Book Description

Best for grades 3 to 8, Math for Humans has a triple purpose: joining the liberal arts type of teacher to solid math education technique; inspiring the more seasoned math teacher to a new level of commitment to "colorful" lessons that reach more students; providing parents concerned about their children's math development the insights and home activities to intelligently supplement school programs.

Math for Humans is both a TEACHING STRATEGY resource in its first 100 pages and an ACTIVITY resource in its last 150 pages. It is designed to add color and life to any math program.The first part is replete with tips, theory, and approaches that can bring to life any math topic. In the second part the over 90 activities tap eight of the intelligences of students regularly, innovatively, and in multiple ways. The two parts of the book afford the widest learning options for teachers or parents: read up on instructional tips and theory or plunge in and learn "in the field" while using the activities in class (or with your child at home) with detailed teacher/parent support.

Some of the book's FEATURES: activities are real-life oriented or have a math "payoff," there are easy ways to extend them up and down in challenge, they are graphically interesting, they cluster in fourteen integrated topical groups, and they have in-depth teacher support that provides a type of inservice training as the activities are used.

PARENTS can profit from Math for Humans if they are concerned that their child is learning "on the wrong channel," or is simply memorizing math mechanically. It will give them an educational viewpoint and vocabulary for choosing appropriate learning experiences or discussing the problem with teachers. It also provides over 90 ready-to-go activities on photocopy masters to create extra challenge and enjoyment for the multiple intelligences as child and parent work together.

Math for Humans is also a wonderful GIFT FOR A TEACHER from a parent if that teacher is someone who has shown an interest in ways to make things better for individual students. As a professional resource book it provides teachers, homeschooling parents, and concerned parents with a wealth of cutting-edge theory, techniques and tips and it offers numerous enriching activities that meet all the intelligences of students. ... Read more

Reviews (1)

Math for Humans by Mark Wahl
This valuable collection of Math {teaching and learning strategies}for humans definitely lives up to its name. Superheros like Math Mole, who touts "the best of what moles have to offer" professes that "the real secret of his success in problem solving is his ability to "get his paws dirty,go after subtle leads (always keeping his sense of purpose and direction), then chomp into real results at the end." Like Math mole, Mark Wahl can "sniff a solution from a distance;" what's more, Mr. Wahl can help younsters sniff out solutions and math know-how by appealing to the best children have to offer: their eight basic intelligences! From merely scanning this book, one might pick up tips to use in the classroom immediately. For example,I used a mind map, or graphic organizer,from this book to show my students how to mulitply fractions times whole numbers. It took less than one minute, and my fourth grade math students were enchanted! I can hardly wait to try the other activities Mr. Wahl has developed for students! ... Read more

Book Description

This text introduces students to basic techniques of writing proofs and acquaints them with some fundamental ideas. The authors assume that students using this text have already taken courses in which they developed the skill of using results and arguments that others have conceived. This text picks up where the others left off -- it develops the students' ability to think mathematically and to distinguish mathematical thinking from wishful thinking. ... Read more

Reviews (4)

A great read to see what lays ahead
I read and worked the problems in this book during my break as I transferred from a community college to a 4-year university, and found it very helpful in introducing me to all the fancy terminology, notation and basic proof writing that I was intimidated by. I found the problems to be hard enough to be challenging, but also neither impossibly hard nor hinging on a silly trick.

If you are a eager HS student, or a curious college student, get this book and work the problems.

Great introduction to mathematics
I bought this book for a course in classical algebra. I found the book well explained and well done. It contains a lot of exercise and example of differents difficulty. It covers logic, set, relation, induction, function, combinatorial proofs, countable sets and uncountable sets, groups and some calculus. The book has a lot of subject in it and it make it very flexible. If you want to ontroduce yourself to mathematics, I would recommend this book if you want to spend some money.

An excellent introduction to mathematical logic!
This book provides an excellent introduction to mathematical logic, set theory, graph theory, number theory, and more -- everything which is "neat" in higher math.

I would strongly recommend this book before any proof-based math class. The authors explain methods of proofs very well, and give some principles universally important in mathematics -- Zermelo's thm., Dirichlet's prin., and such.

The exposition in this book is great. If this is your first exposure to, for instance, the proofs by induction, this probably provides an excellent description of what's going on and how it works, why it works.

The book is slim (at least, the 1992 ed.) and not inexpensive. However, the authors' conversational tone makes it very approachable; at the same time, they are mathematically rigorous and very thorough.

Clear and concise book on math and more
This book is well done. Not only is well done but the explanations are clear and concise. The book offers different approaches. I use it for class and find most revealing. Hope you enjoy too. M. ... Read more

Book Description

Perfect for those afraid of calculus, this book offers an innovative, three-step process for solving almost any kind of basic calculus problem. By unifying coverage and emphasizing similarities across a spectrum of calculus problems, it succeeds in simplifying the subject by providing a conceptual framework. Learning takes place in a comprehensive way, not in unrelated fragments. Numerous illustrations and examples further simplify and illuminate the concepts.

