in the use of the Statistical Analysis System, a statistical software package that is widely used throughout governmental, business, industrial, scientific, and academic sectors. Proficiency in using SAS for data management, analysis, and reporting is developed. The course reviews statistical methodology while focusing on developing computing experience and extensive project work.

**Prerequisite:** EC220 or ST/EG381 or ST210 or ST265 or PY292

This course is required for statistics majors and statistics minors. It is offered only in the Fall Semester of odd numbered years.

Note: This is the same course as EG381. Random experiments, probability, random variables, probability density functions, expectation, sample statistics, confidence intervals, and hypothesis testing.

**Prerequisites:** MA252.

Degree credit will not be given for more than one of ST210, ST265, and ST/EG381. This course is offered only in the Fall semester.

The logic of compound statements, introduction to proof, mathematical induction, set theory, counting arguments, recurrence relations, permutations and combinations. An introduction to graph theory including Euler and Hamiltonian circuits and trees. Applications may include analysis of algorithms and shortest path problems. Problem solving is stressed.

**Prerequisite:** MA 252.

This course is required for the major and is usually taken in the sophomore year. It is offered only in the Fall Semester.

Calculus is an important tool (perhaps the most important) in applied mathematics and in order to apply Calculus successfully it is important that a thorough understanding of Calculus is achieved. In Analysis I we will explore the definitions and rigorously prove many of the results used in differential and integral Calculus, and thus the course will have a theoretical component. The ideas and methods explored play a fundamental role in many applied mathematical areas such as ordinary differential equations, probability theory (and thus statistics), numerical analysis, and complex analysis.

**Prerequisites:** MA 395

This course is required for the major and is usually taken in the junior year. It is offered only in the Fall Semester.

This course is a continuation of Analysis I. We will finish off any unfinished business about functions of 1 variable, including sequences and series of functions. We will then talk about functions from Rn to Rm and what differentiation and integration means in the context of different combinations of values for n and m. For example, functions from Rn to R were studied in Calculus III, leading to partial derivatives and multiple integrals. Functions from R to R3 describe curves in space. Functions from Rn to Rm where n and m are both greater than 1 are new and will be discussed.

**Prerequisites:** MA351 and MA 421

This course is required for the Pure Mathematics Concentrations; it may be used for the Statistics, Operations Research, Secondary Education and General Program Concentrations. It is offered only in the Spring Semester of even numbered years.

The subject of Complex Analysis has both pure and applied components. On one hand, one can think of complex functions as natural extensions of real functions. We will study the topology of the complex plane as we define the concepts of complex functions, the derivative and integral. On the other hand, complex functions are often used to solve problems in a wide variety of applied areas such as electrical engineering (e.g., electric circuits) and physics (e.g., air flow around an airplane wing). While applications will be introduced, our main focus will be on understanding the mathematical concepts.

**Prerequisites:** MA 351

This course, along with MA428, will emphasize the development of numerical algorithms to provide stable and efficient solutions to common problems in science and engineering. MA 427 topics include direct and iterative methods appearing in linear algebra, root finding methods, and interpolation.This is an introductory course in numerical analysis, the study of methods for obtaining approximate values of mathematically-defined quantities. Since most uses of mathematics in modern day society involve numerical approximation, this course is essential for any student who wishes to work in an area which involves applied mathematics.

**Prerequisites:** MA301, MA302, or written permission from the instructor.

This course, along with MA427, will emphasize the development of numerical algorithms to provide stable and efficient solutions to common problems in science and engineering. MA 428 topics include numerical differentiation, initial value problems, two point boundary value problems, and partial differential equations.

**Prerequisites:** MA302, MA304, or written permission from the instructor.

A review of Euclidean geometry and an introduction to non-Euclidean geometry. Rigorous deduction and axiom systems are emphasized. Possible techniques include the use of coordinate geometry, linear algebra, and computer geometry systems.

**Prerequisite:** MA 395.

This course is offered only in the Spring Semester of even numbered years.

An investigation of the fundamental algebraic systems of integers, rings, polynomials, and fields. Topics drawn from homomorphisms, cosets, and quotient structures.

**Prerequisites:** MA 301, MA 395

An investigation of the fundamental algebraic system of groups. Topics include homomorphism, cosets, and quotient structures. May include applications, Sylow theory, combinatorics, coding theory, Galois theory, etc. (Spring only) (Odd Years)

**Prerequisites:** MA 301, MA 395

A deeper study of matrices - their properties and uses. Topics include eigenvalues and eigenvectors, special factorizations of matrices, and computational algorithms involving matrices. This looks to be a nice blend of theory and applications.

**Prerequisites:** MA 301

This course may be used for the Statistics and the Operations Research Concentrations. It is offered only in the Fall Semester of even numbered years.

Number Theory deals with properties of whole numbers and is one of the oldest and most fascinating branches of mathematics. Topics include prime numbers and the mystique surrounding them, modular arithmetic and its uses, and equations, solutions of which must be integers. Public-key cryptography and integer arithmetic on computers provide some applications. A nice blend of theory and practice.

**Prerequisite:** MA 395.

This course is the first in the two semester sequence of probability and mathematical statistics. Probability, discrete and continuous distributions, moment generating functions, multivariate distributions, transformations of variables, and order statistics.

**Prerequisites:** ST 210 or ST265 or ST/EG381 or EC220 or PY292; MA 351.

It is offered only in the Fall Semester of even numbered years

A continuation of ST461. Theory of estimation and hypothesis testing, the central limit theorem, maximum likelihood estimation, Bayesian estimation, and the likelihood ratio test.

