The Greats in Math: Texts to Read & Pre-requisites

[synthetic.]

"The Greats" - and more.

[Edit: I have likely posted this in the wrong forum - any Mods are welcome to move it to a more apt location, apologies]

I'm forming a reading list (Undergrad) for myself comprising of modern texts and "classics" by those such as Euclid and Euler.

Advice often offered to Maths students is "read the greats" - so, suggest which texts constitute work by the Greats and should be read by students. That is, texts which are reasonably applicable today and offer wonderful insight to the respective subject.


I have only two of the aforementioned on my list thus far;


Euclid - Elements (All thirteen)

Gauss - Disquisitiones Arithmeticae


What other works by Greats should i have? And what are the opinions on the two listed above?



Ontop of;


General:

The Princeton Companion To Mathematics

Calculus:

Introduction to Calculus and Analysis - Courant
Calculus - Spivak
Elementary Differential Equations and Boundary Value Problems - Boyce & DiPrima

and Apostol's texts (but at £100+ each they can wait)

Algebra:

Elementary Linear Algebra: Applications Version - Anton & Rorres
Elementary Linear Algebra with Applications - Kollman & Hill

Pure Maths/ Numb Theory:

How to Prove It: A Structured Approach - Daniel J. Velleman (Author)
Concise Introduction to Pure Mathematics - Liebeck

Topology:

Introduction to Topology - Mendelson
First Concepts of Topology - W.G. Chinn (Author), N.E. Steenrod (Author)
Introduction to Topology and Modern Analysis - Simmons

Probability/Statistics:

A Modern Introduction to Probability and Statistics: Understanding Why and How - F.M. Dekking (Author), et al.



I only have a few opinions on any of these texts, i am here for more insight and any other suggestions. Indeed, warning me off of any texts is welcome also.

Oh, and also, for anyone suggesting/advocating texts - would it be possible for you to indiciate the pre-requisites for reading said text?

Thanks.


P.S. - I have already read through a lot of Mathwonks thread and taken a few suggestions from it ("who wants to be a . . ").

 

[Vid]

Anton and Rorres is kind of easy and likes to hold your hand. It's kind of like Stewart's Calculus in style.

 

[mathwonk]

it is strange to see gauss and velleman on the same list. i.e. if you can read gauss you do not need velleman, and conversely if you need velleman, you cannot read gauss or euclid.

and who do you expect to render a valid opinion on books like those by gauss and euclid? if the verdict of hundreds or thousands of years does not convince you, who here can?

i.e. if your goal is to learn some math just start reading and quit making lists.

 

[synthetic.]

it is strange to see gauss and velleman on the same list. i.e. if you can read gauss you do not need velleman, and conversely if you need velleman, you cannot read gauss or euclid.

and who do you expect to render a valid opinion on books like those by gauss and euclid? if the verdict of hundreds or thousands of years does not convince you, who here can?

i.e. if your goal is to learn some math just start reading and quit making lists.

Start reading what? It seems the purpose of my post has passed you by. Try again.

 

[snipez90]

I don't see the point of this thread. You said it yourself that you took most of these books from another thread. Instead of listing a bunch of "great" books, pick one up and actually read it.

A lot of people seem to think that they have to get all the "right" books. They spend so much time finding these "right" books for a collection they think is really admirable. The fact of the matter is, for a person who really cares about learning math, there is no difference between Apostol and Spivak, or Stewart and Spivak. There are plenty of resources out there for people who want to learn calculus or another subject. There is a time for finding those resources when you hit a roadblock, but first of you should pick up ONE book and start doing math.

 

[mathwonk]

i thought it was rather obvious i was recommending you start with euclid or gauss, but if you need to read velleman, i guess that inference passed you by. after your last post, I withdraw my recommendation of gauss and euclid, as they would probably be inaccessible to you.

 

[mbisCool]

I bought Spivak specifically because Stewart is not on par with it and i want to learn math.. but i get the point you are trying to make

 

[PhysicalAnomaly]

Do what I was advised to in the other thread - start with Munkres. Difficult but rewarding.

 

[^_^physicist]

Spivak's Differential Geometry series. Not the little softcover, but the huge anthology (A comperhensive introduction to differential geometry) is very useful if you want to get a handle on Diff. Geo.