Reviews (1)

Clear, simple theory
This book explains the theory of differential and some integral calculus. There are worked problems, but I mostly ignored them in favor of the raw concept discussion.

I read the book in the summer before my university Calc I class, and it seemed to make everything fit together much more quickly for me than most other students in the class. The book may not be as valuable as others for review, however.

Highly recommended reading before you start a calculus adventure. One of the clearest explanations of calculus theory that I've ever seen. A few hours a week with this book in the summer will save you months of frustration during a hectic semester. ... Read more

Book Description

This powerful study tool is ideal for students not majoring in math or the sciences who wish to master the basics for an introductory course or solo study. The clear explanations of fundamental concepts are illuminated by engaging examples from recent news items showing how these concepts are applied. Students follow along with this tutor through a wealth of problems with fully worked-out solutions. Many supplementary questions with answers let them check their comprehension and sharpen their problem-solving skills.

Reviews (1)

Needed help and this book provided it 110%
Great book that explains the statstics concepts very well. Great book. ... Read more

Book Description

Each chapter in Schaum's Outline of Mathematica focuses on a specific application of Mathematica to provide students with a comprehensive, step-by-step approach to understanding the #1 selling programming language. Numerous solved problems and examples demonstrate and reinforce ideas discussed in each chapter. Mathematica commands with examples are clearly classified according to type. Index of Mathematica commands and an easy index of applications expedite referencing.

Reviews (2)

Great book for learning how to use Mathematica
This is an excellent book for people who are new to Mathematica. It gets right to the point by providing hundreds of examples showing how to use Mathematica to solve problems ranging from basic arithmetic through calculus, ordinary differential equations and linear algebra. It also clearly shows how to use Mathematica to draw 2D and 3D graphs. This book is an excellent supplement to the Mathematica Book, which is included on the Mathematica CD.

Schaum's Mathematica is a great introduction.
This is an excellent introduction to Mathematica. I have suggested that they include this with each copy of the software and offer it (free?) to prospective buyers. A great review of the basic aspects of a very extensive software application. ... Read more

Reviews (5)

Good supplemental review
My two sons used this book to help them understand their pre-calculus courses. It was also a big help for them in physics and astronomy.

Refreshing, not stodgy
This book presents trigonometry in a relatively informal and understandable way. Emphasis is on the facts, without getting sidetracked in proofs. The drawings are relevant and straightforward. The book is well-organized and proceeds logically from beginning to end. There are some question-and-answer problems in the text (although I'd like to see more) and plenty of multiple-choice test questions with answers in the appendix. The test questions are especially good, because they resemble the standardized tests schoolchildren are forced to take these days. The four-dimentional stuff is cool (but may be over the top for some readers). This book, combined with a standard school textbook, should make high-school students highly proficient in this subject, and get them ready for more advanced courses such as calculus, analysis, and topology.

This guy blows at writing books
This guy stinks at writing books. The first ten pages of his book are annoyingly vocabulary intensive. Rather than spending a little time familiarizing you with the terminology, the author immediately begins using every possible word in his vocabulary forcing you to have to glance at your notes. He's probably a great math geek, but can't teach if his life depended on it. Don't bother with this book.

Good for beginners
I am a math dummy. I bought this book at a local store because it looked like I could maybe understand it. I do. For the first time I feel like I know something about trigonometry. Too many math books are just professors showing each other how smart they are. This book taught me something without making me feel stupid. It's the only trig book I have ever seen like this.

If You Want to Learn Trigonometry, Find a Different Book!!!
First off, I'm not afraid of math--I had a 100% in my college algebra class last semester, and I bought this book to get a quick overview of trigonometry to give myself an edge before taking a formal class. I bought this book because I had been very satisfied with Algebra: Demystified, and had assumed that all books in the Demystified series would be of a comparably high quality, but I was sadly mistaken. This book is terrible--it will not teach you trigonometry. Mr. Gibilisco wastes lots of space giving you no brainer advice like a whole paragraph on why you should use your calculator if needed or reviewing simple things like the Order of Operations. On the other hand, he gives a formula for circular motion in the first chapter and doesn't even bother to explain the variables or provide an example of it. The second chapter, appropriately titled, "A Flurry of Facts" is an endless series of formulas, most of which don't come with examples. Furthermore, the book doesn't have sufficient exercises. There are only 10 multiple choice questions at the end of each chapter, and they don't have solutions, not to mention that examples of similar problems within the chapter were strangely absent. Although I was able to score 100% on both of the first 2 chapter tests, I gave up in the middle of the third chapter because I realized that if I really wanted to learn trigonometry, I should go elsewhere. Once I have found a better text, I'll edit this review to refer you to it. ... Read more

Book Description

Here is instruction and review in whole numbers, fractions, percentages, and introductions to algebra and statistics, plus a diagnostic test and an end-of-book practice test with answers.

