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Reviews (3)

Splendid and illuminating algebra text.
This text, which is intended to supplement a high school algebra course, is a concise and remarkably clear treatment of algebra that delves into topics not covered in the standard high school curriculum. The numerous exercises are well-chosen and often quite challenging.

The text begins with the laws of arithmetic and algebra.The authors then cover polynomials, the binomial expansion, rational expressions, arithmetic and geometric progressions, sums of terms in arithmetic and geometric progressions, polynomial equations and inequalities, roots and rational exponents, and inequalities relating the arithmetic, geometric, harmonic, and quadratic (root-mean-square) means.The book closes with an elegant proof of the Cauchy-Schwarz inequality.

Topics are chosen with higher mathematics in mind. In addition to gaining facility with algebraic manipulation, the reader will also gain insights that will help her or him in more advanced courses.

The exercises, which are numerous, often involve searching for patterns that will enable the reader to tackle the problem at hand.Many of the exercises are quite challenging because they require some ingenuity.Some of the exercises are followed by complete solutions. These are instructive to read because the authors present alternate solutions that offer additional insights into the problem.

I also highly recommend the other texts in the Gelfand School Outreach Program.They include The Method of Coordinates, Functions and Graphs, and Trigonometry. Also, to gain additional insights into the inequalities at the end of this text, the reader may wish to consult An Introduction to Inequalities by Edwin Beckenbach and Richard Bellman.

Makes you a master of high school algebra and...
This book inspires even those with minimal interest in mathematics. If you are passionate about math, this is a must for you. The book is simply a refresher for high school algebra. It contains numerous gems that you could hardly find in a standard algebra text. If you are a teacher, you would have learned much to improve your teaching style and knows how to make your math classes more interesting...overall, a key source to keep on your bookshelf

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An insightful introduction to analytic geometry.
This brief text provides a clear introduction to analytic geometry.Its scope is narrow.The authors discuss the graphs and properties of linear functions, absolute value functions, quadratic functions, linear fractional functions, power functions, and rational functions (trigonometric functions are discussed in another volume of the Gelfand School Outreach Program).What distinguishes this book from other treatments of the same topics is the extent to which the authors go to explain, using both words and diagrams, why the graphs of the functions they discuss have the form they do and the many challenging exercises they include.

This book concludes with a chapter length exercise set full of challenging problems.The reader who completes these problems will gain a much fuller understanding of analytic geometry than one who reads a typical precalculus text.While calculus is not required to complete the exercises, the reader may wish to revisit these problems once she or he has had calculus in order to analyze the properties of the graphs more fully.

The text was written initially for a correspondence course in the Soviet Union.Since students could send their solutions to the authors when they were at the University of Moscow, answers or hints to only a few of the exercises are included in the back of the text.

I also highly recommend the other volumes in the Gelfand School Outreach Program.They include The Method of Coordinates, Algebra, and Trigonometry.

A great book!
I tend to look at elementary books like this one from the point of someone who doesn't need to learn from it but might want to use it as a text if teaching or tutoring someone. I learned almost nothing from this book, but I didn't expect to, as it's all material I learned ages ago. But for someone encountering this material for the first time, this would be an excellent book.

I see this book as used primarily in a pre-calculus math class or for tutoring someone about to take calculus. It gives a good exposition of material that will be encountered at the time a student takes calculus, but at a level that assumes the student has only the algebra that most students entering a calculus course have taken. And from that point, it explains the elements of drawing graphs of algebraic functions and the ideas of tangency that are so critical to differential calculus, and does so in a clear way, with helpful diagrams. It is a slim book, and probably by itself could not be the only text in a pre-calculus math class, but on the subjects it covers, it is the best I have seen. (And that is underrating it, because there aren't many books on the subject. So one might say that "the best there is" isn't really as high praise as it deserves.)

This book certainly deserves a 5-star rating.

Reviews (1)

A fascinating introduction to coordinate geometry.
The authors of this slim volume demonstrate the power of coordinate geometry, which they describe as a means of translating geometric figures into algebraic formulas, through their lucid exposition, interesting examples, and well-chosen exercises.

The authors begin with the coordinate geometry of the real line.They discuss absolute value and define what distance means.Next the authors examine the coordinate geometry of the plane.They define distance in the plane, show how relations among the coordinates define geometric figures, and discuss different coordinate systems that can be used in the plane.Their examples illustrate how algebraic methods developed by Rene Descartes make it possible to solve geometric problems efficiently that would be quite difficult to solve using synthetic geometry. The authors then treat the coordinate geometry of three-dimensional space in a similar manner.

