Product Description
This text explains the fundamental principles of algorithms available for performing arithmetic operations on digital computers. These include basic arithmetic operations like addition, subtraction, multiplication, and division in fixed-point and floating-point number systems as well as more complex operations such as square root extraction and evaluation of exponential, logarithmic, and trigonometric functions. The algorithms described are independent of the particular technology employed for their implementation.

Numerical examples illustrate the working of the algorithms presented and explain the concepts behind the algorithms without relying on gate diagrams.

This new edition includes sections on floating-point adders, floating-point exceptions, general carry-look-ahead adders, prefix adders, Ling adders, and fused multiply-add units. New algorithms and implementations have been addedto almost all chapters. ... Read more

Customer Reviews (6)

Excellent but challenging book on computer arithmetic algorithms
Although I found this book very challenging to read at times, the author gave enough examples for each algorithm to help steer me in the right direction. To succeed in reading and understanding the book's content one has to carefully work through the examples and practice with self-created ones to help get the needed insight. Many of the terse explanations and equations require careful thought and analysis from the reader. Often I found myself working out the deatails of some equation to convince myself of the author's assertion. In other words, one has to be actively engaged when working throug the book. The reward for doing seems very profound: namely one gains an understanding of how arithmetic is efficiently performed, and how transcendental functions are realized on a computer. The ability to reduce the foundations of mathematics to a Boolean structural level will no doubt find many applications that go far beyond hardware arithmetic component design. With that said, from basic addition to cosh and sinh, the author delivers as advertised. Dr. Koren has an impressive mastery of this subject.

Amazing collection of ideas but terse in explanation
On a first reading, this book looked horrible. Little explanation is given. Well, the author gives you just a clue for you to do a lot of brainstorming to understand the concepts. While this helps to put you right in the mood for the material, since most of it are highly intellectual, but I think some more explanation and insight would have helped anyway. And actually it would have helped a lot. Instead of relying on each reader's understanding, giving more clues and more explanation means more insight for the reader and more getting the big picture. The big picture here is so important since many of the concepts in this book are highly interrelated.
On a second reading, this book was a very good reference. A good collection of well made, highly intellectual algorithms.
I recommend this book for every computer arithmetic enthusiast, but I suggest it to be read sequentially, and be prepared to a lot of brain storming.

Probably one of best arithmetic books
This book is a fantastic book on digital computer arithmetic that covers the basic algorithms.It covers basic addition, subtraction, multiplication, and division in an easy-to-follow manner.A must-have for those concentrating on digital computer arithmetic.

Note:the reviewer who noted that this book doesn't cover Brent-Kung is wrong.It covers things the way it should!

It is a horrible textbook
I am a graduate student. This book is a first horrible textbook I have had. It is very difficult to grasp the basic concepts from the book. And the content jumps all over the place. The author seems to have the ability to make simple things complicated.

Brilliant book for Brilliant minds !
There are very few books in market that are as packed in content. I like the author's lucid style of emphasizing his points while still maintaining the rigor of the subject. Digital hardware engineers have used and willcontinue using this book for sound design practices and optimized designs. ... Read more

Product Description
The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic approach in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. Following a brief discussion of the necessary algebro-geometric results, the book proceeds with an exposition of the geometry and the formal group of elliptic curves, elliptic curves over finite fields, the complex numbers, local fields, and global fields. Final chapters deal with integral and rational points, including Siegels theorem and explicit computations for the curve Y = X + DX, while three appendices conclude the whole: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and an overview of more advanced topics. ... Read more

Customer Reviews (3)

Essential introduction
This is a superbly written introduction to elliptic curves. I like the straight-forward language. I dread the stiff elaborations, one finds in some german books with awkward idioms etc..

I found it fascinating, how the elements of general theory, explicit formulae and geometric ideas (the group law on an elliptic curve is constructed via means of geometry) are interwoven.

