Department of Mathematics and Statistics Course Options for Spring 2012 Semester MAT 317: Linear Programming – Spring 2012 – Professor Richard Thayer Operations Research is a field devoted to the solutions of problems in optimization. It can be roughly divided into two parts: Linear Programming and Applied Probability (STA318 - OR at TCNJ). Linear Programming deals with the problem of maximizing or minimizing a linear function subject to a set of linear constraints. Areas as diverse as finance, the military and medicine extensively exploit the mathematical techniques and theory of linear programming. The field is important to many businesses because it allows complex problems to be represented in the form of mathematical models that can be solved in reasonable amounts of time through the use of efficient algorithms. Major corporations have departments devoted to the applications of Operations Research and Linear Programming, in particular. This course provides an introduction to the algorithms, theoretical underpinnings, and applications of linear programming. Topics may include: the simplex method for solving a linear program (LP), the geometry of LPs, variants of the simplex method, constructing mathematical models using LPs, duality theory, sensitivity analysis, integer programming, transportation and trans-shipment models, network models, program management models, and solving LPs using modern software packages (Excel, LINDO, LINGO, AMPL or MATLAB). Connections to Linear Algebra will be highlighted where relevant. Because the subject matter is based in Linear Algebra and does not utilize calculus, a simplified version is frequently taught in high school mathematics courses. A more extensive discussion is contained in the Syllabus which has been recently updated. If anyone would like to speak with me about the course, you can reach me via Email at firstname.lastname@example.org and I have office hours this semester in the computer lab from 1 – 2pm on Tuesday and Friday. MAT 326: Differential Equations – Spring 2012 – Dr. Leona Harris Prerequisite/Co-requisite: The prerequisite for this course is MAT 128. There is also a co- requisite or prerequisite requirement of MAT 205 or PHY 306, which means that students should take one of these courses either before or while taking MAT 326. Differential equations are used to model the world around us. Understanding the properties of solutions to differential equations is fundamental to the field of applied mathematics. This course provides an introduction to the theory, solution techniques, and applications of ordinary differential equations. Students will develop an intuitive feeling for the approach, creation and formulation of a mathematical model using differential equations that addresses a problem with a real-world application. Course topics will include: solutions to first-order linear and nonlinear (ordinary) differential equations by analytical, qualitative and numerical methods; mathematical modeling with differential equations; solutions to second-order linear differential equations; power series solutions of differential equations; existence and uniqueness theorems; systems of differential equations including the connection to linear algebra, stability theory and phase plane analysis. MAT 453: Seminar in Analysis – Spring 2012 – Dr. Judit Kardos Plane geometry was my favorite math course in high school because I liked pictures and enjoyed proving theorems but hated manipulating formulas. I had an inherent fascination with the concept of the infinite from early on but could not care less if any of the beautiful mathematics would ever find applications. If you share some of my personal traits, real analysis could be your cup of tea. In this course you will continue to build an appreciation for the many uses of the limit concept, from sequences and series of functions to integration. We will provide a certain amount of historical perspective to motivate abstract theories by difficult problems they were intended to solve. We will avoid generalizations for their own sake and proofs that appear magical. Instead, we will stay with the concrete, motivate proofs and draw lots of pretty pictures. Our goal is to focus our attention on questions that give analysis its inherent fascination. If a function has a positive derivative at a point does it have to be locally increasing in a neighborhood of that point? Is there a function that is continuous at the rationals but continuous everywhere else? Are derivatives continuous? Is an infinitely differentiable function the limit of its Taylor series? The course provides the necessary background for graduate analysis courses. It is also my secret hope that l will be able to sweeten the practice by helping you fall in love with the study of analysis." MAT 454: Partial Differential Equations – Spring 2012 – Dr. Karen Clark Prerequisite/Co-requisite: The prerequisite for this course is MAT 326 Differential Equations. In this course we will begin by studying in more depth Laplace Transforms and series solutions, which are two topics that may have been covered briefly in Differential Equations. From here we will explore Fourier series, which are ways of expressing functions as a sum of trigonometric functions. These series will be used in our analysis of Partial Differential Equations, which are differential equations that contain partial derivatives. We will study in depth three classic Partial Differential Equations – the wave equation, the heat equation, and Laplace’s Equation. The heat equation describes heat flow through a wire whose ends are kept at a constant temperature. The wave equation describes the motion of a vibrating string. Laplace’s Equation describes steady state temperature in a region. We will investigate how we can determine solutions to these fundamental equations. At the end of the course we will consider numerical solutions to Partial Differential equations and students will be expected to approximate solutions numerically. No prior computing experience is expected. As this is a 400 level seminar, students will be assigned several projects during the course of the semester, in addition to weekly homework, two in-class exams, and a final examination. STA 303: Design of Experiments – Spring 2012 – Dr. David Holmes The course will introduce students to problems and techniques inherent to the design of experiments. Design of experiments refers to the process of planning an experiment so that appropriate data will be collected that can be analyzed by statistical methods, resulting in valid and objective conclusions. This course will cover the two aspects to any experimental problem, the design itself and the analysis of the resulting data. There are broad applications across numerous disciplines in the sciences and the humanities. Statistical software packages are essential to the course and will be used throughout. STA 307: Data Mining and Predictive Modeling – Spring 2012 – Dr. Chamont Wang Prerequisite/Co-requisite: Course prerequisite is ONE of the following: (1) BIO-352, (2) CSC-320 and STA-215, (3) ECON-231, (4) MAT-316, (5) PSYC-303, or (6) any 300-level Stat course. Data mining is a field of study on mathematical models and algorithms originated from different disciplines including statistics, machine learning, fuzzy logic, and evolutionary computation. MIT Technology Review (Jan/Feb/2001) and Bayesian Machine Learning (Feb, 2004) ranked data mining as one of the ten emerging technologies that will change the world. Techniques of data mining have been used successfully in science, engineering, business intelligence, biomedical research, political campaign, data base marketing, and educational data mining. The US federal government also has very extensive efforts on data mining, including government services and homeland security (see, e.g., http://www.gao.gov/new.items/d04548.pdf). The primary goal of this course is to introduce students to a variety of statistical techniques that are widely used in modern data mining. The techniques include decision trees, link functions, random forest, profit/loss matrix, text mining, market-basket analysis, fraud detection, and dynamic data visualization. Computer technology will be used extensively throughout the semester.
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