Lecture Slides for AMSC/MATH 420: Spring 2018
Mathematical Modeling

Title	Version	Date of Lecture
General Topics
1. Fitting Linear Statistical Models to Data by Least Squares: Introduction	January 31	January 25
Discovering Structure in Data
1. From Data to Weighted Graphs, and Graph Laplacians	February 1	February 1
2. Geometric Graphs and Spectral Analysis	February 9	February 8
Movies from Lecture 2         Percolation n=100: Uniform.l2 , Uniform.lInf , NonUniform.l2 , NonUniform.lInf         Weighted: bkoff_movie	February 9	February 8
3. Random Graphs	February 20	February 13
4. Phase Transition in Random Graphs	February 20	February 20
5. Cheeger Constant and Spectral Gap	February 27	March 1
6. Mid-Semester Review: Random Graphs and Predictive Graphs         Movies: Percolation , PermuteVertices , PermuteEdges         Fish Reef Movies: High Resolution (640x360) .mp4 , low resolution (10x10) .avi	March 8	March 8
7. Convex Optimizations .         Matlab codes: sdp_ex1.m , sdp_ex2.m , sdp_ex3.m	March 22	March 27
8. Geometric Graph Models. Factorizations and SDP Approach	April 3	April 3
9. Laplacian Eigenmaps	April 3	April 12
10. Dimension Reduction Techniques	May 3	April 17,24
11. Review of Geometric Graph Discovery	May 3	May 1
Portfolios that Contain Risky Assets
1. Risk and Reward	March 21	January 30
2. Covariance Matrices	March 21	January 30
3. Markowitz Portfolios	March 21	February 6
4. Solvent Portfolios	March 21	February 6
5. Limited Portfolios	March 21	February 15
6. Markowitz Frontiers for Unlimited Portfolios	March 21	February 22
7. Markowitz Frontiers for Long Portfolios	March 21	February 27
8. Markowitz Frontiers for Limited Portfolios	March 21	February 27
9. Unlimited Portfolios with Risk-Free Assets	March 21	March 6
10. Limited Portfolios with Risk-Free Assets	March 21	March 6
11. Indenpendent, Identically-Distributed Models	March 21	March 27 and 29
12. Growth Rate Mean and Variance Estimators	April 2	March 29
13. Law of Large Numbers (Kelly) Objectives	April 22	April 5
14. Kelly Objectives for Markowitz Portfolios	April 21	April 10
15. Central Limit Theorem Objectives	April 21	April 10
16. Optimization of Mean-Variance Objectives	April 21	April 19
17. Fortune's Formulas	April 21	April 19
19. What Can Go Wrong?	May 5	May 3

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.)