Lecture Slides for AMSC/MATH 420: Spring 2017
Mathematical Modeling

Title	Version	Date of Lecture
General Topics
1. Fitting Linear Statistical Models to Data by Least Squares: Introduction	January 27	January 26
Discovering Structure in Data
1. Graphs, Adjacency Matrices, and Graph Laplacians	March 8	January 31
2. From Structured Data to Graphs and Spectral Analysis	February 8	February 9
Movies from Lecture 2         Percolation n=100: Uniform,l2 , Uniform,lInf , NonUniform,l2 , NonUniform,lInf         Weighted: Example on 7 vertices	February 9	February 9
3. Random Graphs	February 20	February 14
4. Phase Transition in Random Graphs	February 28	February 23
5. Cheeger Constant and Spectral Gap	March 8	March 2
6. Mid-Semester Review: Prediction in Random Graphs         Movies: Percolation , PermuteVertices , PermuteEdges	March 8	March 9
7. Geometric Graph Models. SDP Approach	April 4	April 4
8. Convex Optimizations . Matlab codes: sdp_ex1.m, sdp_ex2.m, sdp_ex3.m	April 11	April 11
9. Laplacian Eigenmaps	April 19	April 18
10. Dimension Reduction Techniques	April 19	April 20
11. Review of Geometric Graph Discovery	May 1	May 2
Portfolios that Contain Risky Assets
1. Risk and Reward	January 31	February 2
2. Covariance Matrices	January 31	February 2 and 7
3. Markowitz Portfolios	January 31	February 7
4. Solvent Portfolios	February 6	February 16 and 21
5. Leveraged Portfolios	February 6	February 21
6. Basic Markowitz Portfolio Theory	February 25	February 16
7. Unlimited Portfolios with Risk-Free Assets	February 25	February 21
8. Long Portfolios without Risk-Free Assets	February 25	February 28
9. Long Portfolios with a Safe Investment	February 25	February 28
10. Survey of Markowitz Portfolio Models	March 7	March 7
11. Indenpendent, Identically-Distributed Models	April 11	March 30
12. Growth Rate Mean and Variance Estimators	April 11	March 30
13. Law of Large Numbers (Kelly) Objectives	April 11	April 6
14. Kelly Objectives for Markowitz Portfolios	April 12	April 6 and 13
15. Central Limit Theorem Objectives	April 12	April 13
17. Fortune's Formulas	April 27	April 25 and 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.)