If Creativity were anything but Random, Someone would have figured out the Algorithm by now. -- Dilbert

The best thing about search is you always find what you want. The worst thing about search is you never find what you do not want. -- Joshua Cohen, Book of Numbers Joel Spencer

# Joel Spencer

## Email: {lowercaselastname}@cims.nyu.edu

Department of Computer Science and Department of Mathematics
Courant Institute, New York University

## Contact

Room 829, 251 Mercer St.
New York, NY 10012, U.S.A.
212-998-3219 (voice) 212-995-4124 (fax)-- but email is MUCH better

## CV/Papers/Talks

• Vita--Selected Work (short form)
• Vita--Publication List (long form)
• Papers Description of selected papers. Vita and those papers in postscript.
• Talks Slides for various talks.

## Course Information

In Spring 2016, I taught Algebra Honors II. Click here for website.

Fall 2016 I will be on Sabbatical Leave. I will be teaching Fundamental Algorithms (CS) and Algebra Honors II (Math) in Spring 2017.

## Asymptopia

This book is aimed at strong undergraduates, though it is also suitable for particularly good high school students or for graduates (or senior faculty!) wanting to learn some basic techniques. From the back cover: Asymptotics in one form or another are part of the landscape for every mathematician. The objective of this book is to present the ideas of how to approach asymptotic problems that arise in discrete mathematics, analysis of algorithms, and number theory. A broad range of topics is covered, including distribution of prime integers, Erdos Magic, random graphs, Ramsey numbers, and asymptotic geometry. The author is a disciple of Paul Erdos, who taught him about Asymptopia. Primes less than n, graphs with v vertices, random walks of t steps--Erdos was fascinated by the limiting behavior as the variables approached, but never reached, infinity. Asymptotics is very much an art. The various functions nlnn, n^2, (ln n)/n, \sqrt{\ln n}, ln(ln n) all have distinct personalities. Erdos knew these functions as personal friends. It is the author's hope that these insights may be passed on, that the reader may similarly feel which function has the right temperament for a given task.

Asymptopia is a beautiful world. Enjoy!

Click (Material will be slightly different from the text here and below) for preface

Chapters: An Infinity of Primes; Stirling's Formula; Big Oh, Little Oh and All That; Integration in Asymptopia; From Integrals to Sums; Asymptotics of Binomial Coefficients; Unicyclic Graphs; Ramsey Numbers; Large Deviations; Primes; Asymptotic Geometry; Algorithms; Potpourri; Really Big Numbers!

## The Probabilistic Method -- Fourth Edition

The FOURTH Edition of The Probabilistic Method is here!

Click here for the algorithmic version of the Lovasz Local Lemma fixit

Click here Hannah1 Hannah2 Hannah3 Hannah4 for our most beautiful and most attentive reader. She's a fox! And, in strong competition: johanna and jazmin and emily

SPECIAL OFFER: Yes, your child (grandchild, niece, nephew, sibling) can have an Erdos Number of 1+\sqrt{-1}! Just send a photo of him/her absorbed in reading/playing/teething our book and I'll post it!

## The Erdos-Selberg Controversy

Over 60 years ago a controversy erupted between Paul Erdos and Atle Selberg over the elementary proof of the Prime Number Theorem. Ernst Straus -- then a young mathematician at the scene -- wrote a description of the events. These have been published in Math Intelligencer, along with commentary by Ron Graham and myself, and a mathematical postscript by Carl Pomerance.

Photo by MA

## High School MathCamps

This is a topic dear to my heart. I am former chair of an AMS committee that gives grants to High School Math Camps. Click for camp information or for information about donations to a worthy cause!