The second part of the book begins with a problem concerning lattice points in the plane.The authors use this example and its generalizations to justify exploring the coordinate geometry of four-dimensional space.They carefully treat the example of a four-dimensional unit hypercube, examining its properties by considering its analogues in lower dimensions:the segment [0, 1] of the real number line, the unit square in the coordinate plane, and the unit cube in space.

Since the book was initially written for a correspondence course for high school students in the Soviet Union, it is designed for self-study and accessible to students who have had high school courses in algebra and geometry. Since students in the Soviet Union were able to mail their solutions to the exercises to the authors when the authors were professors at the University of Moscow, answers to most of the exercises are not provided.The exercises are thought-provoking and some are quite challenging.

Reviews (9)

The Way I Wish I'd Been Taught Algebra!
At the time I started homeschooling my sixth grader last year, I was completely math-phobic. I had forgotten every bit of algebra I ever learned (and any math I did learn in high school, more than 20 years ago, was just barely learned at that). My now seventh grade son and I are learning algebra together with Harold Jacobs's Elementary Algebra book.

This is really an exceptional self-study guide. We will read a chapter, then independently try to solve the problem sets given. We then compare our answers. If our answers don't agree, I will either explain to him how I solved a problem that he got stuck on, or vice versa.

The delightful thing about this book is that I am learning to enjoy a subject I always thought I detested. Harold Jacobs makes everything clear, comprehensible, meaningful and often humorous. I am learning that I am not left-brain impaired, as I've thought I was ever since second grade, and actually look forward to my algebra time with my son! My son, too, has overcome his own math phobia, and become a math lover. I can't recommend it highly enough.

An engaging introduction to elementary algebra.
Harold R. Jacob's text is a lively and clearly written introduction to elementary algebra.Jacobs engages the reader through puzzles, including the number trick with which he starts the book, humor, and references to actual persons and events.He finds intriguing ways to introduce topics, then explains the concepts well.Concepts are introduced incrementally.Often, Jacobs introduces a concept in a particular context so that the student gets the idea before reintroducing it later in a broader context after the student has learned additional material.This reinforces the concepts and contributes to the student's conceptual understanding of the material, as do his problem sets.While Jacobs makes sure that the student can perform the algorithms presented in the text, the problems that he poses are designed to reinforce the concepts by exploring all aspects of the topics that he covers.

Each section concludes with four problem sets.The first set is a brief review of earlier topics (aside from the first five sections of the first chapter).The second covers the topics in the section.Jacobs provides answers to the problems in the second set in the back of the text, making the book suitable for self study.The third set is a variation on the second.The fourth set consists a puzzle or a problem that extends the concepts learned in the section.I particularly enjoyed these problems, often turning to them to see what Jacobs was asking before I finished the other problems. Each chapter concludes with a chapter summary and two sets of review problems.

Jacobs begins the text with a review of arithmetic, including the order of operations and properties of integers and rational numbers. He introduces algebraic concepts gradually as he does this.This leads to a discussion of functions, linear equations, lines, systems of linear equations, and exponents.Jacobs pauses for a midterm review.Then he covers polynomial, rational, and radicalexpressions and equations.He also discusses the properties of the real numbers, inequalities, and number sequences before finishing his text with a final review.

If you enjoy this text, and I think you will, you may also want to explore Jacobs' other texts.They include Geometry:Seeing, Doing, Understanding and Mathematics:A Human Endeavor.

Reviews (5)

Book and guide provide a thorough geometry course
There is some criticism that this textbook has lost the rigor of the 2nd edition. Having used that for 5 years and this for two years, I would argue that the current edition demonstrates far more care toward the reluctant student and causes the math nerds to stop and think about who is interested in knowing or needing geometry.

There are good reasons for every change. One is simply that there are only 180 days in the school year.I use this text with homeschoolers. We meet 72 days per year, and we do every chapter, every problem, plus a fair bit of other supplements.

I do not understand the criticism that the book is disorganized and chaotic. In the last 8 years I have taught math from more than 10 different texts, from pre-algebra to pre-calculus.Harold Jacobs sense of organization is a relief.I suspect that since the 2nd edition has been around since 1987 and has stood the test of time, that the criticism stems from the fact that even mathematicians dislike change. (What in the world is wrong with geometry students using a protractor?) I do not believe the book is a nod to political correctness defined by the NCTM. I think it rather corrects the course taken by other publishers in their interpretation of the NCTM standards.

Proofs from the 2nd edition are available online from the Freeman publisher website, so you can add that back in, as I do. The teacher guide that accompanies the text, written by Peter Renz (above reviewer), adds several more levels of richness and complexity. Use as much or as little as you want.You now have the flexibility to use this text with those enthralled by math as well as those resistant to math.