However, if you want to get a glimpse of such fundamental theorems like the Mordell-Weil theorem, you will need a solid understanding of the basics of algebraic number theory.

Also, if the author tells you "it is clear", it may take you two or three pages of your own thoughts and scribblings to actually see, why it is "clear". Sometimes it really is clear, but sometimes he might be referring to basic results from algebraic number theory. For example in VIII.$1 Proposition 1.6, a field is constructed, which is unramified outside a certain set of places of the number field K. The notion "It is clear .... is unramified if and only if ord_v(a) = 0 ..." had me puzzled for a while, until it dawned on me, that I needed a certain separability criterium for the polynomial to show what was needed.

All in all, still a great book.

Excellent introductory text
This is a standard text now, and indeed it has it merits. The book uses algebraic geometry of curves throughout, instead of using the so-called 'Lefschetz principle' as done in older texts like Serge Lang's. Using general theorems of algebraic geometry instead of explicit polynomial calculation simplifies discussion, and at the same time paved the way for the reader towards the higher dimensional version of elliptic curves --- abelian varieties, whose geometry and arithmetic predate much of modern number theory research.
After preliminary chapters on the underlying geometry of elliptic curves, the book take up its main aim -- proving the Mordell-Weil theorem, in chapter 8. The Mordell-Weil theorem states that the group of rational points over a number field is finitely generated, and finding the rank of this finitely generated abelian group effectively is subject to much current research (c.f. the Birch Swinnerton-dyer conjecture).
The proof of Mordell-Weil theorem in this book is standard: one first establishes the weak version: E(F)/m E(F) for any integer m >1 , is a finite group. To prove this one has to know basic algebraic number theory, Kummer theory, and some Galois cohomology. For those who are not familiar with Galos cohomology, the author has provided an appendix on Galois cohomology, which should contain all that 's needed.
To deduce the full Mordell-Weil from the weak one, one establishes an important device: the theory of heights on elliptic curves. The height of a point is roughly a kind of norm, which measures the arithmetic complexity of the point (i.e. set of rational points with height bounded is finite) . The height function come with a whole family, but there's a canonical one , the so-called Neron-Tate height, which actually is a quadratic form on the algebraic points of the elliptic curve. After establishing the property of this height, one nearly trivially deduce that the rational points must be finitely generated.
The heights on elliptic curves and abelian varieties contain lots of (conjectured) information about the arithmetic of the varieties. One readily realise this when one look at the BSD conjecture, the Gross-Zagier formula, and various Diophantine approximation type conjecture (e.g. Vojta's) .Therefore it's worth spending time to study the theory of height. Unfortunately the author develop just that amount of theory to prove the Mordell-Weil theorem. For those who want furhter information , one can look at the book "Introduction to Diophantine Geometry" by M. Hindry and Silverman. But to really go to the heart of the matter, one must learn the intrinsic formulation of height by Arakelov (so-called Arakelov theory), as witnessed in Faltings' work on this subject.
The Final two chapters are: Chapter 9 on integral points, Chapter 10 on computation of the weak Mordell-Weil group. Superficially, these 2 chapters are of completely different style: the theory of integral points employ classical Diophantine approximation technique, such as Roth's theorem and Baker's transcendence theory; while the theory of rational points (i.e. the structure of the Mordell-Weil group) employs the theoy of principal homogeneous space, Galois cohomology to measure failure of Hasse's principle, etc. As J. Tate had remarked in a 1974 article 'The theory of integral points on elliptic curves involves completely diffrent concepts (from rational points) and that we mention it only in passing...'. The situation now changed completely. The classical style of Diopahntine approximation, is employed by Vojta, Faltings, Bombieri to prove even stronger version of Mordell conjecture, which is about finitebess of rational points! The proof is much more elementary when compared to Falting's original proof. One can look at the book 'Diophantine approximation and abelian varieties' by Edihoxen and Everste for an introduction to this revival of the subject.
But now back to this book written in 1986, the most importanr result of chapter 9 is Siegel 's theorem: finiteness of integral points on hyperelliptic curves, with application to the establishment of the Shafarevich conjecture of elliptic curves: finiteness of isomorphism class of elliptic curves with good reduction outside finite set of primes. (Note: the general Shafarevich conjecture lies at the heart of Faltings' original proof of the Mordell conjecture!). While Chapter 10 is an introduction to the Galois cohomology methos of calculating the weak Mordell -Weil group. Both theories and numerical examples are richly presented. In particular the important Selmer groups and Tate-Shafarevich group are introduced.Finding the 'size' of these two groups is subject to much current research. For example, bounding the size of a certain Selmer group lies at the heart of Wiles' proof of the semistable case of Shimura-Taniyama conjecture( hence Fermat). This is indeed a very rich subject. For further information, one must studt further Galois chomology, arithmetic duality, Iwasawa theory, and finally Euler system.
Overall, I think this book will appeal to anyone who want to know how to apply algebriac geometry to study Diophantine problems.

