Algebra

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."

I'm writing this review from the perspective of a mathematics graduate student reading more "basic" math books in order to better tutor younger students. This book by Gelfand and Shen is amazing at provoking deep contemplation on simpler math that many take for granted. Although the problems are not too hard for me, I find myself constantly confronting new ways of thinking about basic algebra. For example, the exercises in the book outline fun periodic patterns arising from division that I've probably considered but never really thought about. The problems also encourages the reader to come up with tricks/shortcuts, essentially forcing the learner to arrive at key insights. For those looking for a step-by-step tutorial, you won't find it in this book. However, working actively through the problems will definitely deepen one's understanding of algebra beyond standard plug-and-chug textbooks. I highly recommend this book to people looking to review mathematics or motivated/talented first time students.

Good book

It would be interesting to understand more about the context that this text was intended to be used within. It covers basic algebra with breezy informal prose, but the problems are much harder than you would think. The author expects students to think deeply and in an open-ended way about the concepts and strategies behind solving problems. There are no repetitive drill exercises, each problem is unique and challenging. For students in typical American math curriculums, this would be like an algebra text with only the "starred" problems. This text is optimal as a supplement for gifted and very motivated first-time algebra students. It's ALSO is good for tutors who can use the material to harden their own understanding and then share the insights with their students. Older students who want to "start over" and review the fundamentals of algebra would do well with this too. I like the approach of this text. It's so different from contemporary texts targeting this level. The emphasis is on understanding rather than teaching students to memorize procedures without explaining what's really going on.

Bought this book because it was recommended in a Reddit forum. Why it cost $60 (as much as a 900 page used textbook) I have no idea. It’s only about 100 pages long if not less, and examples are incredibly brief and lack any real explanation. It’s meaningful to figure out problems by yourself, but this book seems to lack evidence-based methods that currently inform how students learn math. Buy this book if you want to feel important. Buy another if you want to learn.

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.

The material in the book, the knowledge, its great and wonderful. The style with which the information is presented is beautiful because it does so in the form of questions but in the process of answering the questions is how you obtain the information; the book makes you think. The way with which the book is bound is another story though. My book started coming apart after only a few days, the pages are glued with no string to hold the pages together at all; they easily rip at the binding and from what I notice is that there is no way around it. It just spontaneously happening while I was trying to hold the pages open in a way so that the book is full open. It is getting 4 stars because of the information and not five because of the binding. this isn't a primary algebra book; I would most definitely recommend it to use as a supplement along with any other text though because it is great in that role.

Posting similar review as I did for Gelfand's Algebra book. Both are great books for reviewing and learning to think about the material with a bit more depth. It's a little easy for me but still stimulating and helped me review stuff that I never really gave enough attention to in high school. Probably a great book for kids. I think the Algebra one is a little easier than the trig one, so I've spent less time with it so far - but I look forward to the later sections and do think this is good material to review. In higher math, sometimes I was finding myself stuck on really simple algebraic things that I just didn't notice or took me too long to figure out.

although it's not the deepest realm of mathematics available if you're playing catch-up buy it, revision is a good thing.

Uno de los mejores libros de álgebra que he tenido la oportunidad de tener en mis manos.

Good product

Excelente libro. Contiene todos los tenas de un curso de algebra de nivel bachillerato. Lo mejor es la forma tan sencilla como el autor explica los conceptos. El mejor libro de algebra.