Over the years, Barron?s popular and widely-used Easy Way books have proven them-selves to be accessible self-teaching manuals. They have also found their way into many classrooms as valuable and easy-to-use textbook supplements. The titles cover a wide variety of both practical and academic topics, presenting fundamental subject matter so that it can be clearly understood and provide a foundation for more advanced study. Easy Way books fulfill many purposes. They help students improve their grades, serve as good test preparation review books, and provide readers working outside classroom settings with practical information on subjects that relate to their occupations and careers. All Easy Way books include review questions and mini-tests with answers. All new Easy Way editions feature type in two-colors, the second color used to highlight important study points and topic heads. ... Read more

Reviews (5)

Helpful.
I checked out quite a few books to help me review basic math and algebra concepts, not knowing which ones would click with me and which wouldn't. Of the six hefty workbooks I selected, this one was my favorite. It offers lots of pre-tests, exercises, and follow-up tests with explanatory answers at the back. The first test in the book tests what you already know overall before studying the information inside, and then each answer is listed in an index next to a label of what sort of problem it is, allowing the reader to pinpoint areas where help is needed. The book has some cartoon drawings which some people might find distracting but I liked the light-approach, the actual verbal descriptions are clear and not 'jokey' or distracting like some of the other books were. I found the methods and how they were presented easier to work with than the other books.

Does a great job
This book helped me get my "math" legs back under me. I feel that it is primarily aimed at those with a prior knowledge and only need a good refresher. It starts out with basic things such as percents and long division, and it ends up touching upon some basic algebra. If you need a good refresher, this book is great.

really great book!
this was a brilliant book for 6th graders going into 7th, it reviews elementary maths, and explains the subjects you hadnt got before, or widens your knowledge on that subject. it provides examples, tests and exercises, it also has the solutions, and answers at the back, if your not quite sure how to do it.

this book is truely the easy way!

Great Review!
I found this book to be extremely helpful. I have never been very good in the math department and this book has helped me considerably. It is very easy to understand and it makes problems such as (6/2)-(8/9)=? seem very simple.

The author first gives you a basic outline and then he goes into more detail, with many sample problems. This book explains basic concepts much better than any of my former teachers ever did. I am going back to college and I needed a refresher course, I could not have asked for or found a better book to get the math review I needed. I recommend this book wholeheartedly.

OK if you can add, subtract, multiply, and devide everything
This book assumes so much it should be considered a small refference and not a learning tool.

I am terrible at math and have been all my life, and now I am going to be taking it in college. I thought I should study math before I tried to attempt it at college, so I got this book. Boy was this the wrong book for me. It starts out assuming you are very good at addition, multiplication, subtraction, and division. They give you problems like 6 - (4 + 2) + 8 ÷ 4 before they even discuss any of the operations used. Look in the table of contents and you won't even find a section on addition, subtraction, multiplication, or division. Its all covered very minimaly in one section on whole numbers. Before you can even say the word you into adding, subtracting, multipling and deviding fractions.

This book is definetly not for people who have real problems with math. ... Read more

Reviews (3)

A very interesting notion
Disclaimer: I actually have no children at this time on which to try this method, so unfortunately I have only to pester my friends to read the book to try it out and cannot speak to the results. That aside, the book was, in itself, tremendously interesting to me.

The idea of the "Gentle Revolution" is that children are able to take in and process tremendous amounts of information beginning at birth. This period of intense and specialized learning is to come to a close around the age of five, coincidentally the same time at which most children begin to be formally trained. The author developed his theory, originally, through his work with children who had sustained all different types of brain injury. His discoveries about their learning processes, led to discoveries about the learning process for all children.

The reason that I had to give this book four stars, although I did find it so fascinating, is that, if you have read How to Teach Your Baby to Read, you will find that at least half of this book is a reprint of that, with reading taken out and mathematics put in its place. The book does pick up again when they get away from convincing you that you should try this and why, and get to the actual method.

The author believes that babies can learn math instantly and quantitatively. He believes that a baby can look at an 11"x11" white card with a lot of 3/4" red dots on it, and immediately know that there are 79 dots. It all seems very "Rainman". He suggests that numbers, or numerals, only serve to confuse the situation, and that babies can be taught math using pure quanities, without the numbers getting in the way. The steps involved include recognizing quanities instantly, addition, subraction, multiplication and division, simple algebra, sequences, etc..

The method seems simple enough, if one is willing to put forth the effort to make up the flash cards and spend the few minutes each day it takes to go through them with the baby.

The book also decribes the different ways one might approach this program given different age groups, such as newborn to three months, eighteen to thirty months, up to five and six year olds, and encourages that whatever you do and whatever effort at whatever stage you do it, can only benefit your child.

I would recommend this book if you are interested in raising an exceptional child, or even if you just have a general interest in the brain and the learning process.

Excellent!!!
The method that Glenn Doman explain in this book is wonderful my baby enjoy his lessons a lot. In fact I've was looking for others ways to estimulate the intelligence of my baby and I'd just want to have more time to do all of them.

