Louisb19
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I was thinking about picking up 'Godel, Escher, Bach' with any money I get for Christmas. Maybe an Analysis and a Linear Algebra book for the summer. I could always burgle TeeEm and save myself some $$$.

What is on your Christmas list? (Maths related)
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TeeEm
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this has been on my list for 18 months (the original that is)

http://www.waterstonesmarketplace.co...qwork=17933387
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physicsmaths
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(Original post by Louisb19)
I was thinking about picking up 'Godel, Escher, Bach' with any money I get for Christmas. Maybe an Analysis and a Linear Algebra book for the summer. I could always burgle TeeEm and save myself some $$$.

What is on your Christmas list? (Maths related)
Buy a place at Cambridge 😂.
But seriously, some analysis books!


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DylanJ42
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I'm thinking of getting "numbers and proofs" by Allenby, simply because I haven't got the slightest idea how to write proofs and this book looks like a nice introduction

Also TeeEm any suggestions for books on topology (introductory of course), it looks very interesting indeed. However I've noticed universities don't teach it until 3rd year (at least going by the course content) so finding a book I could understand and appreciate might be like finding a needle in a haystack :ahee:
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TeeEm
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(Original post by DylanJ42)
I'm thinking of getting "numbers and proofs" by Allenby, simply because I haven't got the slightest idea how to write proofs and this book looks like a nice introduction

Also TeeEm any suggestions for books on topology (introductory of course), it looks very interesting indeed. However I've noticed universities don't teach it until 3rd year (at least going by the course content) so finding a book I could understand and appreciate might be like finding a needle in a haystack :ahee:
I have not done any topology.

I am unfortunately the most non pure person you will ever come across
(basic analysis and basic algebra my knowledge is limited to 5 compulsory courses which were part of my degree over 30 years ago)

I do own possibly 100- 150 pure books which is a small fraction of my library purely because I cannot resist the temptation of buying a Maths book with a price tag under £1. (Besides I still live in hope that during my lifetime, the elixir of immortality will be found and I might get a chance to study them)
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DylanJ42
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(Original post by TeeEm)
I have no done any topology.

I am unfortunately the most non pure person you will ever come across
(basic analysis and basic algebra my knowledge is limited to 5 compulsory courses which were part of my degree over 30 years ago)

I do own possibly 100- 150 pure books which is a small fraction of my library purely because I cannot resist the temptation of buying a Maths book with a price tag under £1. (Besides I still live in hope that during my lifetime, the elixir of immortality will be found and I might get a chance to study them)
Don't you ever get the temptation to read some? Ever thought of calling in sick to work some week and binge reading them?
Spoiler:
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even just once, even just a little bit
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TeeEm
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(Original post by DylanJ42)
Don't you ever get the temptation to read some? Ever thought of calling in sick to work some week and binge reading them?
Spoiler:
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even just once, even just a little bit
I am retired so I do not need to call sick, but I find other mathematical "projects" far more satisfying than doing pure.
In saying that I want to stress there is nothing wrong with pure and I wish "it did it for me".
I have immense respect for the purists.
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DylanJ42
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(Original post by TeeEm)
I am retired so I do not need to call sick, but I find other mathematical "projects" far more satisfying than doing pure.
In saying that I want to stress there is nothing wrong with pure and I wish "it did it for me".
I have immense respect for the purists.
Which area of maths would you say is your favourite?

When I was at a local university for work experience I shared a workroom with two pure maths PHD students and met a pure mathematician, they definitely are an intriguing bunch to say the least :laugh:
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TeeEm
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(Original post by DylanJ42)
Which area of maths would you say is your favourite?
these days just mathematical techniques
I adding resources here so I am very busy
http://madasmaths.com/archive_maths_...ed_topics.html
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DylanJ42
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(Original post by TeeEm)
these days just mathematical techniques
I adding resources here so I am very busy
http://madasmaths.com/archive_maths_...ed_topics.html
I have seen some posts about these IYGB papers, I definitely will avail of these for my C3 and C4 exams
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Blondie987
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I'd really like someone to buy me flowers for Christmas lol
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Louisb19
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(Original post by TeeEm)
this has been on my list for 18 months (the original that is)

http://www.waterstonesmarketplace.co...qwork=17933387
Very nice.

I very well may be studying independently next year, do you have any recommendations for topics or textbooks? I'm thinking about covering the basics likes Linear Algebra and Analysis however I'm not sure what else, maybe some more calculus?

Thanks.
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DylanJ42
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(Original post by Blondie987)
I'd really like someone to buy me flowers for Christmas lol
http://www.amazon.co.uk/The-Golden-Ratio-Fibonacci-Numbers/dp/9810232640 I'm sure there's some flowers in here
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Blondie987
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Oh I didn't realise this thread was maths related lol
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Banana virus X
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(Original post by Louisb19)
I was thinking about picking up 'Godel, Escher, Bach' with any money I get for Christmas. Maybe an Analysis and a Linear Algebra book for the summer. I could always burgle TeeEm and save myself some $$$.

