Master Basic Algebra with Knapp's Comprehensive Textbook

In summary, the conversation is about whether a certain textbook, "BASIC ALGEBRA" by Anthony W. Knapp, is a good choice for someone taking their first "serious" math course, particularly in abstract algebra. The author has some sample pages on his website and the conversation discusses the possibility of finding a copy at the library or purchasing it from the campus bookstore. One person who has used the book recommends it and mentions its clever organization and approach to proofs. Overall, the consensus is that the textbook would be appropriate for someone with a background in linear algebra, multivariable calculus, ODE, and proof-oriented courses.
  • #1
PieceOfPi
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  • #2
Can you find a copy at the library to try it out and see if you enjoy it?
 
  • #3
I have both the Basic and Advanced Algebra by Knaap. Is it any good? I dunno, I'm not a fan of Math so I can't really judge on it.
 
  • #4
I looked at the preview of chapter 2, and if this is your first "serious" maths course, then it looks quite advanced to me, but wait for other opinions.
 
  • #5
morphism said:
Can you find a copy at the library to try it out and see if you enjoy it?

It seems like a copy is not available for now (don't ask me why... it's supposed to be the textbook for the abstract algebra class this year). But one thing I can do is to buy this book at the campus book store, and if I didn't like it, I can return it while the return policy still works.

qspeechc said:
I looked at the preview of chapter 2, and if this is your first "serious" maths course, then it looks quite advanced to me, but wait for other opinions.

I think I should have clarified what I meant by a "serious" math course (although I think you got it right). I've already taken linear algebra, multivariable calculus, ODE, and some proof-oriented courses like number theory and elementary analysis. I haven't, however, taken any advanced undergraduate math courses such as abstract algebra, real analysis, and topology. So I was wondering if taking the abstract algebra course with that particular textbook would be appropriate for me. I think I have an enough preparation, though, but I would never know until I take the course.
 
  • #6
Hi PieceOfPi,

Knapp's algebra course is very cleverly arranged.
It starts with basic number theory (unique prime
factorization, chinese remainder theorem etc. ),
some basics on systems of linear equations and
permutations.
Then comes linear algebra. I think it is a good start to repeat
some well known stuff from a more abstract point of view.

As a rule Knapp proceeds from the concrete to the more
abstract which is seldom in a book on this topic.

Knapp sometimes shows how you can improve on
a proof-idea which actually does not work for some reason.
For example in his chapter on Abelian groups he points out the
analogies to vector spaces. The categorization of finetely generated
Abelian groups starts with a proof-idea inspired by Gaussian elimination.
This try fails, because finitely generated groups can only almost
be viewed as vector spaces. Then he shows how to save this approach by
modifying the elimination process.

Knapp gives many examples and motivates the theory well. His proofs
are beautiful and not based on tricks, which leave you wondering
how someone can have such clever ideas.

You are certainly well prepared to work through Knapp's course.
I like this book and recommend it.
 

1. What is Basic Algebra by Knapp?

Basic Algebra by Knapp is a textbook that covers the foundational concepts of algebra, including topics such as equations, inequalities, functions, and graphing. It is designed for students who are new to algebra or need a refresher on the basics.

2. Who is the author of Basic Algebra by Knapp?

The author of Basic Algebra by Knapp is Anthony W. Knapp, a mathematician and professor emeritus at the State University of New York at Stony Brook. He has written numerous textbooks and has over 40 years of teaching experience in mathematics.

3. Is Basic Algebra by Knapp suitable for self-study?

Yes, Basic Algebra by Knapp can be used for self-study. The textbook is organized in a clear and concise manner, with plenty of examples and exercises for practice. It also includes solutions to selected exercises at the end of the book.

4. Is Basic Algebra by Knapp suitable for high school students?

Yes, Basic Algebra by Knapp is suitable for high school students. It covers all the essential topics in basic algebra that are typically taught in high school math courses. The language and explanations used in the textbook are accessible to high school students.

5. Are there any resources available to supplement Basic Algebra by Knapp?

Yes, there are additional resources available to supplement Basic Algebra by Knapp. These include online practice problems, video tutorials, and study guides. These resources can help reinforce the concepts learned in the textbook and provide additional practice for students.

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