Who could ask for more?
The theory of elliptic curves has to rank as one of the most fascinatingfields in all of mathematics. Being around for almost two centuries,elliptic curves are finding myriads of applications, includingcryptography, superstring theory, and computer imaging. The author does abrilliant job of organizing and explaining the theory in this book.Although the book requires a thorough understanding of algebraic geometryand modern algebra, the book is packed full of insights without sacrificingmathematical rigor. This is rare in most textbooks on modern mathematics.Numerous exercises exist at the end of each chapter, which allow readers totest their understanding of the subject as well as giving extensions to themain results in the text. The author reserves the cases of elliptic curvesin characteristics 2 and 3 to the appendix. This may be disappointing forthose reading the book for cryptographic applications of elliptic curves,but it does prepare one for further reading on the subject. By far the bestchapter in the book is Chapter 10 on computing the Mordell-Weil group asthe author does a nice job of detailing the relevant constructions.Thisbook is well worth the time and effort required to study, and could servewell in an actual class on the subject. The author does have a follow-upbook called "Advanced Topics in the Theory of Elliptic Curves"for those who need further stimulation in this intriguing and importantfield of mathematics.

Addendum to review, Dec 12, 2009:
The second edition of this book respects the same quality as the first.The new chapter on the algorithmic aspects of elliptic curves reflects the importance of elliptic curve cryptography since the appearance of the first edition and can be viewed as a warm-up for the study of cryptography over general Abelian varieties and for a study of group schemes. The author mentions group schemes when he discusses Lenstra's algorithm for elliptic curve factorization: the need for elliptic curves over rings Z/NZ when N is composite, and in the case of the elliptic curve discrete logarithm problem where there is a need for an "elliptic scheme", i.e. an elliptic curve over Z/p^2Z, where p is prime and greater than or equal to 3.The reader will get a taste of one of the algorithms for computing the Weil pairing and its generalization the Tate-Lichtenbaum pairing. By some specialists in cryptography, the latter is considered to be a pairing that makes up for the deficiencies in the Weil pairing, namely that the Weil pairing is skew-symmetric. The author proves the nondegeneracy of the Tate-Litchtenbaum pairing in this chapter. Both the Weyl and Tate-Litchtenbaum pairings can be viewed in the more abstract, general framework of arithmetic duality theory and arithmetic geometry if one is willing to learn the appropriate techniques from Galois cohomology. In this framework the Tate-Litchtenbaum pairing for a (principally polarized) Abelian variety relates its Mordell-Weil group, its first cohomology group, and its Brauer group. For the author the value of the Tate-Litchtenbaum pairing over the Weil pairing is that the Miller algorithm for the Tate-Litchtenbaum pairing is twice as efficient as the Weil pairing. Included also in this chapter is a brief discussion of elliptic divisibility sequences (but delegated to the exercises), and references are given for their generalization in what are now called "elliptic nets", the latter of which is a recent development, and so it remains to be seen how much impact it will have on the computation of pairings. ... Read more

Product Description

Noted coastal geologist Orrin Pilkey and environmental scientist Linda Pilkey-Jarvis show that the quantitative mathematical models policy makers and government administrators use to form environmental policies are seriously flawed. Based on unrealistic and sometimes false assumptions, these models often yield answers that support unwise policies.