The babies are eager to learn!
Initially I was skeptical about teaching my 18-month daughter math. But after reading the book, I found out that that Glenn Doman and Janet Doman have discovered the completely different method of teaching a baby math, not the same that is using in junior schools. Their method suits for a baby from zero moths old, i.e. from birth. The are three lessons a day, each lesson last fifteen seconds and give such a joy to the baby that she woke me up in the mornings asking me to teach her math. When she hears my steps when I return from my job, she runs to me to teach her math. The babies CAN and WANT to learn!

The babies are eager to learn, they want desperately to learn everything they can, as quickly as possible, but the adults are often fail to provide for the babies the adequate opportunity of learning.

Glenn Doman and Janet Doman offer funny and inexpensive way of teaching the baby math, by means of special inventory: cards with red points indicating a real quantity.

A few words from my own experience on producing the inventory: don't even imagine of cutting the cards or the points by yourself. Order the empty cards of the specified size in a nearby company, which prints business cards. Order five thousand 0.75-inch sticky red circles on a roll of ORACAL in a nearby company, which decorates the shop windows. The authors do not emphasize on ORACAL, but the process of putting the circles to the cards should be as easy as possible. ... Read more

Book Description

Book Description

This eminently readable book focuses on the people of mathematics and draws the reader into their fascinating world. In a monumental address, given to the International Congress of Mathematicians in Paris in 1900, David Hilbert, perhaps the most respected mathematician of his time developed a blueprint for mathematical research in the new century. Jokingly called a natural introduction to thesis writing with examples, this collection of problems has indeed become a guiding inspiration to many mathematicians, and those who succeeded in solving or advancing their solutions form an Honors Class among research mathematicians of this century. In a remarkable labor of love and with the support of many of the major players in the field, Ben Yandell has written a fascinating account of the achievements of this Honors Class, covering mathematical substance and biographical aspects. ... Read more

Reviews (8)

A great work
Due to rapid development of mathemtics in the last century, now one cannot master all subfects of mathematics. This is also true for those historians. Most of the boods of " History of Mathematics " end in the beginning of 20th century. So we know very little about the conteporary mathematicians. This book can be described as a gap for it. After readiming this book, not only you have a knowledge about the life of the great mathemaitcians, you also get the period in World War II how Nazis forced those mathematicians out of Germany and the reason why U. S. A. is now the leading centre of mathematics.

Useful and insightful
The book is well written with the right mix of anecdote and theory. What I do like about it is the fact that we find out a little more about the lives of mathematicians, and they are portrayed as people rather than idols.

Where the book falls down is that it goes into a little too much detail of the theorems, something which the non-mathematician will undoubtedly find hard to follow.

A page turner
Fascinating historical comments, lively portraits of mathematicians, and their times. While the narrative is about the lives of some great mathematicians, it sucessfully outlines main ideas in the subject,--the personal and scientific context. The author does a great job in sharing his fascination with the rest of us. The book covers roughly the past hundred years. It is a great service to the mathematics community,-- and especially, it is an enjoyment for everyone.
It reads like a novel, fast paced, and it is hard to put down. I meant to look at it before going to sleep, but instead read it to the end, finishing in the morning. As a professional mathematician, I am often saddened by how little our work is perhaps understood and appreciated. Books like this can do a lot of good. I can now tell my children that dad does stuff like that.
The author brings the events and the mathematical people to life, and he has a story to tell. This book is and will be a success for a long time to come.

Best since "Fermat's Enigma"
In 1900, David Hilbert gave an address to the International Congress of Mathematicians that outlined the twenty three most important unsolved problems of mathematics, as he saw them. In "The Honors Class", Benjamin Yandell describes the problems and the very remarkable people who worked on them. More than a century later, there are still a few that remain unsolved, and some of those that have been successfully attacked withstood assault for many decades. I was familiar with many of the names in book because they are associated with equations that I have used and that I teach my students about. It was not until reading this attractive and well-written history that I was able to put those names and their contributions into context. This is the best popular book about mathematics that I have read since "Fermat's Enigma" by Simon Singh.

Almost a biography of math itself
The "Honors Class" is the set of mathematicians who have solved, or heftily contributed to solving, one of the famous 23 problems proposed by David Hilbert a hundred years ago.

Energetically researched, Yandell's book naturally presents numerous morsels of biography, spotlighting the eccentricities, the sobrieties, the childhoods, travails, philosophies (he got me to understand, finally, why the intuitionists cared so much about their program), and politics of the members of the Honors Class. But from all these snippets, what emerges is a biography of mathematics itself in the 20th century; a sense for the marvelous, moving, growing organism that has been the mathematical quest.

Many bright men and women, many geniuses, populate these pages. But with two exceptions (Georg Cantor, the mystical grandfather of modern logic and set theory; and the remarkable Teiji Takagi, who built Japanese mathematical culture, and the class field theory that led to solutions for three of Hilbert's 23, all seemingly with his bare hands) they didn't wield their chalk in solitary splendor. They formed a web made of learning, mentoring, competing, collaborating, inspiring; a web that converged on and spread out from two tumultuous epicenters of the century's math activity: Goettingen in Germany (until Hitler drove out all its best minds), and Princeton's Institute for Advanced Studies.

