Mathematics & Science Division
Undergraduate Electives
2008
_________________________________________________________________________________________
QTM2600
Linear Algebra & Dynamical Systems
This course begins with the study of the funadamental mathematical techniques used to solve systems of equations. Applications to difference equations, Markov Chains, economics and dynamical systems will be introduced. Topics include: Gaussian eliminiation, matrix algebra, determinants, and introduction to vector spaces, null spaces and linear transformations, eigenvalues, eigenvectors, and orthogonality. The computer algebra system MATLAB will be introduced and used throughout the course.
Prerequisite: QTM1300 or QTM1301
QTM2601
Applications of Discrete Math
(Advanced Lib Arts)
Discrete mathematics is used whenever objects are counted, when relationships between finite sets are studied, and when processes involving a finite number of steps are analyzed. The kind of problems solved include: How many ways are there to choose a valid password on a computer system? What is the shortest path between two cities using a transportation system? How can a circuit be designed that adds two integers? How can you send secret messages? You will learn the discrete structures and techniques (found in mathematical logic, combinatorics, graph theory, Boolean algebra, and cryptology) needed to understand and solve these problems. You will develop mathematical maturity and problem solving skills by studying models in such
diverse areas as computer science, data networking, business, engineering, chemistry, and biology.
Prerequisite: QTM1300 or QTM1301
_______________________________________________________________________________
QTM2670
Cryptology
(Advanced Lib Arts)
This course introduces students to elementary yet challenging mathematics from several
different branches of the subject including number theory, abstract algebra, matrix algebra,
probability and statistics, all of which play a role in enciphering and deciphering secured
messages. Topics covered will include a short history of Cryptology, the One Time Pad, the
Vigenere Cipher, Modern Symmetric Ciphers, Block Ciphers, Complexity and Public Key
Ciphers. As the internet becomes the primary channel for personal and commercial intercourse,
it is of paramount importance that information and transactions are protected and secure. You
will examine and evaluate various schemes for securing information and exchanges, and
simultaneously study contemporary techniques for breaking security ciphers.
Prerequisite: QTM1300 or QTM1301
_______________________________________________________________________
QTM3610
Applied Multivariate Statistics
(Advanced Lib Arts)
This course extends the modeling tools presented in prior statistics courses and focuses on the application and validation of models developed using real data in the context of finance, economics, and marketing research. Examples of applications include modeling the impact of advertising on sales, admission yields for business schools, patterns of voting behavior and a variety of survey data. This course focuses on implementing data analysis techniques using a statistical software package and interpreting the results in a decision-making environment. Emphasis is placed on understanding the limitations of modeling approaches, as well as the diversity of potential applications in business.
Prerequisite: QTM2420 or QTM2421
___________________________________________________________________________
QTM3612
Applied Data Mining & Business Analytics
(Advanced Lib Arts)
This course will examine the methods and challenges faced in competing on analytics in business. As databases become data warehouses, extracting meaningful information to successfully compete is essential. You will accomplish this by learning new techniques for data gathering and data analysis as well as in discussion with companies currently trying to turn the information in their databases into increased business opportunities. We will examine the changing data privacy landscape and learn a variety of new methodologies for finding patterns in large datasets as well as how to create data warehouses from internet data and legacy systems. Guest speakers will be executives and consultants in the field of competing analytics. We will discuss both the methodologies and software they are using as well as the ethical issues they face in using this data.
Prerequisite: QTM2420 or QTM2421
QTM3620
Operations Research
(Advanced Lib Arts)
The focus of this course is upon the development, solution, analysis, and implementation of
optimization models and their applications within business, government, education, and sports.
The topical emphasis is primarily upon mathematical programming, optimization of flows across
networks, and the interrelationships between these two classes of methodologies. The learning
process is oriented toward problem solving. There typically is a problem statement leading into
each topic followed by the construction of a mathematical model, solution of the model, and the
resulting analysis. Many of these illustrative examples are supplemented with the discussion of a
journal article relating how a larger-than-classroom scaled model has been successfully
implemented in practice.
Prerequisites: QTM2420 or QTM2421
______________________________________________________________________________________
QTM3615
Time Series Analysis & Forecasting
(Advanced Lib Arts)
This course will introduce time series models and discuss advanced forecasting methods in the
context of real financial data and decision-making situations. The objectives of the course are to
provide experience in using time series data (e.g., sales, profits, stock prices, economic
indicators, industry sector indicators) to explain the impact of various internal and external
factors and predict future trends; to provide a framework for comparing alternative forecasting
models for validity, accuracy, and feasibility; to enhance an appreciation for the limitations of
forecasting models; to provide exposure and experience in using statistical software to develop
forecasting models; and to develop skills at communicating statistical results, and inferences
effectively in a managerial context. Teamwork and professional presentation of analysis and
recommendations will be required during this course.
Prerequisite: QTM2420 or QTM2421 or permission from instructor
QTM3625
Financial Modeling using Simulation and Optimization
(Advanced Lib Arts)
This course is an introduction to quantitative techniques that enable marketing, finance, and
management professionals to make optimal decisions under uncertainty. While theoretical
background for these techniques is provided, the focus is on their applications and mastering software that is widely used in industry, such as Excel, Solver, and @RISK. Topics include simulation of important probability distributions, bootstrapping, random walks, linear and nonlinear optimization. Lectures draw on examples such as asset allocation under different definitions of risk; index tracking; scenario approaches to project and portfolio management; hedging and arbitrage; and derivative pricing.
Prerequisite: QTM2420 or QTM2421
____________________________________________________________________________________
QTM3675
Probability for Risk Management
(Advanced Lib Arts)
The fundamental objective of this course is to prepare students for the successful completion of the first level probability examination (Exam P) of the Society of Actuaries. While the necessary theory is addressed, this course focuses on problem solving, so it is well suited for any student with an interest in applied probability concepts and how they are related to a wide variety of situations within and beyond actuarial science, finance, and economics. Topics include general probability and univariate and multivariate probability distributions.
Prerequisites: QTM2420
________________________________________________________________________________________ QTM3676
Financial Mathematics
(Advanced Liberal Arts)
This course provides an understanding of the fundamental concepts of financial mathematics and how those concepts are applied in calculating present and accumulated values for various streams of cash flows for future use in reserving, valuation, pricing, asset/liability management, investment income, capital budgeting and valuing contingent cash flows. Topics include: inflation, force of interest, term structure of interest rates, equivalent measures of interest, yield rate, annuities, spot rates, forward rates, duration, convexity, immunization, and short sales. This course is designed to prepare students for Exam FM administered by the Society of Actuaries.
