Free PDF Algebra, by Israel M. Gelfand, Alexander Shen
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Algebra, by Israel M. Gelfand, Alexander Shen
Free PDF Algebra, by Israel M. Gelfand, Alexander Shen
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This book is about algebra. This is a very old science and its gems have lost their charm for us through everyday use. We have tried in this book to refresh them for you. The main part of the book is made up of problems. The best way to deal with them is: Solve the problem by yourself - compare your solution with the solution in the book (if it exists) - go to the next problem. However, if you have difficulties solving a problem (and some of them are quite difficult), you may read the hint or start to read the solution. If there is no solution in the book for some problem, you may skip it (it is not heavily used in the sequel) and return to it later. The book is divided into sections devoted to different topics. Some of them are very short, others are rather long. Of course, you know arithmetic pretty well. However, we shall go through it once more, starting with easy things. 2 Exchange of terms in addition Let's add 3 and 5: 3+5=8. And now change the order: 5+3=8. We get the same result. Adding three apples to five apples is the same as adding five apples to three - apples do not disappear and we get eight of them in both cases. 3 Exchange of terms in multiplication Multiplication has a similar property. But let us first agree on notation.
- Sales Rank: #211903 in Books
- Brand: Brand: Birkhäuser
- Published on: 2013-10-04
- Released on: 2013-10-04
- Original language: English
- Number of items: 1
- Dimensions: 9.25" h x .37" w x 6.10" l, .50 pounds
- Binding: Paperback
- 150 pages
- Used Book in Good Condition
Review
“The idea behind teaching is to expect students to learn why things are true, rather than have them memorize ways of solving a few problems, as most of our books have done. [This] same philosophy lies behind the current text by Gelfand and Shen. There are specific ‘practical’ problems but there is much more development of the ideas … [The authors] have shown how to write a serious yet lively look at algebra.” ―The American Mathematics Monthly
“Were ‘Algebra’ to be used solely for supplementary reading, it could be wholeheartedly recommended to any high school student of any teacher … In fact, given the long tradition of mistreating algebra as a disjointed collection of techniques in the schools, there should be some urgency in making this book compulsory reading for anyone interested in learning mathematics.” ―The Mathematical Intelligencer
Most helpful customer reviews
19 of 19 people found the following review helpful.
Beautifully written!
By Shelly S
I bought this book for my daughter (10 years old) and we read it together. We went very slow and I supplement it with a work book. She likes it. I was impressed by the beauty of this book. It might be a little too slim for a textbook but every kid who wants to learn algebra should read it. More than teaching algebra it shows what math should be: simple and beautiful.
My daughter's math textbook is 5 pounds and I can't even stand looking at it. I understand that not every is enthusiastic about math and not everyone can feel the beauty of math. But you don't have to make math so ugly.
Learning math with a 5 lb textbook is simply terrifying but if your kid goes to public school you probably have no choice. Let you kid read a good book like this one, as early as possible, before he(she) grows a life time aversion to math.
21 of 22 people found the following review helpful.
I can't think of a title. Just buy the book!
By Herbert Powell
Well, H. Wu on his page and N.F Taussig here have written quite good reviews, so I guess I can't really add anything new. Still, I feel the need to praise this book some more. Could it be used for a main text or should it be just a supplement? I don't know, but there is much more mathematics contained in these 149 pages than in any standard 500 page high school text on the market today. That's the unsurprising result of accomplished mathematicians writing a math book. Sure, some topics are missing. You won't find 3 or 4 chapters devoted to the several "different" ways to graph a line. There aren't fifty problems in a row that start with "suppose Sam rows upstream at 5 miles per hour and it takes her seven times as long as..." Unfortunately, there isn't even a treatment of complex numbers, the only omission that seems wrong.
You will find several interesting and serious topics that would be dangerous to bright students who insist they hate math, or rather what they've been told is math. Imagine their initial embarrassment when they find out that they can enjoy the subject! Maybe more importantly, imagine their relief when they realize that there IS a reason why we "FOIL", there IS a reason why negative times negative is positive, there IS a reason why we say a^(-1)=1/a, and it's not because "the teacher said so" or "that's just the rule" (ok, it is the rule, but now you'll see why). And there's no attempt to sneak anything by the reader. The authors are quick to acknowledge any gaps in their reasoning, and to assure the reader that in the future he or she will fill them.
