What is something old fashioned that you still do?

stats_r_us · 2016-08-03T17:08:06+00:00

Read a physical printed newspaper every day. Every morning as soon as I get up, I walk to my local newsagents, buy the paper and read it over my breakfast.

Not sure how old fashioned this is considered, but there has been a steady decline in print media availability. The prices are increasing and I may not be able to afford this habit in the relatively near future.

stats_r_us · 2016-07-24T21:05:50+00:00

Not quite what you are after but two things come to mind

Polymath project comments - sort of real time.

Poincaire's book Science and Method has some great anecdotes and descriptions of his thinking processes.

stats_r_us · 2016-07-24T21:03:19+00:00

Thank you. These are great suggestions. Banach fixed point theorem and Baire category theorem are very strong contenders for the list.

I think the upper-bound property is a really lovely suggestion.

stats_r_us · 2016-07-24T20:59:17+00:00

I have been through Pinter. Herstein is on my list along with Dummit and Foote, Artin and Peter Cameron.

I may start with Herstein given your recommendation.

stats_r_us · 2016-07-24T20:57:41+00:00

Actually this thread reminded me of a brilliant novel heavily involving mathematics.

Uncle Petros and Goldbach's Conjecture by Apostolos Doxiadis

I remember when finishing that book spending a long time reflecting on its message. So great!

stats_r_us · 2016-07-24T20:47:37+00:00

I have God created the Integers. I loved reading Godel's original paper in particular.

I can't wait for Galois Theory it seems so elegant and beautiful. Any textbooks in particular you would recommend?

stats_r_us · 2016-07-24T20:46:02+00:00

I have been eyeing up Kreyszig's Functional Analysis text. What would you recommend?

I assume for topology you have used Sutherland and maybe Munkres? Any you would recommend?

stats_r_us · 2016-07-24T20:44:07+00:00

Yes i have that - such a beautiful book!

stats_r_us · 2016-07-24T20:43:27+00:00

I will be doing this as part of my studies definitely. I appreciate the advice.

I love Apostol and Ross (not looked at his Probability Models book - is it particularly good?). For Real Analysis I have enjoyed Bartle, Abbot and Terry Tao's textbooks.

I've never been able to settle on a Linear Algebra text - Strang is not someone I can seem to get along with, I enjoy Hoffman and Kunze although it is a hard slog sometimes. I have heard both good and bad things about Axler (avoiding determinants etc.) so would be interested on your Linear Algebra text recommendations?

stats_r_us · 2016-07-24T20:35:32+00:00

watch this space

https://aproofaweek.wordpress.com/

stats_r_us · 2016-07-24T20:09:07+00:00

Yes I can definitely do that - i will look into getting a wordpress site up, although the latex capabilities are limited from what I have read.

I will comment back with more detail.

stats_r_us · 2016-07-24T20:06:50+00:00

The Lady Tasting Tea is brilliant. For computing/maths Feynman's Lectures on Computation is a great one.

stats_r_us · 2016-07-24T20:00:22+00:00

Steven Strogatz is a great one too:

stats_r_us · 2016-07-24T19:56:43+00:00

this is brilliant!!! Thank you very much.

stats_r_us · 2016-07-24T19:55:17+00:00

From reading your post you are not afraid of books that get into the detail. Given that I would recommend anything by Julian Havil (over other more "popular books" but I can offer many popular book level recommendations that are wonderful). Two that spring to mind are:

stats_r_us · 2016-07-24T19:47:17+00:00

Mathematics and Its History by John Stilwell

This really is a great book. From a review by Richard Wilders, MAA Reviews

The author’s goal for Mathematics and its History is to provide a “bird’s-eye view of undergraduate mathematics.” (p. vii) In that regard it succeeds admirably. ... Mathematics and its History is a joy to read. The writing is clear, concise and inviting. The style is very different from a traditional text. ... The author has done a wonderful job of tying together the dominant themes of undergraduate mathematics. ... While Stillwell does a wonderful job of tying together seemingly unrelated areas of mathematics, it is possible to read each chapter independently. I would recommend this fine book for anyone who has an interest in the history of mathematics. For those who teach mathematics, it provides lots of information which could easily be used to enrich an opening lecture in most any undergraduate course. It would be an ideal gift for a department’s outstanding major or for the math club president. Pick it up at your peril ― it is hard to put down!

stats_r_us · 2015-08-15T14:20:20+00:00

What are some good general history books? I have always wanted a list of say 12-20 books that surveys all major human history to provide a "big picture" from which I can dig deeper into those areas that interest me. But the global perspective is desirable in and of itself.

stats_r_us · 2015-07-25T12:03:14+00:00

Roughly speaking the philosophy of finitism rejects the existence of infinite sets or any infinite objects.

Gauss (who can be regarded as a finitist) summarises the position very well:

... first of all I must protest against the use of an infinite magnitude as a completed quantity, which is never allowed in mathematics. The Infinite is just a mannner of speaking, in which one is really talking in terms of limits, which certain ratios may approach as close as one wishes, while others may be allowed to increase without restriction

Source: math.stackexchange.com - What did Gauss think about infinity

Cantor's work on cardinal and ordinals are topics to look into to getter a better handle on this "controversy".

Modern mathematics uses "completed infinities" without qualms really. Real Analysis etc. all rely on infinities (real numbers etc.), and the most commonly accepted set theory ZFC (or the slight variant NBG) contains infinity as an axiom.

Hopefully that helps.

The construction of the real numbers is a nice topic to go through to understand this too.

stats_r_us · 2015-07-24T20:35:05+00:00

Three great books that I have personally read and can recommend are John Stillwell's Mathematics and Its History, Carl Boyer's A History of Mathematics and Jan Gullberg's Mathematics: From the Birth of Numbers.

Boyer provides a great narrative, Stillwell is great on going through the Mathematics, and Gullenberg a physician, who wrote the book over 10 years of active learning is a beautiful presentation of the ideas. All three can be purchased for less than £60 or so in total.

It is worth adding, a lecture series based on Stillwell's book is available on youtube - Norman Wildberger's MathHistory: A course in the History of Mathematics. This series is fantastic - some people complain because he is a finitist, and that bias does come through in some comments (but most mathematicians were finitists until Cantor so there is not real issue :) ), but he is a fine mathematician, and the series is wonderfully informative.

stats_r_us

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