Algebra Abstract and Concrete by Frederick M. Goodman
Book Details :
LanguageEnglish
Pages587
FormatPDF
Size10.3 MB



Algebra Abstract and Concrete by Frederick M. Goodman



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The Author Algebra Abstract and Concrete PDF Book.

Frederick M. Goodman is the editor of Algebra Abstract and Concrete PDF Book.

Main Contents of Algebra Abstract and Concrete PDF


  • Algebraic Themes
  • Basic Theory of Groups
  • Products of Groups
  • Symmetries of Polyhedra
  • Actions of Groups
  • Rings
  • Field Extensions – First Look
  • Modules
  • Field Extensions – Second Look
  • Solvability
  • Isometry Group

Preface to Algebra Abstract and Concrete PDF


This text provides a thorough introduction to “modern” or “abstract” algebra at a level suitable for upper-level undergraduates and beginning graduate students.

The book addresses the conventional topics: groups, rings, fields, and linear algebra, with symmetry as a unifying theme. (Algebra Abstract and Concrete by Frederick M. Goodman)

This subject matter is central and ubiquitous in modern mathematics and in applications ranging from quantum physics to digital communications.

The most important goal of this Algebra Abstract and Concrete by Frederick M. Goodman PDF Book is to engage students in the active practice of mathematics. Students are given the opportunity to participate and investigate, starting on the first page.

Exercises are plentiful, and working exercises should be the heart of the course. The required background for using this text is a standard first course in linear algebra. (Algebra Abstract and Concrete by Frederick M. Goodman)


I have included a brief summary of linear algebra in an appendix to help students review. I have also provided appendices on sets, logic, mathematical induction, and complex numbers.

It might also be useful to recommend a short supplementary text on set theory, logic, and proofs to be used as a reference and aid; several such texts are currently available.

Acknowledgments

The first and second editions of this text were published by Prentice Hall. I would like to thank George Lobell, the staff at Prentice-Hall, and reviewers of the previous editions for their help and advice.

Thanks to many readers for suggestions and corrections. Thanks especially to Wen Jia Liu for compiling a long list of corrections. (Algebra Abstract and Concrete by Frederick M. Goodman)

A Note to the Reader

I would like to show you a passage from one of my favorite books, A River Runs Through It, by Norman Maclean. (Algebra Abstract and Concrete by Frederick M. Goodman)

The narrator Norman is fishing with his brother Paul on a mountain river near their home in Montana.

The brothers have been fishing a “hole” blessed with sunlight and a hatch of yellow stoneflies, on which the fish are vigorously feeding.

They descend to the next hole downstream, where the fish will not bite. (Algebra Abstract and Concrete by Frederick M. Goodman)

After a while, Paul, who is fishing on the opposite side of the river, makes some adjustment to his equipment and begins to haul in one fish after another.

Norman watches in frustration and admiration until Paul wades over to his side of the river to hand him a fly: He gave me a pat on the back and one of George’s No. (Algebra Abstract and Concrete by Frederick M. Goodman)

2 Yellow Hackles with a feather wing. He said, “They are feeding on drowned yellow stone flies.” I asked him, “How did you think that out?” He thought back on what had happened like a reporter.

He started to answer, shook his head when he found he was wrong, and then started out again. “All there is to thinking,” he said, “is seeing something noticeable which makes you see something you weren’t noticing which makes you see something that isn’t even visible.”

I said to my brother, “Give me a cigarette and say what you mean.” “Well,” he said, “the first thing I noticed about this hole was that my brother wasn’t catching any.

There’s nothing more noticeable to a fisherman than that his partner isn’t catching any. (Algebra Abstract and Concrete by Frederick M. Goodman)

“This made me see that I hadn’t seen any stone flies flying around this hole.” (Algebra Abstract and Concrete by Frederick M. Goodman)

Then he asked me, “What’s more obvious on earth than sunshine and shadow, but until I really saw that there were no stoneflies hatching here I didn’t notice that the upper hole where they were hatching was mostly in the sunshine and this hole was in shadow.”

I was thirsty to start with, and the cigarette made my mouth drier, so I flipped the cigarette into the water. “Then I knew,” he said, “if there were flies in this hole they had to come from the hole above that’s in the sunlight where there’s enough heat to make them hatch.

“After that, I should have seen them dead in the water. Since I couldn’t see them dead in the water, I knew they had to be at least six or seven inches under the water where I couldn’t see them.

So that’s where I fished.” He leaned against the rock with his hands behind his head to make the rock soft. “Wade out there and try George’s No. 2,” he said, pointing at the fly he had given me. (Algebra Abstract and Concrete by Frederick M. Goodman)

In mathematical practice, the typical experience is to be faced by a problem whose solution is a mystery. (Algebra Abstract and Concrete by Frederick M. Goodman)

Even if you have a toolbox full of methods and rules, the problem doesn’t come labeled with the applicable method, and the rules don’t seem to fit.

There is no other way but to think things through for yourself. The purpose of this course is to introduce you to the practice of mathematics; to help you learn to think things through for yourself.

To teach you to see “something noticeable which makes you see something you weren’t noticing which makes you see something that isn’t even visible.”

And then to explain accurately what you have understood. (Algebra Abstract and Concrete by Frederick M. Goodman)

Not incidentally, the course aims to show you some algebraic and geometric ideas that are interesting and important and worth thinking about.

It’s not at all easy to learn to work things out for yourself, and it’s not at all easy to explain clearly what you have worked out.

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These arts have to be learned through thoughtful practice. You must have patience, or learn patience, and you must have time.

You can’t learn these things without getting frustrated, and you can’t learn them in a hurry. (Algebra Abstract and Concrete by Frederick M. Goodman)

If you can get someone else to explain how to do the problems, you will learn something, but not patience, and not persistence, and not vision.

So rely on yourself as far as possible. But rely on your teacher as well. Your teacher will give you hints, suggestions, and insights that can help you see for yourself.

An Algebra Abstract and Concrete by Frederick M. Goodman PDF Book alone cannot do this, because it cannot listen to you and respond. I wish you success, and I hope you will someday fish in waters not yet dreamed of.

Meanwhile, I have arranged a tour of some well known but interesting streams. (Algebra Abstract and Concrete by Frederick M. Goodman)

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