Lecture Slides for AMSC/MATH 420: Spring 2020
Mathematical Modeling

Title	Version	Date of Lecture
General Topics
1. Fitting Linear Statistical Models to Data by Least Squares: Introduction	January 28	January 28
2. Fitting Linear Statistical Models to Data by Least Squares: Weighted	January 29	January 30
Discovering Structure in Data
1. From Data to Graphs, Weighted Graphs and Graph Laplacians         Matlab high-res figure , Matlab low-res figure , movie	April 4	February 4
2. Geometric Graph Embeddings: (1) Full Data	February 16	February 11
3. Geometric Graph Embeddings: (2) Partial Data	February 25	February 18
4. Alignment Problems	February 25	February 25
5. Visualization and Continuous Object Transformation,	March 2	March 3
6. Graph Embeddings. Spectral Theory	March 5	March 24
7. Random Graphs	April 7	March 31, April 7
8. Cheeger Constant and Spectral Gap	April 16	April 14
9. Community Detection: Spectral Methods and SDPs	April 23	April 23
10. Dimension Reduction and Data Embedding Techniques	March 5	April 28, May 5
11. Review of the Discovery Thread	March 5	May 5
Portfolios that Contain Risky Assets
1. Risk and Reward	February 6	February 6
2. Covariance Matrices	February 6	February 6
3. Markowitz Portfolios	February 6	February 13
4. Markowitz Frontiers	February 6	February 13
5. Portfolios with Risk-Free Assets	February 6	February 20
6. Long Portfolios and Their Frontiers	February 6	February 20
7. Long Portfolios with a Safe Investment	February 6	February 27
8. Limited Portfolios and Their Frontiers	February 6	February 27
11. Indenpendent, Identically-Distributed Models for Assets	April 20	April 2
12. Assessment of Indenpendent, Identically-Distributed Models	April 20	April 9
13. Indenpendent, Identically-Distributed Models for Portfolios	April 20	April 16
14. Kelly Objectives for Markowitz Portfolios	April 21	April 21
15. Cautious Objectives for Markowitz Portfolios	May 3	April 21 and 30
16. Optimization of Mean-Variance Objectives	May 3	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.)