When designing slides for a class I am teaching, I like to derive inspiration from slides others have given before me. However, it is difficult to find concrete examples of such slides outside of a typical Google search. Can you give me examples of slides you or your colleagues have given for entire classes?
I am happy to share my Beamer slides, available through each course webpage at my homepage. The courses that have slides are:
- Combinatorics: A course in enumeration, including simple counting, combinatorial proofs, bijective combinatorics, and generating functions. The page also has information about the structure of the course project involving individual research and poster presentation. (Example set of notes)
- Graph Theory: Basic graph theory, graph statistics and properties, coloring, planarity, graph algorithms. There is a course project where students research and write about mathematicians. (Example set of notes)
- Mathematical Modeling: The focus is on the modeling process from start to finish. Students learn to use Mathematica and apply it to function fitting, probabilistic models, queuing theory, and linear optimization. The course project is a group research project where students take some real world situation and try to understand it mathematically. (Example set of notes)
- Multivariable Calculus: Parametric and Polar curves, including area and arc length. Vectors, vector functions, functions of multiple variables, gradients, multiple integrals. These notes are the most newly created (as of 2014), so they have a more advanced use of color and graphics. In this example I use color to explain the chain rule and include graphics about the directional derivative.
Slides are broken down by lecture and are intended to encourage active learning by leaving out certain details and examples that will be worked out on the board. Students download the notes before class and bring them to class on paper or on their electronic devices.
Below is a list of slides assembled by the community, organized by subject area.
Algebra and Combinatorics
Analysis, Geometry, and Topology
Numerical Analysis and Scientific Computing
Optimization and Control
Ordinary Differential Equations and Dynamical Systems
Partial Differential Equations
Probability, Stochastic Processes, and Financial Mathematics
Material for all my courses is at http://neil-strickland.staff.shef.ac.uk/courses/. For the following courses, there are complete sets of lecture slides:
- Methods for differential equations: I will be teaching this in Nanjing starting next week, so there are various bits of Chinese in the slides. There are a large number of diagrams, often with some kind of animation. Separate from the slides, there are also web pages with interactive animations of phase portraits.
- Mathematics IV (Electrical): This is basically vector calculus for electrical engineers. Again, there are many diagrams, often with some kind of animation. Separate from the slides, there are also web pages with three-dimensional diagrams that can be rotated by mouse.
- Linear mathematics for applications: In this case, only the handout version of the slides is currently on the web. Various bits of these handouts have been blanked out and replaced with light green patches. The students were encouraged to work out for themselves what should go in those patches, or failing that, fill them in during the lecture. Some of my colleagues have been using that system for a while, but last semester was the first time I tried it. I am not sure how successful it was.