Product Description
This traditional, straight-forward, extremely popular book is noted for its one-step, one-concept-at-a-time approach.In the new edition, the authors have brought in new coverage to meet NCTM standards where appropriate. ... Read more

Customer Reviews (4)

Front Cover Page Missing
The book arrived without a front cover page.School had already started, and I did not want to wait.. By week three, I've had pages falling out of the book.

Better Than Described!!
Book was better than i had expected! I purchased 3 other books on the same day from different vendors who lived closer to me and still received this book first.I couldnt have asked for for a better product and transaction! Thanks!!!!

Essential Arithmetic
This book came in exclent condition. I needed it for school. My school was selling it for $58.99 I was able to get it under $20. Thank you great book easie to understand and use.

Generally good, but has a few errors and bad sections.
It is like most math text books, meaning that everything in it is explained sounding harder than it is, but, as far as math books go, it's not bad. It has some mistakes and some really bad sections, bu all in allits pretty good. Not worth the price, though. ... Read more

Product Description
Many useful procedures explained and taught: two-column addition, left-to-right subtraction, direct multiplication by numbers greater than 12, mental division of large numbers, more. Also numerous helpful short cuts. More than 8,000 problems, with solutions. 1945 ed.
... Read more

Customer Reviews (11)

Math? Oh NO!
My brain would lock up when it came to Mathematics.
Not anymore! The book simply erased Math Anxiety for me.
Thank you very much!

A+
The book shipped quickly, arrived on time and in good shape. They were also extremely cheap, so buy with confidence.

Great book for your odd-study hours and improvement of mental math
I am just a simple college student. While browsing a used book store I picked up this book and for some reason couldn't help but buy it and bring it around with me.

This book was first published in 1945, but the art still remains the same. The author attempts to build your skill in quick calculations by bringing you series of exercises that practice vital techniques and skills needed to perform speed math. Each excercise introduces something new and are placed in a way that you will not get bored when practicing. The placement is also strategetic so you will learn one new skill at a time. There are about 15000 possible questions if you wish to do them all.

Also, the book is pocket sized and can be brought anywhere. I find myself bringing it out any time I have to wait around. An excersize can be knocked out in a couple of minutes and I have learned something new! It is also entertaining when I am bored. I also find that doing excercises keeps my mind active and less sluggish during the day.

The book is straight to the point. You know exactly what you are learning and why you are learning it.

Essential for the novice bookkeeper
A few years back, I had just started a job in payroll and was using a calculator to do things I really should have been able to do in my head. Quite frankly, this made me pretty terrible at that job. I had just figured I was not a "math person" with bad "number sense" and was not very long for that job without some help.

Lo and behold, a supervisor recommended this book when I expressed my concerns and willingness to do whatever it took to become better at my job. With a little work over the next month or so I proved myself entirely wrong at not being a "math person". There's no real magic to calculations in your head, but some techniques are better than others, especially for error-checking. A bit of hard work at drills and memorization can make you that much better. I stayed in the job for 3 more years and when I left I was one of the top people in a large office (200+) in terms of accuracy.

Provided you're not lazy and do the drills in the book, you'll increase your computation time after learning the practical tricks that bookkeepers have used for decades that the academy doesn't know and that your teachers never taught you in school (e.g. the division by 3 check, digit checks, adding from right to left, grouping tens, etc).

No academic jargon or nonsense or high-falutin theory. Just a regimen for improving your mental calculation speed designed for business. It's like exercise. It takes continuous work over time, and it's not always fun, but the results are worth it. Everything worth doing takes work, so beware of any "magic math systems" that instantly make you faster. There are no steroids when it comes to math.

If you're new in a payroll, bookkeeping or other field that requires fast mental calculation, an absolute must have.

quick turnaround
I received the item within a couple of days, and the quality of the item matched my expectations. ... Read more

Product Description

The book is an English translation from Hebrew of a very popular in Israel guide for parents eager to help their kids to understand math. It reflects the author's unique experience as both a research mathematician and elementary school teacher.

