Handouts

Over time, I have written handouts for various academic subjects, most commonly for mathematics. Hopefully they can be of some use to you. They are sorted in chronological order, and are followed by descriptions.

These are written in LaTeX.

GENERAL

HIGH SCHOOL – COLLEGE MATHEMATICS

  • MA 35100
    • Course notes for Elementary Linear Algebra, MA35100, taught by Beichuan Deng, based on chapters 1-5 of Linear Algebra: Ideas and Applications by Richard C. Penny. The last few sections are not in LaTeX.
  • Notes on Convergence
    • This describes the PDARRLING mnemonic for convergence tests in calculus-II/BC, a few tricky geometric series and a method to quickly guess if a given series is convergent.
  • Algebraically Identifying Quadric Surfaces
    • Describes an alternative method for identifying “simple” quadric surfaces instead of resorting to traces and graphical analysis.
  • Integration by Parts
    • Discusses the integration by parts formula.
  • Finding Absolute Extrema on a Closed Interval
    • Discusses the “Candidates Test” method for finding absolute extrema on a closed interval. When written, it contained every single absolute extrema problem ever on the AP calculus FRQ.
  • A Sample Optimization Problem
    • A walk through a sample optimization problem in calculus.
  • On Taylor Series
    • Describes what is, and how to compute Taylor Series. Parts of it are unfinished, and this will probably get a rewrite eventually.
  • Interpreting Units (of Measurement) in Calculus
    • Discusses some methods to determine the unit of an expression

COMPETITION MATHEMATICS

  • Number Theory by Final Digits
    • Discusses numerous number theory techniques from the context of finding the final digit of some computation.
  • Solving Systems of Linear Congruences
    • Describes how to solve systems of linear congruences. There is a better exposition on some of the topics in the Number Theory by Final Digits handout.
  • Modular Arithmetic
    • This is really old and bad, but I have yet to rewrite it. There is a better exposition on some of the topics in the Number Theory by Final Digits handout.
  • Exploring Vieta’s Formulas
    • This is really old and bad, but it’s my very first document in LaTex and I have yet to rewrite it.

CHEMISTRY