Math 450 - Introduction to modelling

Final Exam

Our final exam is Monday, May 2, starting at 8 am in Willard 173.

I will be in my office 2-4:30 Saturday and Sunday for students with questions.

Here are some practice problems


This is the web page for Math 450, taught by Tim Reluga in the spring semester of 2016.

We will learn to model problems and systems using mathematics and computers. We'll be using the python computer language (which I will teach everybody at the start of the course). We'll cover statistical models, cellular automata models, and classical applied-math models. We'll also discuss the nature of modelling, based on readings from Nate Silver's Signal and the Noise.

Course syllabus

Office hours will be Mondays, 1:30 - 2:30, or by appointment.

Computer labs: Jan. 20 and 22, 216 Osmond



  1. Partner presentation of a new use of python for us.

  2. Every year, the Consortium for Mathematics and its Applications holds a modelling competition for students interested in applying mathematics.

  3. Possible topics for a third project:

Computer labs

For a formal, structured introduction to computer programming using python, MIT's online course Introduction to Computer Science and Programming is a very helpful reference. Check it out, if you feel like you need more background.


  1. Introduction
  2. Geometric curves
  3. The Black-body theory of global climate - an example model with predictions.
  4. Lab 1, introduction to python
  5. Lab 2, Scientific computing with python
  6. Compartment modelling with differential equations (part 1)
  7. Compartment modelling with differential equations (part 2)
  8. Predators, Prey, and the Law of Mass action
  9. Epidemics and Zombies
  10. Optics, Femat's law, and differential equations
  11. Pendulum motion
  12. The hanging chain
  13. Introduction to probability
  14. Poisson model for meteors
  15. Fitting distributions and curves
  16. Linear Least Squares
  17. Scaling laws by least squares
  18. Scaling laws by dimensional analysis 1
  19. Scaling laws by dimensional analysis 2
  20. Wrapping up scaling laws and model fitting
  21. Introduction to Markov Chains
  22. Introduction to Markov Chains (cont)
  23. 1/2 Inning of Baseball
  24. Zipf's Law and Preferential attachment
  25. Cellular automata models
  26. Symmetry in discrete systems
  27. The Heat equation and the Age of the Earth

Software Links

Links of diverging from course content, but of interest