In my first review, since withdrawn, I was critical of the tests provided by the publisher as being for weenies. They are being replaced by a set that Harold Jacobs wrote himself. I have been given the opportunity to test drive some of them, and I am satisfied that this completes a first-year presentation of geometry.

Harold Jacobs is a master mathematician, and a master teacher.He clearly loves doing both. (Confessional:) I do not own a degree in mathematics, and I my greatest growth in math has been a result from working with texts by Harold Jacobs. This is not a text generated by a publisher to fill a hole in a lineup of texts. This is a successful presentation of a difficult subject.

Agree with the other 2 star rating
Very overrated.

1- too much in the book, things such as non-euclidean geometries need to be cut out

2- far too much of the learn it bydrawing approach, the book actually requires you to use a protractor to solve a lot of problems, this might be good for 7th graders, but not what I was looking for

3- not much information given in the text itself, mainly hidden in the problem sets, which some might like

4- very chaotic organization, topics just blendinto the next.

5- rigour is notup to the second edition's standards.

6- All you really need to know about the book is what the back cover states

"more focus on informal and paragraphproofs reflecting current nctm standards and recommendations"

and this

"the thoroughly redone art program, now in full color, brings this book to a new level. Over 2200 NEW photographs, drawings, and cartoons illustrate new examples and exercises"

This book unfortunately was designed under the guidance of the reform mathematical community.Look up" mathematically correct"in google to see what actual mathematicians think of this movement, and the nctmguidelines.

Reviews (4)

Math as science, art and life
What's so truly impressive about Jacobs' book is the way in which hedemonstrates that math is all around.His choice of subjects provides thereader with a broad introduction to the mathematical sciences, includinggeometry, probability, combinatorics, statistics, topology and more.Moreimportantly, his examples and explanations make it relevant andfun.

Jacobs' writing is clear (which cannot be said for many books onmath at any level) and his organization sweeps the reader right along.Though technically a textbook, this is excellent reading for anyone who'sinterested in learning about math.I read it in junior high school, andhave re-read bits and pieces as I progressed through college and graduateschool.His subjects are complex enough to merit rethinking, yet hisexplanations clear enough to be grasped by the first time reader.

Trulyone of the great introductory math texts -- especially for those who thinkthey don't need to know or can't understand math.

This book fosters true love of math.
I'm a 36-year old homeschooling mother who had done calculus in high school and college, and mechanically got some right answers, but never knew why.I hadn't bothered to slow down and notice the beauty and power of thelanguage of mathematics.In his textbook, Mathematics: A Human Endeavor,Harold Jacobs smashed my lack of confidence into a million pieces.Heshowers the student with so much real-life relevance and humor, that even aslight amount of curiosity about the subject bears delicous fruit.Workingthrough this book will convince any human being, of almost any age, that heor she is a born mathematician.

Reviews (2)

one of a kind treasure
The book is very good for people who want to be a high-school teacher of math, or be a mathematician.Even if you don't take a class with this book, read it on your own before taking real analysis.It will make your thought and logic complete and precise.A really nice training and practical preparation to do analysis.

The book is very simple and short.It deals with number system from natural to complex, gently.Simple things are usually not easy, though.

I took real analysis twice long time ago, but this book still improved my thinking of numbers very effectively.

I recommend this book to those who want to be precise and correct, no matter you are math or theoretical physics people.

And also for high-school students who want to know what pure mathematicians really do.

And also for independent thinkers of mathematical science, and would-be philosophers!

Reviews (11)

My God? What a book!
Godfred Harold Hardy is one of the greatest mathematicians of the 20th century. A Course of Pure Mathematics is an introduction to Analysis, but he only starts Limits on page 110. Until there he talks about real numbers, Dedekind cuts and complex numbers as vectors. I have no words to describe his style: it seems that he is talking with you. If you are looking about a book of Calculus, stop here in buy it.

Best introduction to mathematical analysis
This book is simply beyond any rating whatsoever. Giving 5 stars is to undermine the value of this classic.
The first time I got this book, I was neither aware of it not of its author. I just picked it up randomly from school library. From the contents I figured it was a book on calculus. I immediately searched for the proof that "every continuous function is integrable." This was the first book I encountered which had a rigorous proof of this.
Then I began reading the chapters sequentially thinking that this seems to be a good book on calculus. The book went much beyond my expectation and it satisfied all my mathematical curiousities. All the mysteries of calculus were revelaed. Hardy demystified calculus in the first chapter itself by creating reals out ot rationals.
The Dedekind's construction of reals as presented in this book is the best I have seen. The properties of reals were not stated as axioms (common approach in books on analysis) but rather deduced from those of rationals.
The concepts of functions, limits, continuity, derivative etc. were explained in a prosaic style which has no parallel. This was also my first book on maths which had far more english words than mathematical symbols.
After finishing the entire book I was wondering who was this guy G. H. Hardy who has written such a masterpiece.
Only a few months later I came to know that he was one of the greatest British mathematicians of the century and was responsible for making our Indian Ramanujan famous. After that I read most of his books including "A Mathematician's Apology" and "An Introduction to Theory of Numbers"
Any persons who thinks maths is dull should just read few pages from this book and I bet his old beliefs would be shattered.