There are four parts biography to one part math here. That should make the book as approachable for laymen as it is delightful for the math sophisticates who'll get to put faces on all those familiar old names. The address in which Hilbert set out his problems is given in full as an appendix; and those who wish to pursue the technical topics further get a bibliography rich enough to keep them occupied for years.

You'll get only tantalizing tastes, best in the earliest and latest chapters, of the nitty-gritty content of 20th century mathematics. But you will get a doubleplusgood, full-length portrait of what it became as a social and cultural enterprise. ... Read more

Book Description

This text provides guidance for elementary teachers who are looking to learn the basics of the varying levels of elementary math. Sonnabend provides an active, engaging approach that illuminates the underlying concepts of mathematics in grades K8. The text includes coverage of reasoning, sets, arithmetic, geometry, measurement, algebra, statistics, and probability. The text's interactive lesson format encourages students to participate in the development and explanation of concepts, establishing a solid understanding of mathematics. ... Read more

Book Description

Getting a Grip on Algebra, Geometry & Trigonometry


Contains hundreds of practice exercises with worked-out solutions
Includes a complete glossary of mathematical terms
... Read more

Reviews (7)

Good Review book, but don't buy it to learn new information
I bought this book a few years ago, and I was like, wow! now I get to learn all about trigonometry and inequalities and polynomials! gee whiz! but reading it, I found that the explanations weren't deep enough to actually TEACH me the concepts, that there weren't enough excercizes for people new to the algebra, and it wasn't until I finished my Algebra 1 class last year that I could fully understand the topics covered in this book, because I had learned all of them during the year(i.e. polynomails, quadratic equation). Looking back at this book, I think, however, that it is a good review book, in part because its coverage of topics is so superficial. So, if you've seen the stuff in this book before (algebraic expressions, equations, exponents, roots, logarithms, polynomails, inequalities, permutations, combinations, binomial therom, plane,solid and analytic geometry, parabolas, conics, trigonometry of degrees, radians) then you'll understand them, but if you haven't, go buy another book with better (and more) excercizes, more accurate answers to them, and better explanations.

Good Learning Supplememtary
I began this book in the fouth grade. I wanted to excel in mathematics and geometry. Answers were somewhat accuarate; when they were not I was utterly perplexed.

The Algebra section was clear; I often needed to re-read sections to understand information expressed. Geometry was almost clear, again I needed to re-read and was sometimes confused. Analytic geometry was very puzzling- I needed adult assistace. Trig was very clear, and I now have a good grip on trig. Readers for this book should consider buying another ^workbook^ as to achieve stronger levels of understanding from practice. Being determined to understand, this was essential.

Be careful of the wrong answers in the book
I am willing to give this book three stars because it provides a good review of high school math. I bought it as a warm up for future studies on Calculus and for preparation for the GRE.

However, there are several wrong anwers that I have seen in the book. I am grateful to the Princeton Review for confirming these mistakes by e-mail for me.

For those of you who decide to get the book, here they are:

1) page 26, #7, x= -10/3 (not 10/3)

2) page 28, #5, should be -3x squared -2x +1 over 2x squared -2x

3) page 120, exercise 8.4, #1, should be 64 (not 32)

Part of the problem here may be the fact that the author, Marcia Lerner, only has a Bachelor's degree. The publisher, Princeton Review, should consider hiring people with at least Master's degrees in the future. "Math Smart II" is marginally acceptable as a learning tool.

I did find that it was more helpful in studying for the GRE math section than the Princeton Review's "Cracking the GRE CAT." That's because with that book (and some other GRE books), the idea is to teach you the best strategy for answering the questions rather than making sure you understand all the concepts behind the answers. So in that aspect, "Math Smart II" can be of help for GRE test takers.

Good Sample Problems
I love using this book to present my daughter with sample problems for test review or when I think the school is not teaching at the level of my expectations. My daughter is in 7th grade, I think this book may be elementary for high school students, however. Still could provide good review problems at test time.

A solid foundational book
This book provides the basics required for higher level mathematics. It breaks down the concepts so that they can be better understood, without simplifying them beyond use. Good for a high school review, and preparation for pre-calculus. The style of the prose is easy going, upbeat and contains even a hint of humor, which makes understanding the sections more enjoyable. It should be noted that a mathematical background, pre-algebra, is assumed, and answers are not given for all questions. Not meant for those interested in reviewing pre-calc or calculus. ... Read more

Book Description

This book gives readers a comprehensive look at the most important concepts in the mathematics taught in grades 9-12.Real numbers, functions, congruence, similarity, area and volume, trigonometry and more.For high school mathematics teachers, mathematics supervisors, mathematics coordinators, mathematicians, and users of the University of Chicago School Mathematics Project materials for grades 7-12 who want a comprehensive reference book to use throughout their careers or anyone who wants a better understanding of mathematics. ... Read more

Reviews (1)

Sui Generis
This book is one of a kind. It affords an integrated perspective of traditional high school mathematics, making explicit the intimate relationships between arithmetic, algebra, and geometry. Additionally, it indicates and suggests lines of development that are pursued in undergraduate courses. Both purposes - showing the unity of the subject, and indicating further development - are accomplished by placing traditional high school topics in a broader conceptual and historical perspective.