Part 1 discusses the nature of mathematics, its power, its beauty, and the source of the difficulties in studying it. Part 2 introduces the reader into principles of good teaching. Part 3 is an easy going, informal guide, filled with personal stories, historical anecdotes and teaching suggestions, addressing all twists and turns of basic arithmetic taught in grades 1 through 6.

To a mathematics educator, the book sends two important messages. One is that basic mathematics, although unsophisticated, is rather deep, consisting of many neatly aligned layers, none of which can be skipped without the danger of causing "math anxiety"; The other is that good pedagogy depends not so much on various tricks and cognitive theories, but on thorough understanding of basic mathematics and its neatly layered structure. And the book teaches the reader -- a parent, or a teacher -- to really understand the subject and this structure.

By Alexander Givental, Prof. of Math., UC Berkeley and Sumizdat.

There is a Wikipedia article about the book.

Reviews of the book can be found in: "Opinion" column by Linda Seebach of "Rocky Mountain News" for March 24, 2007; Homeschool Math blog by Maria Miller; "Read This!" column of "Online Book Reviews" by The Mathematical Association of America; the award-winning math web resource "Cut The Knot" by Alexander Bogomolny. ... Read more

Customer Reviews (7)

Arithmetic for Parents
A must read for parents; I believe this book is profoundly important.It provides a clear, deep understanding of the operations and the history of arithmetic.In it the author-- to whom I am most grateful-- quotes the aphorism "mathematics is the queen of science."After my second reading of this book (which immediately followed the first) I speculate that arithmetic may well be the queen of mathematics.

This book is the best arithmetic teaching manual you will read.Caution:Ron Aharoni's sensible approach and "big picture" understanding of his subject fosters mathematical creativity in children-- something that may not be appreciated by your child's elementary school teacher.Indeed, that teacher is most likely programmed to suck the life and enjoyability out of arithmetic in deference to "progressive teaching standards."After you guide them "The Aharoni Way" your children may well be bored, if not stupefied in class.They could rebel with ridicule and contempt.And your child could be ostracized accordingly.Such was my experience.Still, it's worth it.Good luck!

Bob Hager
Westlake Village, California

Arithmatic for Parents
I have enjoyed the book so fare.It was exactly what I was looking for.

Love this book
I am not home school my kids and I do not have the background in eduction. I love math and I use math in my profession,but my kids does not understand math. This book gave me the method to teach and to present idea in a child friendly way that is easy for my kids to understand.I use it with Singapore math text books so that I have a set curriculum to teach my kids.I wish I known this book earlier.

A must read for anyone loving or hating maths
Ron Aharoni writes clearly and deeply about the crucial concepts of fundamental maths, how to teach them and how not to teach them. He explains the layered and subtle structure of elementary maths and how missing a layer can lead to frustration and maths anxiety. "There's no royal road the maths", an Euclidian quote he emphasizes which summarizes well the message in this book. I'm not sure the book is for "Parents" as its title suggests, but I highly recommend it for both lovers and "haters" of maths, regardlessof their "parental status". Looking forward to Ron's next book.

you can make your child like math
Parents sometimes can't help their children with elementary school mathematics even if they know how to do the calculations, because they don't know why things are done the way they are.This book explains the logic and the meaning of Arithmetic in a pleasant, easy to read and easy to understand way, and gives some insights about teaching in general and about teaching of mathematics in particular.After reading the book even not-mathematically-oriented parents can say that "after all - arithmetic does make sense"' and "I see that there are some ways in which we can help our children understand, and even like mathematics". ... Read more

Product Description
For almost four decades, Made Simple books have set the standard for continuing education and home study. In answer to the changing needsof today's marketplace, the Made Simple series for the '90s presents a thoroughly up-to-the-minute portfolio of skills, information, and experience, with revised and updated editions of bestselling titles, plus a whole range of new subjects from personal finance to office management to desktop publishing.

B & W illustrations throughout ... Read more

Customer Reviews (5)

Arithmatic made simple
Its been a long time since I was in school,and using this book has made a world of difference. Its very easy to understand. I highly recomend it.

