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 2010-03-18, 18:11 #1 blob100   Jan 2010 37910 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 2010-03-18 at 18:15
 2010-03-24, 18:49 #2 cmd     "(^r'Β°:.:)^n;e'e" Nov 2008 ;t:.:;^ 3E716 Posts Last fiddled with by cmd on 2010-03-24 at 18:53 Reason: single rif. 1-120
2010-03-25, 10:40   #3
R.D. Silverman

Nov 2003

22×5×373 Posts

Quote:
 Originally Posted by blob100 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.
Try the Schaum Outline Series.

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.

2010-03-25, 10:55   #4
rajula

"Tapio Rajala"
Feb 2010
Finland

32×5×7 Posts

Quote:
 Originally Posted by blob100 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.
Silverman's reply prompted me to point out one short book on the concept of proving. You might want to take a look at it to see if it is too elementary for you or something useful.

Franklin & Daoud: Proof in mathematics: an introduction
(notice the pdf-files at the end of the page)

I have used this book as a reference book for the non-finnish speaking students on my "introduction to mathematics" -course at our university.

2010-03-26, 10:52   #5
blob100

Jan 2010

17B16 Posts

Quote:
 Originally Posted by R.D. Silverman Try the Schaum Outline Series. 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.
I do learn Geometry in my school, But while reading "solved and Unsolved Problems in Number Theory" by Shanks (as you told me to read), It was really hard for me to understand the proofs of the theorems.
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...
Tomer.

Last fiddled with by blob100 on 2010-03-26 at 11:39

2010-03-26, 11:45   #6
R.D. Silverman

Nov 2003

22·5·373 Posts

Quote:
 Originally Posted by blob100 I do learn Geometry in my school, But while reading "solved and Unsolved Problems in Number Theory" by Shanks (as you told me to read), It was really hard for me to understand the proofs of the theorems.
Which illustrates WHY you are not ready for Calculus.
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 Grothendieck-Hirzenbruch extension to the Riemann-Roth 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.

2010-03-26, 11:54   #7
blob100

Jan 2010

1011110112 Posts

Quote:
 Originally Posted by R.D. Silverman Which illustrates WHY you are not ready for Calculus. 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 Grothendieck-Hirzenbruch extension to the Riemann-Roth 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.
I don't think it is easy to prove or understand proofs.
If you say that this book is too high level for me, why did you tell me to read it?

2010-03-26, 12:09   #8
xilman
Bamboozled!

"πΊππ·π·π­"
May 2003
Down not across

1068210 Posts

Quote:
 Originally Posted by blob100 I don't think it is easy to prove or understand proofs. If you say that this book is too high level for me, why did you tell me to read it?
I don't know Bob's precise reasoning when making that recommendation.

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

2010-03-26, 12:12   #9
blob100

Jan 2010

379 Posts

Quote:
 Originally Posted by xilman I don't know Bob's precise reasoning when making that recommendation. 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
So should I read this book?

2010-03-26, 13:08   #10
R.D. Silverman

Nov 2003

1D2416 Posts

Quote:
 Originally Posted by blob100 I don't think it is easy to prove or understand proofs. If you say that this book is too high level for me, why did you tell me to read it?
It is NOT too high level. The mathematics is almost entirely
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.

2010-03-26, 13:44   #11
blob100

Jan 2010

379 Posts

Quote:
 Originally Posted by R.D. Silverman It is NOT too high level. The mathematics is almost entirely 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.
I didn't say I can't understand anything, but it made me upset that I didn't understand the proofs of some important theorems.
As everyone knows, proofs are an important thing in mathematics, and thats why I wanted to understand these.

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