This page has a number of resources I have developed to help people learn about science. For now, they're roughly separated into subject areas.
I'm pretty sure I own copyright on all documents below, since I wrote them. I plan to later release these under a Creative Commons license. Until then, please consider all rights reserved unless the document states otherwise.
- Units [PDF]: A few useful unit conversions. [Qual prep notes].
- Complex Numbers [PDF] ... Solutions [PDF]: Review packet for undergraduate PChem students
- Differential Equations [PDF] ... Solutions [PDF]: Review packet for undergrad PChem students
- Statistics [PDF] ... Solutions [PDF]: Another review packet
- Linear Algebra : [COMING SOON] a packet for PChem graduate students
- The large c limit of det(A+cB), where B is singular [PDF] : solution to a math question asked at Miller Group Meeting, 5 June 2008.
- Precision in the Computation of Polynomials [PDF]: Not sure if anyone will use this, but I found it interesting
- Implementation of Maslov Tracking [PDF] : notes on an optimal implementation of Maslov index tracking
- Stat Mech Study Notes, 27 June 2006 [PDF]: Notes for fellow grad students. Covers the beginning of David Chandler's Introduction to Modern Statistical Mechanics. (I never got around to writing up more of these.)
- Solutions to various problems from Chandler's Introduction to Modern Statistical Mechanics.
- The WKB Approximation [PDF]: Notes on WKB aimed to help fellow grad students (temporarily removed because it was a bad document, and too many people were downloading it!)
- Bonus Problems for Undergrad PChem: I came up with a few bonus problems while teaching the quantum side of physical chemistry. I never got around to writing up the answer for the last one (but there is a solution!)
- Details on Problem 7-31 [PDF]: Clarification of the source of a formula used in problem 7-31 of McQuarrie and Simon's PChem text. (for undergrad PChem)
- Solutions to problems from a gradute-level quantum mechanics course.
The following are scans of various notes I wrote in preparation for my qualifying exam. To exonerate any mistakes, let me remind you that these notes reflect my understanding as of the dates written on the top. For what it's worth, I managed to pass my qualifying exam (in May 2007: my committee was Martin Head-Gordon (chair), Graham Fleming, K. Birgitta Whaley, and Robert Littlejohn (outside: Physics)), so I must have known enough at the time!
- Some Molecular Dynamics Algorithms. Verlet, Leapfrog Verlet, Velocity Verlet
- Coding up Manolopoulos's Symplectic Integrator/Notes on a Symplectic Classical Integrator. (Note: after further study, I've learned that the credit for this integration scheme belongs not to Manolopoulos (who has done plenty of other good work) but to Candy and Rozmus: J Computational Phys 92 230 (1991).)
- Runge-Kutta Algorithm for Molecular Dynamics (RK4).
- Adams-Bashforth-Moulton Predictor-Corrector Algorithms for Molecular Dynamics
- Applications of Correlation Functions
- Detailed Balance in (Metropolis) Monte Carlo
- Perturbation Theory
- Transition Path Sampling. Actually, these notes came much after my qualifying exam, but they're also worth putting up.