Gr8 book!
this is a great book book for use as a refresher course on math you studied in grade school. However I could not give it 5 stars because of the 7 typographical errors I found while reading the book.

Review Of:Arithmetic Made Simple by Robert Beige
An excellent publication for those who want a basic refresher in Arithmetic. Highly recommended for anyone who want to strengthen their basic math skills before engaging in any highler level mathematics courses.

excellent service and product
very useful product and fine service -- highly recommended for home schooling parents and those looking to supplement standard curricula

Great math homework reference book for parents.
Arithmetic Made Simple has really helped our family.It contains easy-to-understand mathematics concepts from 4th grade level up to 9th grade. Each math topic is organized in a way to allow step-by-steplearning.The sections on use of percentages has been extremely helpful -even to our 9th grader. This book would be extremely useful for anadult that is persuing their GED.After the explaination of each topicthere are sample problems and practice problems.Even the answers in theback have explainations of how many of the problems were worked.I highlyrecommend this book for every parent that has school-aged kids. ... Read more

Product Description
The theory of automorphic forms is playing increasingly important roles in several branches of mathematics, even in physics, and is almost ubiquitous in number theory. This book introduces the reader to the subject and in particular to elliptic modular forms with emphasis on their number-theoretical aspects. After two chapters geared toward elementary levels, there follows a detailed treatment of the theory of Hecke operators, which associate zeta functions to modular forms. At a more advanced level, complex multiplication of elliptic curves and abelian varieties is discussed. The main question is the construction of abelian extensions of certain algebraic number fields, which is traditionally called "Hilbert's twelfth problem". Another advanced topic is the determination of the zeta function of an algebraic curve uniformized by modular functions, which supplies an indispensable background for the recent proof of Fermat's last theorem by Wiles. ... Read more

Customer Reviews (1)

modular forms classics
This is a classical masterpiece in the area. Although much of the matherial is now available in other books, I am sure that this book must be on the bookshelf of anyone whose research is seriously connected with modular forms. As a warning, the book is no easy reading, and despite its title, should not be considered as an introductory text. ... Read more

Customer Reviews (7)

Inspiring and foundational
I'm a self-directed learner and had been struggling with generating interest in mathematics for some time. I had bought this book in the hopes that it would bridge my love and interest in logic with a new found interest in mathematics. It did exactly that.

Foundations of Arithmetic
This subtitle, "A Logico-mathematical Enquiry into the Concept of Number," indicates very well the nature of the work.The first three quarters of the book are devoted to a critical analysis of the idea of previous writers (Kant, Leibnitz, Grassmann, Mill, Lipschitz, Hankel, Jevons, Cantor, Schröder, Hobbers, Hume, and others) on the subject of number, and Frege does not find the ideas of any of these philosophers and mathematicians entirely satisfactory.His conclusions is "that a statement of a number contains an assertion about a concept," and his definition of number is: The number which belongs to the concept F is the extension of the concept "equal to the concept F."

Frege regards the number zero as belonging to to the "natural" or "counting" numbers, whereas we subscribe to the view that zero is not a counting number at all (the first of the counting numbers being 1) and is only properly used when we regard a number as a "relative-magnitude," zero being the relative-magnitude of two equal counting numbers.

This work of Frege's has considerable historical interest as a forerunner of the work of Whitehead and Russell.The translation is excellent and the printing leaves nothing to be desired.

The first escape from the Elencus...
You know how _frustrating_ it is, reading a platonic dialog? Some question like "What is virtue?" or "What is justice" is asked, and Socretes goes on for pages showing that the so-called "experts" don't have a clue about what it really is?

But what's _really_ frustrating is that you're all expecting, at the end of the dialog, after following a hard line of argument, that you'll be rewarded with THE definitivie definition of 'virtue' or 'justice' or whatever--only to be disapointed.All you get in the end is a new appreciation of your own hopeless ignorance...

...well, imagine a platonic dialog which started the same as any other platonic dialog, but with the question "What is a number?"Only this time, at the end of the dialog, you actually get an answer to the question?

