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The OTIS Excerpts

OTIS logo, v2022


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 consist of selected problems from the following twelve topics from the OTIS catalog:

  • Standard inequalities
  • Functional equations
  • Monsters
  • Global
  • Local
  • Rigid
  • Free
  • Anti-problems
  • Orders
  • 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.

Updated Mon 24 Jul 2023, 21:47:48 UTC by 91def99b1f69