Graduate Advising Resources

Notices of the AMS, Early career collection

On writing

William Strunk, Jr and E. B. White, The Elements of Style, Fourth Edition

Igor Pak, How to tell a good mathematical story

Francis Su, Handouts

Bjorn Poonen, Practical suggestions for mathematical writing

Leonard Gillman, Writing Mathematics Well: A Manual for Authors

J.P. Serre, How to write mathematics badly (YouTube), 2007

Giving Talks

Terrence Tao, Talks are not the same as papers

Gian-Carlo Rota, Ten Lessons I Wish I Had Been Taught

Jordan Ellenberg, Tips on giving talks and associated blog posts here and here

John Baez, Advice for the Young Scientist

Joe Gallian, Advice on giving talks

Joe Gallian, Advice on Giving a Good PowerPoint Presentation

Chad Orzel, How to Do a Good PowerPoint Lecture

Geometric Group Theory texts

Bestvina, Sageev, Vogtmann Eds., Geometric Group Theory, IAS/Park City Vol 21, 2014

Bux, Groups and Spaces, Lecture Notes, 2007

Brady, Riley, & Short, The Geometry of the Word Problem for Finitely Generated Groups, 2007

Bridson & Haefliger, Metric spaces of non-positive curvature, 1999

Clay & Margalit (Eds.), Office Hours with a Geometric Group Theorist, 2017

Dehn, Papers on Group Theory and Topology, translated by Stillwell

Drutu & Kapovich, Geometric group theory, 2017

Gromov, Asymptotic Invariants, 1991

Löh, Geometric Group Theory, 2017

Lyndon & Schupp, Combinatorial group theory, 1977

Group theory problem collections

AIM workshop problem lists

Open Problems in Combinatorial Group Theory,

G.Baumslag, A.G.Myasnikov, and V.Shpilrain (also here) Questions in Geometric Group Theory, Collected by Mladen Bestvina

The Kourovka Notebook, E.I.Khukhro and V.D.Mazurov

Rigidity properties of free-by-cyclic groups, edited by Monika Kudlinska

Some group theory problems, Mark Sapir

Asymptotic invariants, complexity of groups and related problems, Mark Sapir

On mathematical research

Yuri Manin, Mathematics as metaphor, AMS, 2007

David Mumford, Numbers and the World: Essays on Math and Beyond

Dan Rockmore, The myth and magic of generating new ideas, New Yorker, November 7, 2019

Francis Su, Mathematics for Human Flourishing, Yale University Press, 2020

Bill Thurston, On proof and progress in mathematics, 1994

Stan Ulam, Adventures of a Mathematician