Lecture Slides for AMSC/MATH 420: Spring 2021
Mathematical Modeling

Title	Version	Date of Lecture
General Topics
1. Fitting Linear Statistical Models to Data by Least Squares: Euclidean	February 2	January 26
2. Fitting Linear Statistical Models to Data by Least Squares: Weighted	February 2	January 28
Discovering Structure in Data
1. From Data to Graphs, Weighted Graphs and Graph Laplacians         movie	February 4	February 4
2. Geometric Graph Embeddings: (1) Full Data	February 2	February 11
3. Geometric Graph Embeddings: (2) Partial Data	February 23	February 23
4. Alignment Problems	February 23	March 2
5. Visualization and Continuous Object Transformation,	March 2	March 2
6. Random Graphs , Phase Transitions	April 8	March 25, April 1
7. Cheeger Constant and Spectral Gap	April 8	April 8
8. Community Detection: Spectral Methods and SDPs	April 29	April 15
9. Dimension Reduction and Data Embedding Techniques	April 22	April 22, 29
Portfolios that Contain Risky Assets
1. Risk and Reward	February 2	February 2
2. Covariance Matrices	February 2	February 2
3. Markowitz Portfolios	February 9	February 9
4. Markowitz Frontiers	February 9	February 9
5. Portfolios with Risk-Free Assets	January 22	February 16
6. Long Portfolios and Their Frontiers	January 22	February 16
7. Long Portfolios with a Safe Investment	January 22	February 23
8. Limited Portfolios and Their Frontiers	January 22	February 23
11. Indenpendent, Identically-Distributed Models for Assets	April 19	March 23
12. Assessment of Indenpendent, Identically-Distributed Models	April 19	March 30
13. Indenpendent, Identically-Distributed Models for Portfolios	April 19	April 6
14. Kelly Objectives for Markowitz Portfolios	April 19	April 13
15. Cautious Objectives for Markowitz Portfolios	April 19	April 20
16. Optimization of Mean-Variance Objectives	April 27	April 27

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.)