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math notes

booklet

Sheila Liming: Writing is the act of trying to create a record of your understanding of something. (from the Ezra Klein Show Podcast, Episode ‘The Quiet Catastrophe’)

Collection of math/cs notes and problems written up over the years for my own amusement. Topics are at the undergraduate college level. Normally notes like these would be written with a pencil in a notebook. LaTeX makes it very easy to produce publishing quality typesetting of mathematical texts, so blame LaTeX for this collection. Hopefully others will find some of these useful. Also available is the whole collection as one book and the Github repo with all the LaTeX sources.

Errors and misunderstandings in these notes are solely my fault. Nothing here is original. I tried to be complete about attributions and citations but if I missed something, I apologize.

Also caveat emptor: Nobody has done any proofreading on these notes.

Grasshopper

Induction and integer inequalities are the topics of this note. open full screen ↗ Your browser can't display this PDF inline. Open it directly.

Two decks of cards

Inclusion-exclusion principle and the number of derangements are the topics of the problem in this section. open full screen ↗ Your browser can't display this PDF inline. Open it directly.

Cat vs Dog

Bipartite graphs, network flows, matchings and vertex covers are the topics of thisproblem1in this note. open full screen ↗ Your browser can't display this PDF inline. Open it directly.

Hamming Code

Hamming codes are used to solve the problem in this note. open full screen ↗ Your browser can't display this PDF inline. Open it directly.

Paying dollar

In how many combinations of half-dollars, quarters, dimes, nickels and pennies can you pay out one dollar ? open full screen ↗ Your browser can't display this PDF inline. Open it directly.

Twelve Coins

Coin weighings are the topics of the problem in this note. open full screen ↗ Your browser can't display this PDF inline. Open it directly.

Bernoulli

We explore some variants of the Bernoulli Inequality. open full screen ↗ Your browser can't display this PDF inline. Open it directly.

Completeness

Completeness and related properties are the topic of this note. open full screen ↗ Your browser can't display this PDF inline. Open it directly.

Counting

Countable sets and counting schemes for infinite countable sets are the topics of the problem in this note. open full screen ↗ Your browser can't display this PDF inline. Open it directly.

Penn Teller

Counting words with constraints is the topic of the problem in this note. open full screen ↗ Your browser can't display this PDF inline. Open it directly.

Divisible by three

Loop invariants and a constraint relaxation are used to solve this problem. open full screen ↗ Your browser can't display this PDF inline. Open it directly.

Groovy

Groovy Numbers. open full screen ↗ Your browser can't display this PDF inline. Open it directly.