Writing for the general, nonmathematician reader and using examples from throughout the environmental sciences, Pilkey and Pilkey-Jarvis show how unquestioned faith in mathematical models can blind us to the hard data and sound judgment of experienced scientific fieldwork. They begin with a riveting account of the extinction of the North Atlantic cod on the Grand Banks of Canada. Next they engage in a general discussion of the limitations of many models across a broad array of crucial environmental subjects.

The book offers fascinating case studies depicting how the seductiveness of quantitative models has led to unmanageable nuclear waste disposal practices, poisoned mining sites, unjustifiable faith in predicted sea level rise rates, bad predictions of future shoreline erosion rates, overoptimistic cost estimates of artificial beaches, and a host of other thorny problems. The authors demonstrate how many modelers have been reckless, employing fudge factors to assure "correct" answers and caring little if their models actually worked.

A timely and urgent book written in an engaging style,Useless Arithmetic evaluates the assumptions behind models, the nature of the field data, and the dialogue between modelers and their "customers."

Customer Reviews (22)

Number bashing of number crunchers
The key points regarding this book have been well summarized by previous reviewers. The star ratings are somewhat deceptive. Basically everyone who reviewed this book accepts that his tenants that there are serious limits to mathematical models used to predict future events and that he does a great job of presenting this in a format understandable to a non-technical audience. For this reason alone I recommend this book. History will look back at our "quants" in a way that is similar to how we now view the Oracle at Delphi or the Chinese sages who made predictions on the basis of how animal bones cracked.

Those who are mathematical insiders who have the courage to speak out regarding the misuse of these models to make predictions where much is at stake need to be encouraged particularly in an environment that encourages the ostracism of those who hold reasonable but unpopular positions.

useless book
The authors of this book do not provide useful criticisms of environmental modeling and only highlight their own ignorance. While models have been used problematically (some examples are aptly employed by the authors), this should not deter us from using models to seek insights into environmental systems. The authors essentially point out that that non-scientists who employ the models are uniformed and use them inappropriately. If they were to spend some time learning a little more than what is provided in an introductory modeling course they would be better equipped to argue their point, however such knowledge would likely change their opinion. It is inappropriate and little more than a slur tactic to criticize methods that the authors clearly do not understand.
Note that no actual quantitative scientists are consulted for this book, however MIchael Crichton and C.S. Lewis make the cut.
Please do not read this book if you're interested in modeling, but don't know much about it. A nice alternative is David Quammen's 'Song of the Dodo',which describes how some simple models have been useful in solving ecological problems. Its a much more compelling story and is actually well written.

They should've read more before writing this...
I am a modeler.I was happy to hear one of mentors, Charlie Hall, mentioned in another review here.The authors fail to realize that most of their objections to modeling are recognized by good model-builders and that techniques have been developed to deal with these issues.Also, they do not seem to realize that all human knowledge is a modeling exercise, in a sense, and that magnitudes (numbers) are vital to these endeavors.Sadly, they think they have come up with something new, but have just badly represented what is well known.Hey, on the bright side, if this can get published by Columbia U, then we all have hope!

Both, Good and Bad.But, widely applicable!
"Usless Arithmetic" was, both, good and bad.The authors seem to know the subjects upon which they are writing.Mostly, they write that quantitative computational models of complicated natural processes have severe limitations and tend to give misleading answers.They seem to believe that a better approach is to form stronger qualitative notions as to what is happening, before attempting quantitative models.Their evidence is the damages that can happen and which have happened.So much for the good.

