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Old 2010-03-18, 18:11   #1
blob100
 
Jan 2010

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Default 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.

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Old 2010-03-24, 18:49   #2
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http://books.google.it/books?id=foiV...bebbop&f=false

http://books.google.it/books?q=relat...rbooks_s&cad=1

...

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Old 2010-03-25, 10:40   #3
R.D. Silverman
 
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Quote:
Originally Posted by blob100 View Post
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.
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Old 2010-03-25, 10:55   #4
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Quote:
Originally Posted by blob100 View Post
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.
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Old 2010-03-26, 10:52   #5
blob100
 
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Quote:
Originally Posted by R.D. Silverman View Post
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...
Please help me
Tomer.

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Old 2010-03-26, 11:45   #6
R.D. Silverman
 
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Quote:
Originally Posted by blob100 View Post
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.
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Old 2010-03-26, 11:54   #7
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Quote:
Originally Posted by R.D. Silverman View Post
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?
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Old 2010-03-26, 12:09   #8
xilman
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Quote:
Originally Posted by blob100 View Post
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
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Old 2010-03-26, 12:12   #9
blob100
 
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Quote:
Originally Posted by xilman View Post
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?
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Old 2010-03-26, 13:08   #10
R.D. Silverman
 
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Quote:
Originally Posted by blob100 View Post
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.
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Old 2010-03-26, 13:44   #11
blob100
 
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Quote:
Originally Posted by R.D. Silverman View Post
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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