Lecture Slides for AMSC/MATH 420: Spring 2019
Mathematical Modeling

Title	Version	Date of Lecture
General Topics
1. Fitting Linear Statistical Models to Data by Least Squares: Introduction	January 28	January 29
2. Fitting Linear Statistical Models to Data by Least Squares: Weighted	January 31	January 31
3. Maximizing Profit with Modeling	May 7	May 7
Discovering Structure in Data
1. From Data to Weighted Graphs, and Graph Laplacians	February 7	February 5
2. Visualization Problems and Spectral Analysis	February 11	February 12
3. Alignment Problems	February 19	February 19
4. Visualization and Continuous Object Transformation	February 28	February 26
5a. Principles of Statistical Model Selection     5b. Mid-Semester Review: Data Embedding, Alignment and Continuous Registration	February 28	March 5
7. Random Graphs	April 7	March 26, April 4
8. Cheeger Constant and Spectral Gap	April 3	April 11
9. Community Detection: Spectral Methods and SDPs	April 18	April 18
10. Dimension Reduction and Data Embedding Techniques	April 29	April 25
11. Isometric and Nearly Isometric Embeddings of Geometric Graphs	April 29	May 2
Portfolios that Contain Risky Assets
1. Risk and Reward	February 27	February 7
2. Covariance Matrices	February 27	February 7
3. Markowitz Portfolios	February 27	February 14
4. Markowitz Frontiers	February 27	February 14
5. Portfolios with Risk-Free Assets	February 27	February 21
6. Long Portfolios and Their Frontiers	February 27	February 21 and 28
7. Long Portfolios with a Safe Investment	February 27	February 28
8. Limited Portfolios and Their Frontiers	February 27	February 28
9. Limited Portfolios with Risk-Free Assets	February 27	March 7
10. Bounded Portfolios and Leverage Limits	February 21	March 7
11. Indenpendent, Identically-Distributed Models for Assets	April 27	March 28
12. Growth Rates	April 27	April 2
13. Indenpendent, Identically-Distributed Models for Portfolios	April 27	April 9
14. Kelly Objectives for Markowitz Portfolios	April 27	April 16
15. Cautious Objectives for Markowitz Portfolios	April 27	April 16 and 23
16. Optimization of Mean-Variance Objectives	April 27	April 23
17. Fortune's Formulas	April 30	April 30

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.

Additional Material on Graphs:
Spectral Graph Theory 2nd Edition, by F. Chung, AMS 1997. See online information at: Spectral Graph Theory . Particularly useful: Chapter 1.

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.)