Download the most recent draft.
The OTIS Excerpts is a mini-book that I put together from lecture notes I use during the year. It is a collection of 192 problems and solutions. It is designed to mostly be beginner-friendly though some of the chapters are more challenging.
There is also a user-created forum for discussing the examples and problems from the text.
The Excerpts consists of selected problems from the following twelve topics from the OTIS catalog:
- Standard inequalities
- Functional equations
- Prime exponents
- Heavy number theory (called “advanced techniques”)
- Constructions in Number Theory
Most of the lecture material is adapted from existing handouts of mine but some of it is new. In addition, there is a chapter for beginners in proof-writing, and three chapters consisting of selected problems and solutions to recent USA team selection test problems.
Geometry is not covered; there is already a textbook for that.
The source code is sludge, but if you really want it here’s a ZIP. Much of the underlying TeX is actually machine generated (by interactions with my problem database), so don’t learn any habits from it.