I have no home. The world is my home. -- Paul Erdos

It suffices that a book be possible for it to exist. -- Jorge Luis Borges 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

## Disambiguation

Looking for a fine jazz drummer. Sorry, thats the other Joel Spencer! Try: joel spencer drums

## 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.

## Courses

I shall teach Basic Algorithms Spring 2021. Tentative information is given here

## 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

Winner of the 2021 Steele Prize of the American Math Society. Click here for the citation

Click here Hannah1 Hannah2 for our most beautiful and most attentive reader. She's a fox! And, in strong competition: johanna and jazmin and emily alsoemily1 alsoemily2 joe tomo fiona alice-bryan advait

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!

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!