However, by dispensing with the math, the authors force the reader to depend on the abilities of the authors and on their honesty.Unfortunately, the authors appear to choose to believe in global warming and disregard their own advice.After criticising models that don't work well, the authors grasp onto global warming, while mentioning some of the oddities of the warming models.Very strange.

My problem with the above situation is that the criticism of complex quantitative models has extremely wide applicablity in today's world.Apparently, one of the reasons for the housing-finance meltdown was a flawed model that did not, properly, consider the cyclic nature of financial markets, nor consider the possibility of a 'bubble' seriously enough. The result was that about one trillion American dollars got flushed down the drain. Ouch!Worse, the problem in financial banks added to a couple of other problem areas and the stock market retreated.The result of that is a few trillion dollars vanished and the Congress is about to throw another trillion dollars at the problem.So, yes, quantitative models can cause very serious, very wide-spread toubles, when they go wrong.

Which leads me back to global warming.The authors may accept global warming, but why do they not apply their own reasoning to that situation?They should have said: "The quantitative models for global warming need to be improved.Thus, a consideration of the qualitative factors shows that ..."That would lead to enough room to contemplate things like the cyclic nature of solar storm activity and its effects on Earth's climate.

Also, I do wish the authors had gone into more detail on the fallacies involved in accepting the predictions of the far future, without showing the degree of success or failure in predicting the near and the middle future, first.Interpolation far beyond the available data is, usually, a very bad idea.

Finally, I have one last grump.The authors seem to be all or nothing folks.If something is somewhat in error, it is in error.Thus, problems in models have lead to their title: "Useless Arithmetic".My own experience is that one can take a failed model and improve it.So the fact that the original model is inadequate is only another step in the direction of an acceptable model.

Comprehensive review of mathematical models
The Pilkey's have given a thoughtful and thorough review of how mathematical models can be used improperly.While the emphasis in this book is on using environmental models for political purposes, their logic is valuable in any situation.Unfortunately, in our culture, scientific thought is seen as solving all problems. Science is about discovering what we don't know.Just extrapolating what we have learned to date is dangerous and will give scientific thought a bad name.This book, simply and clearly written, outlines the case for good science and proper use of mathematical models. ... Read more

Product Description
Practical, engaging, and classroom-tested lessons help build children's numerical understanding and skills. Through manipulative materials and real-world problems, children learn to estimate, understand numerical relationships, develop number sense, compute mentally and with paper and pencil, and use arithmetic as a tool to solve problems. ... Read more

Product Description
Recently there has been considerable interest in developing techniques based on number theory to attack problems of 3-manifolds; Contains many examples and lots of problems; Brings together much of the existing literature of Kleinian groups in a clear and concise way; At present no such text exists ... Read more

Customer Reviews (1)

Sweet book on a really interesting topic
One of the things that attracted me to geometry/topology was the tremendous interconnection between this field and other fields of math.You never feel like you're missing out on algebra, analysis, physics, and, apparently number theory as well.Walk in knowing algebraic number theory and some hyperbolic geometry (I recommend Foundations of Hyperbolic Manifolds by Ratcliffe).This is great fun for anyone interested in both geometry and number theory--even if it's just a passing interest. ... Read more

Product Description
This practice workbook is designed to help students develop proficiency in their arithmetic with decimals by offering ample practice.This book is conveniently divided up into five parts - one for addition, subtraction, and multiplication, and two levels of long division (one with and one without repeating decimals).In this way, students can focus on one arithmetic operation at a time.Each section begins with a concise set of instructions for how to add, subtract, multiply, or divide numbers with decimals, including a couple of examples.Answers to exercises are tabulated at the back of the book.This helps students develop confidence and ensures that students practice correct techniques, rather than practice making mistakes.The copyright notice permits parents/teachers who purchase one copy or borrow one copy from a library to make photocopies for their own children/students only. This is very convenient if you have multiple children/students or if a child/student needs additional practice.An introduction describes how parents and teachers can help students make the most of this workbook.Kids are encouraged to time and score each page.In this way, they can try to have fun improving on their records, which can help lend them confidence in their math skills.A multiplication table is provided to help students who are just learning their multiplication facts. ... Read more