The book is divided into two parts; the first, titled "Algebra and Analysis with Connections to Geometry", deals with numbers, functions, equations, polynomials, and number systems. The second, titled "Geometry with Connections to Algebra and Analysis", deals with congurence, symmetry, similarity, area annd volume, axiomatics, and trigonometry.

To give some idea of coverage, the second chapter (on real and complex numbers) discusses irrational numbers, a proof of the irrationality of e, the nested intervals property of the reals, countable and uncountable sets, and the diagonal proof of the uncountability of the reals. The chapter on equations briefly discusses cubic and quartic equations and states the unsolvability of the general quintic; the names of Gauss, Ruffini and Galois are mentioned. The chapter on integers and polynomials discusses induction, recursive definitions, simple diophantine equations and the fundamental theorem of arithmetic. It also indicates the analogies between the integers and the set of polynomials (both are integral domains). The chapter on number system structures discusses modular arithmetic, the Chinese remainder theorem, and gives examples of number fields other than the real and complex number systems (e.g. quadratic fields, and finite fields).

The projects at the end of each chapter extend the material covered in a natural way, and are challenging. To give some stray examples, the coordinatisation of the Riemann sphere, the Cardano-Tartaglia method for solving cubic equations, Fermat's last theorem for n = 4, constructible numbers, and the impossibility of squaring the circle and doubling the cube.

The chapter bibliographies are annotated, up-to-date, and list excellent books for further study.

I have a few criticisms. The first is that surjective functions are not discussed, and in this connection the Schroder-Bernstein theorem does not get mentioned or proved. A second and more serious criticism is the slender coverage of analytic geometry. Only five or six pages are devoted to this. As a consequence, the authors cannot discuss the rich field of algebraic curves in particular, and algebraic geometry in general. There is also no mention of projective transformations (i.e. projective geometry) or continuous transformations (i.e. topology). Finally, there is no mention of Klein's Erlanger program.

These quibbles aside, the book is well-conceived and well-written. It can join Courant and Robbins' "What is Mathematics", and Stillwell's "Mathematics and its History" as a book that gives a bird's eye perspective of (part of) the discipline.

Professors teaching undergrad courses would want this book on their shelves; it shows some of the connections between high school material and the relatively abstract courses taught at college (e.g. Galois theory, group theory, algebraic number theory, and real and complex analysis). Undergrad students might want this book for the same reasons. High school teachers who want a bird's eye perspective of high school mathematics from a sophisticated point of view might also want a copy; suggested lines of development can be used as enrichment topics. ... Read more

Book Description

Demonstrates a slew of time-saving tips and tricks for performing common math calculations. Contains sample problems for each trick, leading the reader through step-by-step. Features two mid-terms and a final exam to test your progress plus hundreds of exercise problems ranging from simple to more sophisticated. Also includes sections on ``Mathematical Curiosities'' and ``Parlor Tricks'' for math lovers. ... Read more

Reviews (4)

Examples of math that should not be done
This book is designed to do something that simply should not be done. While the mathematical inadequacies of the American public are conceded here, teaching people sixty tricks is hardly the solution. Furthermore, if someone cannot divide by 4 in the normal way, how is it possible that they will learn to do it by dividing by 2 twice? The rules of division are the same in both cases. If someone understands the rules of arithmetic, then all of these tricks are superfluous.
Even if these sixty special cases are thoroughly learned, that is, memorized, the amount of mathematics digested will be minimal, as no generalizations are made. For example, one of the tricks is the rapid multiplication of any one- or two-digit number by 101. But the reasons for this are never explained, so the end result is the reader knows only one particular operation on a small set of numbers.
The accountant or bookkeeper that wishes to increase their ability to compute on the fly may find this book of interest. But, to all others, the message is simple and direct, spend your time learning the general rules of arithmetic!

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This is way better than his first rapid math book!
I have to admit I hated the first rapid math book he wrote.Besides that,this book is way more better than the first.I gave it three stars instead of five because you have to memorize all of the addition ,subtraction ,mutiplication, and division tables.I wish he would teach rapid math tricks to remember your tables.You'll keep saying to yourself "If only I knew my facts this trick would be alot easier." I hope he reads this.

Title Somewhat Deceptive
I am a long retired teacher and supervisor of mathematics. In addition to having taught math for many years, I have also written and published materials covering the same subject. I am now using this book with an eight year-old math whiz and find it valuable to introduce him to rapid calculation and then an analysis of why it works (largely based on our place-value system of numbers. The various methods are interesting but most of them are not very practical for everyday calculation since most are special cases rather than general applications. For successful use they also require instant recall of the basic number facts and there is no hint as to how this can be accomplished. Barring that prior requirement not many math phobes will become highly skilled arithmeticians in 30 days using this or any other book.

