Lecture Slides for AMSC/Math 420: Spring 2014
Mathematical Modeling

Title	Version	Date of Lecture
General Topics
1. Fitting Linear Statistical Models to Data by Least Squares: Introduction	February 5	January 27 and 29
2. Simulating an IID Sequence from an Arbitrary Distribution	April 7	April 11
3. Fitting Linear Statistical Models to Data by Least Squares: Weighted	April 21	April 21
4. Fitting Linear Statistical Models to Data by Least Squares: Multivariate	February 5	April 25
5. Maximizing Profit with Modeling	April 30	April 30
Modeling Epidemics
1. Introduction, Simple Models, and Linear Least Squares	February 3	February 3
2. SIR Model and Nonlinear Least Squares	February 7	February 7 and 10
3. Modified SIR Model and Nondimensionalization	February 17	February 10 and 17
4. Assessing How Well a Model Fits the Data	March 25	February 24
5. Two-Group Compartmental Models	March 25	March 24 and 28
6. Two-Group Model with Interventions	March 25	March 28 and April 2
7. Optimizing over Interventions within a Budget	April 7	April 7
8. Final Thoughts and Caveats	March 25	April 16
Modeling Portfolios that Contain Risky Assets
1. Risk and Reward I: Introduction	February 5	January 31 and February 5
2. Risk and Reward II: Markowitz Portfolios	February 5	February 5
3. Risk and Reward III: Basic Markowitz Portfolio Theory	February 21	February 12
4. Portfolio Models I: Portfolios with Risk-Free Assets	February 5	February 19
5. Portfolio Models II: Long Portfolios	February 23	February 21 and 26
6. Portfolio Models III: Long Portfolios with a Safe Investment	February 5	March 5
7. Stochastic Models I: One Risky Asset	March 25	March 26
8. Stochastic Models II: Portfolios with Risky Assets	March 31	March 31 and April 2
9. Stochastic Models III: Growth Rates for Portfolios	March 25	April 4
10. Optimization I: Model-Based Objective Functions	April 13	April 9
11. Optimization II: Model-Based Target Portfolios	March 25	April 14
12. Optimization III: Conclusion	April 21	April 18

Background Material on Linear Algebra: Linear Algebra and Its Applications, Fourth Edition, by David C. Lay, Pearson, 2011.
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.

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.)