Introduction
With luck (and time) we should be able to get through examples of:
one variable optimization,
multivariable optimization,
Lagrange multipliers,
Newton's method,
random search,
linear programming,
dynamical systems,
finite difference methods,
eigenvalue methods,
phase portraits,
simulation,
Runge Kutta (numerical method),
chaos,
probability,
markov chains,
linear regression,
monte carlo methods.
We have some time at the end of the course, and I would like to look at some topics that interest you at that time. We could look at locally weighted linear regression (LOWESS), data smoothing, and chaos and fractals in more detail near the end (or whatever you want!).
Instructor Contact
- My main webpage.
- Questions? Comments? email me
- My current Schedule, which is the most up to date listing of where I am.
Course Guide
- The Course Guide.
Lectures
Here is the lecture schedule, including lecture notes in pdf format, and Mathematica files that I used to generate solutions. I've collected all the Lectures and Mathematica files into zip files for easy downloading. Note that Lectures 6,7, and 18 were only in Mathematica format.
| 1 | Jan 15 | SS 130 | The Five Step Method, Single Variable Optimization and Sensitivity Analysis | Notes |
| 2 | Jan 17 | SS 130 | Modeling Example: Automobile Manufacture | Notes |
| 3 | Jan 22 | Sci 3655 | Unconstrained Multivariable Optimization | Notes Mathematica |
| 4 | Jan 24 | Sci 3655 | Lagrange Multipliers | Notes Mathematica |
| 5 | Jan 29 |
Cam 10 | Mathematica Session | Notes Mathematica |
| 6 | Jan 31 | Sci 3655 | Lagrange Multipliers Example | Mathematica |
| 7 | Feb 5 | Cam 10 | Random Search, Global vs Local | Mathematica |
| Feb 7 | Sci 1380 | No Lecture: I will be in my office available for consultation | ||
| 8 | Feb 12 | Sci 3655 | Continuous Dynamical Systems | Notes Mathematica |
| 9 | Feb 14 | Sci 3655 | Discrete Dynamical Systems | Notes Mathematica |
| 10 | Feb 19 | Sci 3655 | Eigenvalues and Stability for Continuous Dynamical Systems | Notes Mathematica |
| Feb 21 | Sci 1380 | No Lecture: Office Hours (so physics students could partake in interview regarding women in physics) | ||
| 11 | Feb 26 | Sci 3655 | Eigenvalues and Stability for Discrete Dynamical Systems | Notes Mathematica |
| 12 | Feb 28 | Sci 3655 | The Final word on Comparing Discrete and Continuous Dynamical Systems; Simulations | Notes Mathematica |
| 13 | Mar 5 | Sci 3655 | Chaos and Fractals | Notes Mathematica |
| Mar 7 | Sci 1380 | No Lecture: Office Hours (finish up those old assignments!) | ||
| 14 | Mar 19 | Sci 3655 | Discrete and Continuous Probability | Notes Mathematica |
| 15 | Mar 21 | Sci 3655 | Deterministic and Stochastic Battle Simulations | Notes Mathematica |
| Mar 26 | Sci 1380 | Individual Meetings to Discuss Final Project Peter & Dan: 12:00 John & Michael: 12:20 Daniel & Addy: 12:40 Brian: 1:00 Zach: 1:20 |
16 | Mar 28 | Sci 3655 | Markov Process | Notes Mathematica | 17 | Apr 2 | Sci 3655 | Linear Regression | Notes Mathematica | 18 | Apr 4 | Sci 3655 | Synthetic Data Sets | Mathematica | 19 | Apr 9 | Sci 3655 | Locally Weighted Polynomial Regression (lowess) | Notes Mathematica | Apr 11 | Sci 1380 | No Lecture: Office Hours | Apr 16 | Sci 1380 | No Lecture: Office Hours Stop by to iron out any final kinks you may have in your final projects. |
Apr 18 | Sci 3655 | Final Project Presentations Zach: Linear Programming Brian: Difference Calculus, Data Smoothing, Curve Fitting |
Apr 23 | Sci 3655 | Final Project Presentations Daniel & Addy: Owl and Mice Populations |
Apr 25 | Sci 3655 | Final Project Presentations John & Mike: Battle Simulations |
Apr 30 | Sci 3655 | Final Project Presentations Peter and Dan: Chaos and Fractals; Discrete and Continuous Dynamical Systems |
May 2 |
Sci 3655 | Pizza and a Movie: Pi (the symbol), starring Sean Gullette, written and directed by Darren Aronofsky |
Assignments
I want your assignments to be well presented, clearly understandable by a general reader, and typeset using quality typesetting software. This can be LaTeX, Word, or even Mathematica. I recommend Mathematica since you can do symbolic calculations directly in a document, without the need to export/import graphs into some other document. LaTeX will certainly produce prettier documents, but for this class Mathematica is suitable software to use. I would recommend saving each question in a separate file, rather than each assignment, in case the file becomes corrupt.
Here is a Mathematica file which will get you started with formatting documents.
Here are the assignments, in pdf format.
Mathematica
Here are some Mathematica notebooks you may find useful. I am using Mathematica as a text editor, and creating detailed solutions with Mathematica notebooks. It isn't as pretty as using LaTeX, but is gives you access to the computing power of Mathematica as you create your solutions. This is sufficient for this course. Of course, you can typeset more radically with style sheets, etc, but I am content for the moment just using the default settings of Mathematica.
Problem 1.4.1. Automobile Manufacture. An example of the five step method applied to a problem modeled by a single variable optimization. This uses the other expression for the number of cars that is mentioned in Lecture 2.
Social Mobility. An example of the five step method applied to a problem modeled by a system of first order constant coefficient differential equations.
A Final Thought
I will be adding links as time goes on. If the layout of this web page annoys you, let me know! Any and all suggestions for improvement will be considered and acted on as seen fit by me.