Product Description
When the mathematician Felix Klein first went to university, he was surprised at just how little what he had learned up to that point was relevant to his new studies.Professors had their own interests, and these they conveyed without regard for the math students of the future that these prospective secondary schoolteachers would one day instruct.Elementary Mathematics from an Advanced Standpoint was written to help remedy that problem.Though highly regarded as one of the finest mathematical minds of his day, Professor Klein took a great deal of interest in guiding teachers and "reducing the gap between the school and the university."Readers will come away impressed at the clarity of Klein's writing, and the ease with which he conveys complex mathematical ideas.Divided into three parts-arithmetic, algebra, and analysis-and covering such topics as complex numbers, real equations, and logarithmic and exponential functions, Klein's classic is essential reading for math instructors and students planning to become math instructors.German mathematician FELIX KLEIN (1849-1925), a great teacher and scientific thinker, significantly advanced the field of mathematical physics and made a number of profound discoveries in the field of geometry.His published works include Elementary Mathematics from an Advanced Standpoint:Geometry and Famous Problems of Elementary Geometry. ... Read more

Customer Reviews (3)

Still the best book for Math education today !
I read Felix Klein's [1849-1925] 3-volume Math book [publised in German, 1924] in Chinese translation bought recently in Beijing bookshop. The chinese translators are themselves mathematicians, so they corrected some translation mistakes made by the 1939 English translators from whom they translate into Chinese.

Klein was a great mathematician, being the Father of Modern Geometry based on Group Theory [Erlanger Program]. He was also a great Math educationist, who built the Gottingen University into the World Center of Mathematics before WW II, attracted the Germany's and the World's best mathematicians to teach and learn there. eg. David Hilbert, Noether, Laskar, etc.

This 3-volume Math books were compiled by his assistants from the lectures he gave over 20+ years in breaching the gap of Secondary School Elementary Math and University Modern Math, hence the title "Elementary Math from an advanced standpoint". Although written 80 years ago, his concerns and teachning are still valid today. Except for France where they teach modern math concepts in Lycee (secondary school from 3eme to Terminale), other countries' secondary schools don't introduce these modern concepts (Group, Ring, Field...), some with little Set theory at best. For Singapore and the English commonwealth countries, secondary and high school math are still using the same syllabus 100 years ago: 100% computational-bias (calculus, trigo, classical algebra).

Klein spotted this gap 80 years ago, as indicated in the volume 1, which he labelled as Syllabus A, Syllabus B and Syllabus C.

In Syllabus A (which is still used worldwide): all math subjects (algebra, geometry, trigo...) are taught as separate independent modules. The secondary school students don't see them as inter-connected.

In Syllabus B, Klein proposed to base whole math teaching on Functions, which is intuitive as functions can be visualised in Graphs, and link to all branches of math.
eg. Function exponential e: e^x = 1 + x + 1/2! x^2 + 1/3! x^3 +....
also e^ix = Cos x +i.Sin x
where the function exponential has linkage to trigo (cosine and sine), and algebra's complex number i. Same can be applied to calculus: integration and differentiation link to functions like Log, exponential, trigo, etc.

Although he didn't elaborate on Syllabus C (out of his life / book context), but I would presume he had predicted the Bourbaki school of Math based on Set Theory as math structures. This approach of teaching was very prominent in French Mathematics Education. It has proved with little success to students because of being too abstract, distancing the Math from real-life (pure math vs applied math). Klein, although a pure math par excellence, didn't encourage this approach which was advocated after his death by the French Bourbaki mathematicians.

I admire Klein's foresight in Syllabus B intuitive pedagogy which will introduce secondary school students gradually to the University modern math concepts.

