Lecture Slides for AMSC/MATH 420: Spring 2016
Mathematical Modeling

Title	Version	Date of Lecture
General Topics
1. Fitting Linear Statistical Models to Data by Least Squares: Introduction	January 27	January 28
2. Covariance Matricies	February 21	February 18
Portfolios that Contain Risky Assets
Part I: Portfolio Models (New)
1. Risk and Reward	March 21	February 4
2. Covariance Matrices	March 21	February 18 and 25
3. Markowitz Portfolios	March 21	February 9
4. Solvent Portfolios	March 21	February 9 and March 8
5. Leveraged Portfolios	March 21	March 8 and 22
6. Basic Markowitz Portfolio Theory	March 21	February 9 and 23
7. Unlimited Portfolios with Risk-Free Assets	March 21	February 23 and March 1
8. Long Portfolios without Risk-Free Assets	March 21	March 1
9. Long Portfolios with a Safe Investment	March 21	March 3
Part II: Stochastic Models
1. Indenpendent, Identically-Distributed Models	March 23	March 22 and 24
2. Growth Rate Mean and Variance Estimators	March 27	March 29
3. Law of Large Numbers (Kelly) Objectives	April 7	March 29 and 31
4. Kelly Objectives for Markowitz Portfolios	April 7	April 5 and 7
8. Fortune's Formulas	April 18	April 14 and 19
Part I: Portfolio Models (Old)
1. Risk and Reward	February 17	February 4
2. Markowitz Portfolios	March 11	February 9
3. Basic Markowitz Portfolio Theory	March 11	February 9 and 23
4. Portfolios with Risk-Free Assets	March 11	February 23 and March 1
5. Long Portfolios	March 9	March 1
6. Long Portfolios with a Safe Investment	February 29	March 3
7. Survey of Portfolio Models	March 11	March 8 and 22
Pattern Classification
1. Data Representation	February 2	February 2
2. Introduction to Data Classicification	February 2	February 11
3. Introduction to Maching Learning Project	February 2	February 11

Background Material on Linear Algebra: Linear Algebra and Its Applications, Fifth Edition, by David C. Lay, Steven R. Lay, and Judi J. McDonald, Pearson, 2016.
This is the standard text for MATH 240 and 461. It (or an earlier edition) covers all the linear algebra that you need for this course.
Chapter 6 covers some of the material from the first two lectures on fitting.

Background Materials on MATLAB:

• Math 241 MATLAB Materials, by Jonathan Rosenberg
  A brief introduction with examples of graphing commands.

• Getting Started with MATLAB and Simulink Student Version, by Mathworks
  This is a free on-line set of tutorials.

• Chapter 1 of Numerical Computing with MATLAB, by Cleve Moler
  This is a good general introduction to MATLAB.

• MATLAB: An Introduction with Applications, Fourth Edition, by Amos Gilat
  J. Wiley and Sons, New York, 2011
  

• An Introduction to MATLAB for Engineers, by William J. Palm III
  McGraw-Hill, New York, 2010
  

• Getting Started with MATLAB, A Quick Introduction for Scientists and Engineers, by Rudra Pratap
  Oxford University Press, New York, 2009
  (There may be some differences between the MATLAB described in this book and versions 2009b or later.)

• Essentials of MATLAB Programming, Second Edition, by Stephen J. Chapman
  Cengage Learning, Stamford CT, 2009
  (This book covers more advanced material than is needed for this course.
  This is based on MATLAB 7. I do not know if it is current with version 2009b or later.)