Book or books that covers EVERYTHING.

Oct 2015
141
8
Greece
Hello!

I want a book that start's completely from scratch (how and why numbers were invented, how we started counting, 1 apple + 1 apple = 2 apples, etc. :p) and goes up to all the maths that was invented in chronological order (algebra and geometry, calculus, linear algebra, probabilities etc!!!)

Well, it's probably impossible for one book to have all of that, so a collection of books would be fine too.

************************************************************
Also, the books must explain EVERYTHING!
For example, in the chapter of second degree equations I want to learn how did they calculate the discriminant and also the formula:
\(\displaystyle
x = \frac{-b +- \sqrt{d}}{2a}
\)
***********************************************************

Well, to be realistic in general I just want a book about Algebra and Geometry, Calculus, Linear Algebra and finally Probabilities And Statistics.

But also I want a historical book that explains how we started inventing maths from scratch.

Also don't forget what I told you inside the asterisks, it's important for me. :p

Also consider the books i already have as a colleague:

Calculus:
Calculus Michael Spivak
I also have two other books from Thomas &Finney but i don't remember which ones. But I do rember that these books are Part 1 and Part 2 and part 2 is the continuity of part 1 and starts with infinity sums.

Linear Algebra:
Linear Algebra and Its Applications

Differential Equations:
Elementary Differential Equations and Boundary Value Problems

Probabilities and Statistics:
This is greek so use google translate :p


Unfortunately, I lost high school books about algebra and geometry.

Thank you!
 
Last edited by a moderator:
May 2016
1,310
551
USA
The history of mathematics is not a logical progression, but there are excellent histories of mathematics.

Bourbaki was an attempt to develop all of mathematics in a logical sequence. Whether it was a fully succesful attempt is a question beyond my competence to answer.
 
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skipjack

Forum Staff
Dec 2006
21,387
2,410
Surely trigonometry deserved a mention!
 
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Oct 2015
141
8
Greece
The history of mathematics is not a logical progression, but there are excellent histories of mathematics.

Bourbaki was an attempt to develop all of mathematics in a logical sequence. Whether it was a fully succesful attempt is a question beyond my competence to answer.
To tell you the truth I was expecting that.
Then i believe a good algebra book would be fine right? (which covers everything about algebra, trigonometry and geometry things we learned at high school maybe in a more advanced way since I'm a colleague now).

I mean, i already own books like calculus, probabilities etc, so I'll be fine with an algebra book.
 
Jun 2015
915
269
England
First you are not going to find what you want.

The number system is amazingly difficult at high level and even to this day pure mathematicians are still arguing about it (or rather them since there are many number systems)

This does not only apply to numbers but to everything you learn in high school.
At university level all these subjects are revisited and new thinking introduced.

These days the pure mathematicains have separated from the applied ones and pushed their theoretical side well beyond any known application, though new apps are constantly arising.

Then we have the so called 'modern maths' - (actually a couple of hundred years old now but never mind) group theory, set theory, distribution, topology and beyond.
The beginnings of these are now taught because they have found applications in the (mostly) physical sciences.

From the examples you gave you are following a pretty conventional path so here is a book which does exactly what you ask in 1053 pages, though there is not much 'modern math' in it.

Ancillary Mathematics

Massey and Kestelman

Publisher Pitman


There is , of course, another newer branch of mathematics emerging/arising

That of discrete mathematics (also called concrete mathematics) which is emerging from the use of computers.
 
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Oct 2015
141
8
Greece
First you are not going to find what you want.

From the examples you gave you are following a pretty conventional path so here is a book which does exactly what you ask in 1053 pages, though there is not much 'modern math' in it.

Ancillary Mathematics

Massey and Kestelman

Publisher Pitman
This goes for the algebra book, or everything i mentioned in the original post?
 
Jun 2015
915
269
England
This goes for the algebra book, or everything i mentioned in the original post?
Massey and Kestleman offer justification rather than formal maths proofs, though they give a great deal of explanation, starting with about 20 pages on the number system and ending in multi-dimensional calculus, Lagrange-Hamilton mechanics and such.


Not sure what you mean by the algebra book but if you want real depth with explanation




What is Mathematics

Courant and Robbins

Oxford University press

Will take you on a fascinating journey.