Cool Tricks
This book has some very cool tricks. It really helps out a lot on tests. It is fun to show my dad them (he is really interested in math). In math class we are reading this book and doing the problems. I don't see how Mr. Julius figured out these tricks. You should get this book! ... Read more

Book Description

The Princeton Review realizes that acing the SAT II: Math Subject Tests is very different from getting straight A’s in school.We don't try to teach you everything there is to know about math–only what you'll need to score higher on the test.There's a big difference.In Cracking the SAT II: Math, we'll teach you how to think like the test writers and

·Eliminate answer choices that look right but are planted to fool you
·Score higher by reviewing some basic math concepts
·Earn more points by Plugging In and Ballparking
·Learn advanced techniques for tackling the more complicated problems on the IIC test

This book includes four full-length practice SAT II: Math Subject Tests (two for each level).The practice questions are just like the ones you’ll see on the actual exam, and we fully explain every solution. ... Read more

Reviews (16)

An excellent guide for those with a solid math background!
You're nervous, you're sweaty. You see the person in front of the room talking but you can't quite understand what he is saying because you are too focused on the task before you. You know that this test could mean saving thousands of dollars and getting into the college of your choice. Welcome to the SAT II subject tests, a rite of passage for anyone who is applying to more competitive schools. Most students haven't even heard of SAT II's and are unfamiliar with the importance of these specialized tests. This book provides the reader with a guide to understanding the nature and format of the SAT II Math IC and IIC. Before I make any comments on the book I want to provide you with some details about my math background. I am an honors student who is currently enrolled in AP Math (Calculus) and scored a 680 on the math section of the SAT I. When I took the Math IIC for the first time (after having used this book to cram the night before and morning of the test) I scored a 780 out of 800, not bad. I feel that this book is effective only if you have a solid math background and if you are willing to do all of the exercises and practice in the book. Like anything the more you work at it the better you will get. This book is very good when it comes to providing the reader with quality content in an easy format to understand. It is also important to know that this book alone will not make you score well, but will raise your score. Good Luck on the Test!

Comparing with Barrons (For Math IIC)
This is not a bad book for those of us who have a solid background in trig and (pre)calculus. Unlike its Barrons counterpart, this book is a no nonsense guide to the SAT II math iic.

It tells you the sort of topics and questions to expect on the test. It is true that the questions are considerably easier than the real deal, the questions and the practice tests depict the actual test a lot more accurately than the Barrons.

Barrons manages to give you a screwed up impression of the real test, mentioning and giving inadequate explainations for many topics that AP level students haven't heard of (and that you certainly don't need to know for the SAT II). However, Barrons does train you harder and if you manage a score in the upper 30's on the Barrons, you should be OK on test day.

The only flaw with the Princeton Review book is that it doen't give you any security as it doesn't have an in-depth coverage of the topics (but again it is adequate if you are just reiewing topics that you have mastered previously), nor does it have tough questions.

Lastly, if you are willing to put in the effort, I would recommend you to buy this book and the Barrons just to freak you out and make you work harder in addition to the Real SAT IIs book just so you can see where you really stand.

Crap
3 exercises on one page, so few examples, incomplete and misleading, plus the exams are old fashioned; I wish I never bought this book.

excellent book for review!
This book is very helpful and is easy to follow. They seemed to cover everything given on the test and offered great explanations. I believe I did spot a few typo's though? But nothing major. The tests at the end of the book were helpfull too; they seemed to me to be the same level of difficulty that the actual test was. Also, what's cool is that you can actually find your estimated scaled score... After taking the math 2c (got 790) I feel this book really provided me with a good review of math concepts. Good luck to all...

Fine book for reviewing
The SAT Math II tests both cover a wide range of topics. One cannot expect any one book to cover them all. This book tries its best to cover all topics but it should not be a replacement for a precalc / algebra II textbook - only a supplement. It gives you tips and tricks to master the SAT tests that one might forget such as trig methods for calculating areas for parallelogram and triangles.

If you have a strong background in math or have taken a precalc course, this book should almost be a breeze. It covers all of the basics but only touches upon more complex subjects such as binomial combinations and polar coordinates. But the author does have a point - your chances of seeing those questions on an actual test are very slim.

All in all, this book won't let you down ... Read more

Book Description

Essentials of Mathematics is designed as both a textbook and outside reading for college students who want to prepare themselves for mathematics courses beyond the first-year level. The mathematical content includes logic, set theory and a theoretical development of the number systems, giving students practice at proving mathematical statements. There are no answers in the book, but a separate manual provides instructor support. The book makes an excellent reference for students beginning to take courses in which proofs play a major role. In addition to the course material, there are narratives on the nature of mathematics and the mathematics profession. These sections can be read without help or guidance. ... Read more

Reviews (1)