**Prerequisite:** ST 461.

It is offered only in the Spring Semester of odd numbered years.

Concepts and techniques for experimental research including simple, logistic, and multiple regression, analysis of variance, analysis of categorical data.

**Prerequisites:** ST 210, or ST 265, or ST/EG381 or EC 220 or PY292

**Corequisite:** ST 365 (for statistics majors and statistics minors)

It is offered only in the Fall Semester of odd numbered years.

A continuation of ST465. The theory of linear models and its relationship to regression, analysis of variance and covariance. Coverage of interaction, blocking, replication, and experimental designs: split-plot, nested, and Latin squares.

**Prerequisites:** MA 301; ST 365; ST 465.

It is offered only in the Spring Semester of even numbered years.

Quality has become an integral part of the lives of both the consumer and the producer. Covered topics include the ideas of W. Edwards Deming; six sigma; Shewhart concepts of process control; control charts for attributes and variables; CUSUM, EWMA, and MA charts; and factorial experimental designs.

**Prerequisites:** ST 210 or ST265 or ST/EG381 or EC 220 or PY292.

This course will be offered in the Fall of 2014 and next in Fall 2017.

Applications of multivariate statistical methods including: principal components, factor analysis, cluster analysis, discriminant analysis, Hotelling's t-square, and multivariate analysis of variance. An applied journal article is read and summarized verbally, in written form, and rewritten form. A final course project, based on an original study, is presented verbally, in written form, and rewritten form.

**Prerequisites:** Sophomore standing; ST 210 or ST265 or ST/EG381 or EC 220 or PY292 or written permission of the instructor.

This course is offered in the Spring Semester of even numbered years.

R is a free software environment for statistical computing and graphics that is used extensively in academia. Computing topics in R include loops, conditional statements, input/output of data, statistical and graphical functions, simulation, bootstrapping, and permutation tests. Survival topics include hazard functions, survival functions, types of censoring, contingency tables analysis, relative risk, odds ratios, Cochran-Mantel-Haenszel methods, life table analysis, Kaplan-Meier methods, Cox proportional hazards models, and Poisson regression. Parametric methods and various nonparametric alternatives are discussed. (Fall only) (Even Years)

**Prerequisite:** ST 210

This course will investigate mathematical techniques for determining optimal courses of action for decision problems under restrictions of limited resources. These techniques include the simplex algorithm, the traveling salesman algorithm, branch and bound algorithm, shortest route algorithm.

**Prerequisite:** MA 301

This course is required for the Operations Research Concentration. It is offered only in the Fall Semester of odd numbered years.

The fundamental concepts of random phenomena including: Bernoulli processes, Markov chains, Poisson processes, queuing theory, inventory theory, and birth-death processes. Applied and theoretical assignments computer simulation.

**Prerequisites:** ST 210, or ST 265, or ST/EG381 or EC 220 or PY292; MA 301.

It is offered only in the Spring Semester of odd numbered years.

The fundamentals of graphs will be discussed. Topics may include graphs, trees, connectivity, Eulerian circuits, Hamiltonian cycles, vertex and edge colorings, planar graphs, and extremal problems.

Prerequisite: MA395 or permission of the instructor.

This course will provide an introduction to classical and modern cryptology. We will study methods to encrypt messages to keep the contents secret, methods to attack these encryption schemes, and the mathematics underlying these methods.

Prerequisite: MA 301.

Nonlinear programming deals with the problem of optimizing an objective function in the presence of equality and inequality constraints. If all the functions are linear, we have a linear program. Otherwise, the problem is called a nonlinear program. In this course, we will study Unconstrained Optimization, Convex Sets and Convex Functions, Convex Programming and the Karush-Kuhn-Tucker Conditions.

Note: this course is the foundation of nonlinear programming, computer skill is not required. Students may be asked to do one final project using MATLAB.

Prerequisite: MA 301(Linear Algebra) and MA 351 (Multivariable Calculus).

An introduction to topology. Topics include metric spaces, general topological spaces, open and closed sets, bases of topologies, continuity, connectedness, compactness, product and quotient spaces and Urysohn's metrization theorem.

Prerequisite: MA 395 or permission of instructor.

This course will build on mathematical models of stock and bond prices to cover two major areas of mathematical finance that have an enormous impact on the way that modern financial markets operate:

The Black-Scholes arbitrage pricing model of options and other derivative securities;

Financial Portfolio Optimization Theory due to Tobin and Markowitz, and the Capital Asset Pricing Model.

Prerequisite: A very basic familiarity with probability, statistics, and calculus (MA252 and ST210).

Remember when you first learned 1, 2, 3,... Now, years later, you have powerful mathematical tools at your command that will allow you to count more than apples: permutations, partitions, (mathematical) trees, strings, and uncountably more. We will also look at graphs, cliques, probability, existence and external problems as time permits. The course will focus on problem solving. Some of the tools we will study are the pigeon-hole principle, inclusion-exclusion, generating functions, and recursion. The material learned in this course and more importantly the thought processes can be useful in any mathematical field from the most basic to the graduate level. Combinatorics has applications to Computer Science, Statistics, and much more.

Prerequisite: MA 395 or permission of instructor.

We will study a variety of types of partial differential equation and learn techniques to solve them. The emphasis will be on exact techniques but some discussion of numerical techniques will be included. Applications will be emphasized.

$40,000 Scholarships are available in mathematics and statistics with CPaMS Scholars