It's this honesty and attention to rigor without being too formal or dry that give this book some extra charm. It moves smoothly from basic arithmetic (which everyone should still read if only to learn a different way of explaining it to a student/younger sibling/child) all the way to proofs, both algebraic and visual when possible, of some important inequalities. Cauchy's inductive proof, first for powers of two and then filling in the gaps, of the AM-GM inequality is here, as is the standard proof of Cauchy-Schwarz by the discriminant of a polynomial. Go to your local high school and look at its algebra book. I doubt that's in there.
I'll end with a few of the funny, sometimes weird, little remarks:
After illustrating the associative law using the example (sugar + coffee) + milk = sugar + (coffee + milk), the next problem is: "Problem 25. Try it."
"Please keep in mind that a monomial is a polynomial, so sometimes for a mathematician one is many."
"Probably you are discouraged by this solution because it seems impossible to invent it. The authors share your feeling."
One section begins: "62. How to confuse students on an exam: As usual, there are many evil ways to make use of knowledge."
17 of 21 people found the following review helpful.
Great approach, but not suitable to modern study
By B. Hoffert
As a returning college undergrad studying a math-heavy field, I picked up Gelfand's Algebra hoping to rejuvenate my very rusty algebra skills. To be honest, I didn't even learn algebra that well when I first studied it over a decade ago, but I slid by as a stereotypical "math student" in grade school. I wanted to do it right this time, and I'd heard very good things about this book.
I want to start with the positives, because there are many. If you're someone put off by the modern way of teaching math that forgoes all explanations and intuition in favor of step-by-step guides and formulas, then you'll appreciate Gelfand's approach to the field of algebra. Each subject is treated in a learn-by-doing fashion, and nothing is spoon fed. Clever intuitive explanations are provided for many topics that most books just take for granted. If you work your way through the entire book and all of its problems, you'll come away with algebraic understanding and intuition that probably exceeds that of most undergraduate math majors at the college level. As I said, I wanted to learn algebra the "right way" this time around, and I definitely achieved my goal through this book.
That said, this book has some pretty major flaws to the point that I have trouble actually recommending it. In fact, I don't think I'd even recommend it to my past self.
First, of the hundreds of exercises provided throughout the book, it feels like less than half of them have solutions provided. The author tries to explain that any problem without a solution is okay to skip if you can't solve it, but that explanation just isn't good enough. The fact is that the meat of this book is its problems, and if you skipped every problem without a solution, you'd probably learn less algebra than you would from a standard textbook. Like I said, Gelfand's approach is very learn-by-doing, but he doesn't give you the proper tools to actually "do" everything you're supposed to "learn." In fact, many problems build on previous problems, so if you skip any of them you risk triggering a cascade of unsolvable exercises that will leave you frustrated and confused. It's not like these are routine calculations you're doing, either. Most of the problems require creative problem solving, significant trial and error, or out of the box thinking to solve. There's nothing inherently wrong with this (in fact I love this approach, as it builds vital mathematical intuition and "real" math skills), but without solutions there's no way to check the correctness of your answer. If you get stuck (and you WILL get stuck), there's nothing you can do. Simply put, the challenge level of some of these problems is such that the typical math student is bound to encounter several of them that they will never solve on their own, and there's no way for them to help themselves along. I've heard some people suggest that the lack of solutions is good because that way you're forced to work through the problem on your own, but as someone with the self control to give each exercise a nice long, honest attempt, I found it to be a major hindrance to my learning. After hours of searching, I managed to find a document online with solutions to the unsolved problems, and that's the only way I was able to work my way through the book.
Second, much of the wording in this book is ambiguous, and in some cases there are major errors. It's not always clear what an exercise is asking you to do, and the mistakes can really set you back and waste your time. The subject matter is difficult enough without throwing away hours of effort just because the book didn't give you clear instructions or explanations.
Third, there's just not enough reinforcement in this book. On this plus side, this means you're learning something new with each and every exercise, but the problem is that the near-zero repetition doesn't leave much room for the learning to sink in. I would have really appreciated a handful of reinforcement problems for the most essential concepts.
As a tutoring aid, this book would probably get 5 stars. In that situation, the tutor can have worked everything out ahead of time and guide the student through the many challenges in this book. But as a self-study tool, or even a classroom text, this classic tome has a few too many issues. It earns 3 stars for the high quality of Gelfand's approach and explanations, but the issues with the exercises keep it from a true recommendation. If this book were to be republished some day with corrections and a full set of solutions, I would have no problem giving it 5 stars.
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