20100318, 18:11  #1 
Jan 2010
379_{10} Posts 
Recommendations for algebra books
This thread made to suggest me names of algebra books.
Some about me: I'm new to mathematics and my knowledge is: 1) some books as: "fermat's last theorem" by Simon Singh, "The golden ratio" by Mario Livio, etc. 2) Wikipedia. 3) The first 70 pages of "Solved And Unsolved Problems In Number Theory" By Daniel Shanks. 4) own expirience (which means: paying with theorems, playing with conjectures, trying to conjecture, learning conjectures...). 5) "A Possible Approach to Proving Goldbach's Conjecture" by Peter Schorer. I want to read an algebra book becuase I cant understand proofs well, and by reading "solved and unsolved..." I found it hard to understand the proofs. Thanks. Last fiddled with by blob100 on 20100318 at 18:15 
20100324, 18:49  #2 
"(^r'Β°:.:)^n;e'e"
Nov 2008
;t:.:;^
3E7_{16} Posts 
http://books.google.it/books?id=foiV...bebbop&f=false
http://books.google.it/books?q=relat...rbooks_s&cad=1 ... cmd : http://3.bp.blogspot.com/_rvR3ouziO8...ea_pd_sfuo.PNG Last fiddled with by cmd on 20100324 at 18:53 Reason: single rif. 1120 
20100325, 10:40  #3  
Nov 2003
2^{2}×5×373 Posts 
Quote:
If you do not understand how to do proofs, you will have a very difficult time with mathematics. Haven't you taken Geometry in school? It should be nothing but proofs. 

20100325, 10:55  #4  
"Tapio Rajala"
Feb 2010
Finland
3^{2}×5×7 Posts 
Quote:
Franklin & Daoud: Proof in mathematics: an introduction (notice the pdffiles at the end of the page) I have used this book as a reference book for the nonfinnish speaking students on my "introduction to mathematics" course at our university. 

20100326, 10:52  #5  
Jan 2010
17B_{16} Posts 
Quote:
I don't think you understood me. Let me explain myself: I want to learn Mathematics in the university, and when I say proofs, I do not mean proofs of high school's Geometry problems, I mean, I can't understand easily the proofs of theorems in Shanks's book and theorems as: Bertrand's postulate, Prime number theorem, Reciporcity law... Please help me Tomer. Last fiddled with by blob100 on 20100326 at 11:39 

20100326, 11:45  #6  
Nov 2003
2^{2}·5·373 Posts 
Quote:
Most proofs in Shanks' book are developed from first principles and do not use any techniques (except for analytic results that depend on Calculus) beyond that of high school/secondary school algebra. Math is all about proofs. Such trivia as solving (say) a quadratic equation is merely an application of a known ALGORITHM. (which is unfortunately what most people think of as mathematics) BTW, When I pick up a book at (say) my level, it isn't easy for me to understand the proofs either. One must work with them, picking them apart piece by piece. REPEATEDLY. It isn't easy. It takes PATIENCE and PERSERVERENCE. I have had a great deal of frustration (for example) in trying to understand the GrothendieckHirzenbruch extension to the RiemannRoth Theorem. I am not sure that even after multiple readings that I understand even the statement of the theorem, let alone the proof. (And I am sure that I do not understand the proof). Noone said that it is easy. If you expect that it should be, then you should quit. 

20100326, 11:54  #7  
Jan 2010
101111011_{2} Posts 
Quote:
If you say that this book is too high level for me, why did you tell me to read it? 

20100326, 12:09  #8  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
10682_{10} Posts 
Quote:
However, reading mathematical books, articles, papers and proofs isn't always done to gain a thorough understanding of proofs of theorems. Sometimes, for example, it is done in order to gain a feel for what needs to be learned beforehand so that the material can be properly understood on subsequent study. Paul 

20100326, 12:12  #9  
Jan 2010
379 Posts 
Quote:


20100326, 13:08  #10  
Nov 2003
1D24_{16} Posts 
Quote:
secondary school algebra. Whether you have the required mathematical maturity/ability to understand elementary proofs is a separate question from the level of the mathematics. 

20100326, 13:44  #11  
Jan 2010
379 Posts 
Quote:
As everyone knows, proofs are an important thing in mathematics, and thats why I wanted to understand these. 

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