HANDOUTS

Additional Comments on the lectures: click here
Review sheet for the course (definitions, theorems): click here for a review sheet (.ps version version wi'out images)
Upcoming HW and reading: (previous HW) (comments/solutions to the HW) solutions to similar questions
Readings before class: click here for a bullet point summary to help prepare you for class.
Takeaways for undergraduate classes: summarizes key points from this and other undergrad courses

Summary of key points from this and other undergrad courses
REVIEW MATERIAL: Numerous worked out calculus problems (differentiation, integration, statement of topics you should know)
Notes on Induction, Calculus, Convergence, the Pigeon Hole Principle and Lengths of Sets (from the first appendix to An Invitation to Modern Number Theory, by myself and Ramin Takloo-Bighash, Princeton University Press 2006). We will not need all the material there for this course, but it is easier to just post the entire chapter.
Handout on Types of Proofs (from a handout I wrote for math review sessions at Princeton, 1996-1997; this was written for students from calculus to linear algebra).
Intermediate and Mean Value Theorems and Taylor Series (you should know this material already; the main results are stated and mostly proved, subject to some technical results from analysis which we need to rigorously prove the IVT).
The chain rule: this is a slight modification of a handout I wrote for a similar class at Princeton in the mid-90s. Unfortunately it is in MSWord.
Expanded notes on optimization, including the location of the military base or warehouse problem
My notes on the Method of Least Squares.
Lancaster: The Mathematics of Warfare
- Mathematica program I wrote to analyze the Battle of Trafalgar (as discussed in the article). This may be hard to follow without chatting with me.
Equality of mixed derivatives: two articles on the web: here and here (the second link is through JStor, and might only work when you are at Williams).
- See also the write-up by Michael Brofft and Alfred Graves.
Write-up of the Change of Variable Theorem, including the illustrative example, sketch of proof, and formulations for the big three examples (polar, cylindrical and spherical).
Sequences and series:
- From multivariable calculus (Cain and Herod)
- From calculus (Strang)
Notes on Vector Calculus. These are by Frank Benford (grandson of the Frank Benford whom Benford's law is named after, a subject I love and have written numerous papers on). He does applied math work and consulting (see his homepage here) for more on opportunities and services.
Free textbooks:
click here for Mathematica and LaTeX templates
Isaac Asimov: The Relativity of Wrong

MIT Open Courseware

INTERESTING VIDEOS (these are not required readings, but are posted for your enjoyment)

TED Lectures:

Did You Know (2009 version)

Yes, Prime Minister: Manipulation Polls (YouTube video)

FUN MATH (these are not required readings, but are posted for your enjoyment)

The arithmetic and geometric mean: a handout I wrote a few years ago for a freshmen seminar at Brown.

my paper A probabilistic proof of Wallis' formula for π, which appeared in the American Mathematical Monthly (there are a lot of good articles in this magazine, many of which are accessible to freshmen).

Markov chains and cryptography: Persi Diaconis, The Markov Chain Monte Carlo Revolution. (2008). Bull. Amer. Math. Soc. Nov. 2008

RSA reading: Notes on abstract algebra and group theory and RSA cryptography (from my book An Invitation to Modern Number Theory) as well as some history of RSA.

On Buffon machines and numbers: Flajolet, Pelletier and Soria.