First learn the fundamentals
As a youngster, I loved baseball and read everything I could about how to play the game. Each book that I read started with the line, "You must first learn the fundamentals." This also applies to mathematics, where there is a small set of axioms, definitions and theorems that form the basis of most of what else can be learned. Many teachers have started applying this approach to their teaching of mathematics and are beginning to offer a class in the fundamentals of mathematics early in the undergraduate curriculum. This book is an introduction to the fundamentals, as well as the theory and philosophy of mathematics.
The coverage begins with a basic explanation of what mathematics is, what kind of people do mathematics and some of the ways in which it is split into categories. Chapter one is a survey of the fundamentals of logic and chapter two covers set theory. Each of the next four chapters contains a brief coverage of the sets of numbers in increasing order of containment. The natural numbers are described in chapter three, the rational numbers in chapter four, the real numbers in chapter five and the complex numbers in chapter six. The explanations are well-done and a large number of exercises that advance your understanding are included.
Written in a style well within the knowledge base of the beginning undergraduate math major, this is a book that can be used in courses in the fundamentals of mathematics. The highly motivated individual could also use it in a plan of self-study.

Published in the recreational mathematics e-mail newsletter, reprinted with permission. ... Read more

Book Description

This second edition of the immensely popular, "101 Careers in Mathematics," contains updates on the career paths of individuals profiled in the

first edition, along with many new profiles. No career counselor should be without this valuable resource.

The authors of the essays in the this volume describe a wide variety of careers for which a background in the mathematical sciences is useful. Each of the jobs presented show real people in real jobs. Their individual histories demonstrate how the study of mathematics helped them land good paying jobs in predictable places like IBM, AT&T, and American Airlines, and in surprising places like FedEx Corporation, L.L. Bean, and Perdue Farms, Inc. You will also learn about job opportunities in the Federal Government, as well as exciting careers in the arts, sculpture, music and television. There are really no limits to what you can do if you are well prepared in mathematics.

The degrees earned by the authors profiled here, range from bachelors to masters to Ph.D. in approximately equal numbers. Most of the writers use the mathematical sciences on a daily basis in their work; others rely on the general problem-solving skills acquired in mathematics as they deal with complex issues.

Students should not overlook the articles in the Appendix that are reprinted from the MAA’s student magazine, "Math Horizons." These articles provide valuable advice on looking for a job and on the expectations of industry. ... Read more

Reviews (1)

The full spectrum of careers in mathematics
This is one of the few books that should be on the library shelves at all levels of education, from the middle school up through the bachelor's degree. A collection of short essays written by people who work in many different areas, it is a demonstration of the enormous number of ways math is used in the modern world. By reading this book, anyone contemplating a career in mathematics or one that uses mathematics can understand the value of taking mathematics courses.
The people interviewed includes math teachers at all levels, actuaries working for the insurance industry, people who work with computers, others who work in industry and some in the public sector. None of the jobs is the same as any of the others, even if their job descriptions are the same. From these essays, it is clear that no two math jobs are the same. The joy and excitement that these people have about their work also comes through very strongly, demonstrating that mathematics knowledge is a path to exciting and interesting work. Given the unsettled nature of employment at this time, it is comforting to anyone contemplating a career path when they hear that mathematics is a skill that is very transferable and one that employers desire.
There are so many myths that permeate the collective psyche of society. One of the most pervasive (and incorrect) is that there is no use for math outside of the classroom. That is wrong, and this book contains 101 existence proofs of the contrary.

Published in the recreational mathematics newsletter, reprinted with permission. ... Read more

Book Description

• 2 full-length practice tests
• Diagnostic quizzes for each topic tested
• Detailed answer explanations
• Powerful strategies to help you score higher
• Focused review of important rules and formulas
• Practice questions in each chapter, covering all tested material, from Algebra and Geometry through Trigonometry, Statistics, and Probability
• Chapter summaries to help you find what you need quickly
• The most up-to-date information on the test

Level 1Level 2

Content

2 years algebra 2 years algebra
1 year geometry 1 year geometry
1 year trigonometry or precalculus

Difficulty

Less advanced mathMore difficult questions even on the basic topics

Scoring

A score of:Requires a raw score of:
800 50 out of 5043-44 out of 50
500 19-21 out of 50 10-12 out of 50

Kaplan Test Prep and Admissions has helped more than 3 million students achieve their educational and career goals. With 185 centers and over 1,200 classroom locations throughout the U.S. and abroad, Kaplan provides a full range of services, including test-prep courses, admissions consulting, programs for international students, professional licensing preparation, and more.

For more information, contact us at 1-800-KAP-TEST or visit kaptest.com. ... Read more

Book Description

Schools do matter. There is a direct correlation between what schools teach, and what students learn and achieve. With this important study you'll explore the curriculum-learning connection, and the prospects for improving educational outcomes for all kids.

Why Schools Matter emerged from the Third International Mathematics and Science Study (TIMSS)--the largest ongoing educational research effort. TIMSS results have been widely reported in the popular press to underline how far the U.S. lags behind other Western countries in math and science achievement. This important study is the first comprehensive analysis of curriculum for teachers, school and district administrators, directors of curriculum, and educational policy makers. ... Read more