Plane geometry was my favorite math course in high school because I liked pictures by hI14064W

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									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 thayer@tcnj.edu 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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