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I think that the title is self-explanatory but I'm thinking about mathematical subjects that have not received a full treatment in book form or if they have, they could benefit from a different approach. (I do hope this is not inappropriate for MO).

Let me start with some books I would like to read (again with self-explanatory titles)

1) The Weil conjectures for dummies

2) 2-categories for the working mathematician

3) Representations of groups: Linear and permutation representations made side by side

4) The Burnside ring

5) A functor of points approach to algebraic geometry

6) Profinite groups: An approach through examples

Any other suggestions ?

asked Jan 24 2011 at 10:23

Gonçalo Marques

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7

I really like this question... hopefully someone will take a hint and write number (5) and (2) sometime soon! – Dylan Wilson Jan 24 2011 at 10:30

4

Steve Lack wrote something approximating (2): arxiv.org/abs/math/0702535 – Tom Leinster Jan 24 2011 at 11:31

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Regarding the Weil conjectures, have you read the appendix to Hartshorne that discusses these? If so, you could also try Nick Katz's exposition on Deligne's work in the Hilbert's Problems book (in the Proceedings of Symposia in Pure Math series) from the 1970s. Also, Deligne's article Weil I is less technical than you might guess, and there is also the textbook by Freitag and Kiehl. – Emerton Jan 24 2011 at 12:44

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Qiaochu: Demazure and Gabriel wrote a book using the functor of points approach over 3 decades ago. Some people love this book, while others... – Donu Arapura Jan 24 2011 at 17:55

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Maybe there is a place for the dual question: "Books you would like to write (if somebody would just read them)" so people can mention their book ideas and get some feedback. – Gil Kalai Feb 1 2011 at 15:03

show 10 more comments

Colin Tan · Answer 1 · 2011-03-06 07:13:08Z UTC

In pursuit of Hilbert's Problems

I think Hilbert's 23 problems form an organizatory framework for mathematics, that is much more organic than say the AMS classification. I believe that a book that traces the mathematics that grew from these problems can help to organize the burgeoning state mathematics is currently in.

I'm aware there is a book called "The Honours Class" that gives a history of Hilbert's problems up to their solution. However, this book is more biography than mathematics. Also, I'm interested in what happens after the problem is solved. A case study is the 17th problem, which lead to much of real algebra and real algebraic geometry today.

Seamus · Answer 2 · 2011-01-27 13:35:36Z UTC

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An English translation of Curtis and Reiner, Methods of representation theory with applications to finite groups and orders would be nice.

answered Jan 27 2011 at 13:35

Seamus

community wiki

5

An English translation? – darij grinberg Jan 27 2011 at 14:25

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I think Seamus was ironic ;-) – Julien Puydt Feb 2 2011 at 12:30

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That was the easy part. But what's the joke about? – darij grinberg Feb 3 2011 at 17:02

score 2 · Answer 3 · 2011-10-25 20:02:26Z UTC

For a popular account an autobiographical Six Million Dollar Man: How I solved all six of the millennium problems in 1 year by anonymous author would definitely top my shelf.

On a bit more serious note, I am looking forward to...

Continuum Hypothesis Part I and II with a chapter headed The Art of Forcing
Five Pillars of Mahtmeatical Logic (an encyclopedia in the same vein as the Russian EOM with 8000 entries from Logic only)
On formalizing predicative notion: From zero to Γ0 in 2 seconds...
Alan Turing's unpublished papers
Ω: Absolute Infinity (perhaps this being sequel to Heller and Woodin edited Infinity)

Anonymous · Answer 4 · 2011-02-02 10:26:59Z UTC

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I, as an undergraduate student in physics, would really like a comprehensive solutions book for Roger Penrose's The Road to Reality: a complete guide to the laws of the universe (Vintage, 2004)

answered Feb 2 2011 at 10:26

Anonymous

community wiki

1

There is a forum for this: roadtoreality.info But probably you know that – darij grinberg Feb 2 2011 at 11:02

nabil · Answer 5 · 2012-12-13 15:42:48Z UTC

-1

Algebraic topology demystified Differential topology demystified Algebraic geometry demystified Differential geometry demystified D-branes demystified

answered Dec 13 at 15:42

nabil

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Books you would like to read (if somebody would just write them…)

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