Reviews (2)

What ?? Only one review (so far) for this classic?
A well written, classic text written by three larger than life math legends (Hardy, Littlewood, Polya). This is the definitive and monumental text on inequality -- the little angular symbols you see in all fields of mathematics -- from analysis to number theory to topology to combinatorics (i would say all fields of science but I am not a math apologist, mind you, so I would stay with those things I know something about).

Reviews (8)

Old fashioned, unpretentious and solid.
It's kind of like having a friend explain it to you.Also dips into fractions, continued fractions, irrational numbers and other non-integer stuff. I find it interesting how the style of most older math texts differs from most current writing in that the older texts are much friendlier.Also, older books usually lack the annoying drizzle of typos and blunders which mars most recently published "higher" math books.Some of this may be due to correction opportunities afforded by various editions and updates, but I suspect a higher standard of care in the original writing and editing explains a lot of it.The book is sadly overpriced, of course, but that's life.

One of the greatest
First of all, let me say this about the one star review. Do not let yourself be infuenced by lesser mathematicians. Idiots in my opinion. To give this book one star, you must posses some special kind of mediocracy. Keep your stupidity to yourself Lucas.

No one writes like this anymore. Mathematicians like Hardy have passed. The subject has ballooned, and now you have to specialize within Number Theory. There are fewer and fewer that can posses knowledge of the entire subject of Number Theory. Remember what Harold M. Edwards said. You have to read the classics, and beware of secondary sources. Authors give their own spin on ideas. And who is to say they have a greater or lesser understanding of the subject. Furthermore, who can determine how well can they express themselves. How many mathematicians our days bother to study grammar and literature? The best example is Gauss' Disquisitiones Arithmeticae. Would you rather read a book written by Gauss himself, the man that established the subject? Or by some one who learned what some one learned what some one learned over a period of 200 years? Also know what Axler, author of Linear Algebra Done Right, said about reading mathematics books. For a mathematics book, if you spend less than half an hour per page you are going too fast. The last thing i will say is again attributed to Edwards. In his book on Advanced Calculus he encourages the reader to jump chapters. A book does not have to, and sometimes it should not, be read in order. It may take some practice to see how you need to jump around, but you will find that you can maximize your reading by doing so.

There are several point in which this book excels. First, in the writing style. Second, in how many ideas it introduces. Or how good an understanding the reader obtains of Number Theory. It is invaluable to have the big picture. Third, the author has in mind the future material the reader will encounter. He knows you will go beyond this book, and prepares you for what is to come. You do not enter higher courses blind.

The writting style is representative of that of Wiles and Loiville. It will show you how your mathematical writting should be. It takes a lot of practice to learn mathematical formalism and how to write proofs. This is the book to learn from. The author is not afraid to connect the ideas you are learning to other advanced ideas and to mathematical history, unlike present day authors. If you plan to be a mathematician, you must know its history. The writting is in a mathematical sense superfluos. It does not assume you are a genius, but strikes balance between what you should know and what you should be told.

The book is successful in providing you with the big picture, and how ideas you are learning reflect one ideas you will learn or have already learned. Having a big picture of the subject, which he describes in the second chapter, lets you know what you are learning now and puts the entire material in context. Gives you great perspective of the subject. Because a great deal of branches of number theory are discussed, you are not only better equiped to choose which branch might interest you, but it eases the transition to more advanced courses, such as Analytical Number Theory.

The author from the start discusses unanswered questions in Number Theory. I know alot of professors which think that the student should not be exposed to questions that surpass his mathematical knowledge. They are the weak mathematicians. Mathematics is about exploring and breaking limits. You should know what is beyond your reach, and the reach of every one else. The questions that still stand might be answered by some one that was intrigued by the challenge of answering them when they are helpless to do so. Fermat's Last Thorem is such an example. The guy learned it at the age of 10.

The last thing i will say about the book is this. Number theory has one scope. Namely, prime numbers. This book make it clear that the purpose of number theory is to determine the properties of numbers. It discusses the limitations of mathematics in attaining answers to Riemann Hypothesis, Fundamental theorem, trancedental and irrational and algebraic numbers, and so on. Thebook is, in my opinion, an expansion of the section on unanswered questions. And in doing so many more questions are asked and analyzed. There are prime numbers, and nothing else.