After 80 years, his dream is still not fully appreciated by math educationists. It is hard to change the mindset in the math education bureaucrats worldwide.

Elementary Math Analysis
This book was just what I was looking for. Simple to understand, something to bring me up to speed on some long forgotten math.

Still a great resource
About the set: Klein's Elementarmathematik lectures was intended as a survey of mathematics for those who already knew most of the technical detail, especially future teachers, but who perhaps lacked a good understanding of mathematics as a whole. The lack of a broad perspective is probably at least as big a problem today as it was then, so Klein's text is still valuable. Klein also frequently discusses historical and pedagogical aspects, and the tone is quite informal throughout.

About this volume: The first part discusses basic arithmetic, with great emphasis on how it should be taught. Being such an enthusiastic lecturer, Klein cannot resist also including little sections on things like Fermat's last theorem and quaternions. The second part suddenly becomes much more sophisticated, as Klein sketches a rather non-standard approach to understanding algebraic equations, in particular incorporating a bit of Klein's trademarke icosahedron material. To keep up with this presentation one should probably consult his icosahedron book as well. For the third part, on analysis, we are back on familiar ground again, which makes it easier to appreciate this masterful overview, covering many of the great ideas of analysis and putting them in context with interesting discussions that are often partly historical. ... Read more

Product Description
Focusing on multidigit multiplication, the lessons in this book help students learn to multiply by 10, multiples of 10, and powers of 10. Students become more proficient at estimating and mental multiplication, learn to apply the distributive property to multidigit multiplication, and develop paper-and-pencil strategies for computing. ... Read more

Customer Reviews (1)

Math is fun again!!!
As an upper-elementary school teacher, I have used the activities in this book to supplement the regular math textbook with students in grades 4, 5, and even 6.The lessons are all constructivist in theory, so they are all highly engaging for the students, and most of them do not require expensive materials to implement.The students loved the math games and hands-on activities, and I believe that they have helped the students to grasp a greater understanding of the concepts underlying multiplication!The lessons are pretty easy to follow and to assess the students' understanding.Please check out this book, as well as the many other titles by Marilyn Burns and/or Maryann Wickett... you and your students won't regret it!!!
... Read more

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This book of practical suggestions is aimed at helping educators who are transforming mathematics learning and teaching and who are implementing curricula such as Investigations.Grades K-6 ... Read more

Customer Reviews (1)

Elementary Principal
Beyond Arithmetic is an outstanding book. A must read for elementary educators. My entire staff will read this book and implement these practices into their classrooms! ... Read more

Product Description
The lessons in this book present a series of explorations that introduce division to students by helping them relate division to multiplication and learn how division relates to equal groups. Students also learn how to recognize the two types of division problems, think about remainders in different ways, and use division to solve real-world problems ... Read more

Product Description
A combination of a basic mathematics or prealgebra text with an introductory algebra text, Integrated Arithmetic and Basic Algebra provides a unique, integrated presentation of the material for these courses that is extremely beneficial to students. As opposed to traditional texts that present arithmetic at the beginning and algebra at the end, this text integrates the two whenever possible, so that students see how concepts are interrelated rather than learning them in isolation and missing the "big picture." The ideas and algorithms shared by arithmetic and algebra are introduced in an arithmetic context and then developed through the corresponding algebraic concept. For example, operations with rational numbers and rational expressions are discussed together, whereas most texts discuss operations with rational numbers early on and operations with rational expressions much later. The Jordan/Palow text helps students recognize algebra as a natural extension of arithmetic using variables. This approach aligns directly with NCTM and AMATYC standards, which suggest playing upon students' previous knowledge to teach new concepts. ... Read more

Customer Reviews (1)

Intergrated Arithmetic and Basic Algebra (4th Edition)
This book is perfect for my pre-algebra class I am taking this summer. The used book is in great shape. ... Read more