What is on your Christmas list? (Maths related)

I have An Eternal Golden Braid as a perfect PDF its 2.2502x104 KB

yours if u want it
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Gregorius
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(Original post by DylanJ42)
Also TeeEm any suggestions for books on topology (introductory of course), it looks very interesting indeed. However I've noticed universities don't teach it until 3rd year (at least going by the course content) so finding a book I could understand and appreciate might be like finding a needle in a haystack :ahee:
TeeEm has passed on this one, so I'll have a go.

Topology is a very wide field - and the first division you might identify is between General Topology and Algebraic Topology. General topology generalizes the topological notions that we find in good wholesome everyday spaces like \mathbb{R}^n to more general sets (and indeed to some pretty pathological monsters). It tends to get taught in the second year at university after you've understood what the topological aspects of ordinary spaces actually are. There's a very good book by Sutherland called "Introduction to Metric and Topological Spaces" that has been around for donkeys years. But be warned: we do general topology because we have to, not necessarily because we like it! It is not a sexy subject until you get into advanced applications such as fractals.

You've already noted that the fact that universities don't tend to start doing algebraic topology until the third year suggest that it is not really amenable to an elementary treatment. That's very true, it's a subject that builds on what you learn in the first couple of years of university, and represents a pay-off for all that unmotivated slog that you've gone through! So, with that warning in mind, here's a few recommendations:

One of the standard books these days is Allan Hatcher's "Algebraic Topology". It's very good and it's available in a free online version as well as in print. Try reading the first couple of chapters to get a feeling for the subject. Next up is Singer and Thorpe's "Lecture Notes on Elementary Topology and Geometry", which gives a good overview of the subject. Finally Massey's "Algebraic Topology: an Introduction", which is a nice treatment of the beginnings of homotopy theory, but which excludes homology.

Another approach, of course, is to use google and Wikipedia. There's lots of interesting material out there!
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Gregorius
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(Original post by Louisb19)
What is on your Christmas list? (Maths related)
For myself, I quite like the look of the new "Princeton Companion to Applied Mathematics"; perhaps the older "Princeton Companion to Mathematics" should join it too. I'm just rather worried that adding these to my collection might cause a gravitational collapse in the neighborhood of York...

A couple of recommendations for other people's Xmas stockings...

"Gamma: exploring Euler's constant" is very well written and accessible (for the most part) to STEP level students. Despite the title, and much excellent material on gamma, the final aim of the book is the prime number theorem.

If you want to know where much of modern mathematics (in the form we know it) came from, then "Euler: the master of us all" is a good start!
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atsruser
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(Original post by DylanJ42)
I'm thinking of getting "numbers and proofs" by Allenby, simply because I haven't got the slightest idea how to write proofs and this book looks like a nice introduction

Also TeeEm any suggestions for books on topology (introductory of course), it looks very interesting indeed. However I've noticed universities don't teach it until 3rd year (at least going by the course content) so finding a book I could understand and appreciate might be like finding a needle in a haystack :ahee:
Here are some free resources:

1. Hammack, Book of Proof: http://www.people.vcu.edu/~rhammack/BookOfProof/

Introduction to sets, techniques of proofs, etc.

2. Morris, Topology Without Tears: http://www.topologywithouttears.net/

Much better for a beginner than Sutherland, which assumes a starting point of epsilon-delta proofs, and understanding of continuity, etc. (Bear in mind that topology is pretty dry though, and the terminology can cause confusion: here's a video of a tutorial session that demonstrates this: https://www.youtube.com/watch?v=SyD4p8_y8Kw)

3. Nearing, Mathematical Tools for Physics: http://www.physics.miami.edu/~nearing/mathmethods/

*Really* nice book on mathematical techniques useful in physics (and maths, of course).

4. Chen, Lecture notes on various undergraduate topics: https://rutherglen.science.mq.edu.au...-notes/ln.html

These are an absolutely beautiful set of notes on analysis (real and complex, vector), algebra (linear and abstract), number theory, etc such as you would expect to cover during the first couple of years of an undergraduate degree. They are indispensable, IMHO - very clearly and thoroughly written.
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Louisb19
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(Original post by Banana virus X)
I have An Eternal Golden Braid as a perfect PDF its 2.2502x104 KB

yours if u want it
That would be great!

I still might add it to my physical library though, have you read it?
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Banana virus X
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I am just uploading it to my adobe cloud. once its done I will send u the link to download it.

I have only just gotten around to put it on my kindle. I am about 73 pages in
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