Product Description
The investigations in this book help second graders build their understanding of the tens and ones structure of our number system. Lessons engage children in comparing and explaining the relative size of numbers, counting larger numbers in two or more ways, and recognizing that the number of objects always remains the same despite different ways of grouping. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Customer Reviews (2)

An Historian's Delight
Capitalism & Arithmetic is strictly for the serious student of the Renaissance and early European arithmetic. Frank Swetz brings forth a fine description/translation of what is the earliest known textbook, by author unknown, in a 1478 book entitled the Treviso Arithmetic.Treviso was a small town north of Venice Italy in the 15th C that was on one of the main trade routes out of Italy. The merchants of Venice were developing trade and, needing a convenient mathematics, introducing the Hindu-Arabic number system and many computational techniques.The Treviso Arithmetic is a textbook for young merchants to introduce them to the mathematics they will need to carry on trade. I gained a much deepen appreciation for the enormity of what we have inherited from the past that was so hard-won and of such lasting value.
Dennis Riness

Early history of business and computational science
The advent of Hindu/Arabic numbers in Europe made possible "algorithmic" calculation.Math schools were established where parents sent their sons to prepare for jobs with merchants, where abilityto calculate was a requirement.Curiously, there were many different waysof setting up problems for solution with pencil and paper, and only lateron did we agree on the standard "algorithms" for addition,subtraction, etc. that are now taught to children.The ability to computeproportionality, the basis of the money changer's art, was regarded asamazing. ... Read more

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Advantages: Amazing results within the first few days of the program!
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Additional Benefits
* Explore your potential so that you can perform at your optimum level
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* Everything is highly structured and organized in a systematic manner
* Many more solved examples and practice exercise questions with detailed explanations
* Remarkable and noticeable improvement in your performance by utilizing newly acquired learning skills

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Table of Contents:
PART 0.0: Introduction to Arithmetic
PART 1.0: Integers
PART 2.0: Fractions
PART 3.0: Decimals
PART 4.0: Exponents
PART 5.0: Radicals

Guarantee:
We are so confident in our books that we are offering the EZ-peace-of-mind-no-hassle guarantee so that you can buy our books with complete confidence. See our website for more details about other terms and conditions about this offer.
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Customer Reviews (4)

EZ books
In order to get a real GMAT prep - I would recommend you use the EZ Solutions series of 10 books, or whichever book(s) you think you need most help with. These books are very detailed oriented and cover everything on the GMAT math. First use the review modules to get the concepts and then use the workbooks for practice. Some of the most challenging math topics, such as basic arithmetic and number properties, algebraic concepts, complex word problems, logical reasoning problems, etc., are brilliantly explained in these books. Just because of the high price of the book, you can skip the math strategies book. However, the EZ basic workbook is a good refresher to get started and advanced workbook is a "must have" if you are aiming for a high score.

After doing all this, use the OG and you will see a dramatic difference in your scores. You don't even have to take any of those pricy courses. I followed this process and my scores have jumped from the 500-range to the 700-range. Good luck in your prep.

Helpful guide for GMAT
I started my GMAT course and have looked over many books relating to Arithmetic and this book is by far the best book that I have read. The solutions and problems are well laid out. It's both an excellent book for a beginner and the intermediate of us. The collection of books is well worth the money when studying the GMAT.

Rather poor arithmetic review
I did not find this EZ Solutions Arithmetic review very helpful. The main reason is, that it is not very textbook/explanatory-like, but instead lists one definition after the other; this is not what I expect from a good math book (I found the math review in the barron's GMAT book a lot better). Also the first 14 pages are just "we bring you the breakthrough etc."-bla bla.
But, after all, the book does give you some arithmetic review, so its not a total waste.

GMAT Review
Books are great clearly written, and deffinently help with the little nuances.The books also help show you short cuts for calculating math problems quickly.If you couple this series with the Kaplan math you should be set.I would suggest you purchase them. ... Read more