In retrospect, its pretty amazing that Plato didn't write a Socratic dialog concerned with the question "What is number?'After all, Plato considered numbers more real than physical objects, and people like the Pythagorians were going around claiming that everything _was_ made out of numbers.But what the heck _is_ a number, anyways?

Perhaps the reason was that everybody thought they already understood what numbers were.But Frege, like Socretes before him, realized that this so-called knowledge was really just a collective ignorance.So Frege starts out this book with a thorough, merciless review of what his coleages and predicessors were saying about what numbers were, showing that they ranged from cocksure to confused, from pompously-wrongheaded to just plain silly.

But then Frege does something really amazing--for the first time in history, he goes on give a real answer to the question "what are numbers?"Building on the work of Hume, he gives a sustained argument now known as "Frege's theorem" which shows how numbers can be grounded on an understanding of one-to-one correspondence.

Unfortunately, this work had to wait almost a century for the rest of us to really catch up to its significance.Russell found a contradiction in the arguments presented here, and for the next 80 years attention shifted elsewhere.But first Charles Parsons, in 1964, and then Crispen Wright and others in the 80's and 90's begain to realize that Frege's theorem could be reconstructed without the paradox.This sparked a whole flurry of neo-Fregean studies which is one of the most active branches of analytic philosophy today.

This revival means that Frege's importance, and the importance of reading and comming to grips with the arguments presented by Frege in this book, are going to continue to grow.Although tragically Frege didn't live to see the day, we now realize that the line of reasoning he followed in this book was one of those signature moments in human history, every bit as profound as the invention of the wheel or the discovery of the pythagorian theorem--it was the moment where, for the first time ever, the question "what the heck _are_ numbers, anyways?" got a real answer.

Frege, You're Not Supposed To Have...
*The Foundations of Arithmetic*, one of the most durable works of philosophy of mathematics ever produced, is something of a curiosity as presented by J.L. Austin (who translated the work for the use of an Oxford undergraduate course); and perhaps Frege's platonism got the best of Austin, and this work is really just as , well, Kantian as it appears, "a good sight" more Kantian than "standard" Frege is typically allowed to be.Frege's definition of number in terms of equipollence (one-one correspondence of sets) is legendary: that is to say, it is traditionally understood to do a great deal more work than the "thin" version allowed by mathematical logic as reconstructed to avoid Russell's paradox.

But here Frege's work-up of the concept for a general readership is so "genteel" as to suggest that this may not in fact be the case, and that Frege actually partook more heavily of Neo-Kantian bromides than his *theory of arithmetic* suggests; to wit, that this theory was always intended to be situated within a general philosophy of mathematics obeying the strictures of reasoning involving Kantian "intuition" (as is typically said of Frege's last efforts in the field).As such, it would be unfortunate that we cannot effectively read this book (formerly available *en face*, and unfortunately much the worse for the original's omission) in conjunction with its contemporary geometrical counterpart: long out of print, rarely making its way into the philosophical Frege literature, and perhaps in all parts an *anticipatory* if "crochety" rebuke to Hilbertian formalism.

Perhaps Frege was to a certain extent wholly other than the mathematics of his time; perhaps we are not well-served by a Frege "out of time"; we certainly have one of the great prose stylists of English on hand here, and perhaps it would actually do to consider his aptitude for "gold" extraction here as a clue to puzzling out the rest of Frege -- a figure supremely unconcerned with sameness of meaning, and already owing a certain debt to those para-philosophical figures all his work is at cross-purposes with (the German '70s having been quite a time indeed).A great help to understanding number theory, a marvelous thing for a library to have.

Excellent work
His conclusion (p.99e) is that the laws of arithmetic are analytic judgements and consequently a priori.

Note that he is very consistently hard on Mill.

Some interesting quotes: p. 115e #106. "...number is neither a collection of things nor a property of such, yet at the same time is not a subjective product of mental processes either, we concluded that a statement of number asserts something objective of a concept.

... (p. 116e) We next laid down the fundamental principle that we must never try to define the meaning of a word in isolation, but only as it is used in the context of a proposition: only by adhering to this can we, as I believe, avoid a physical view of it.

#107. (p.117e) "A recognition statement must always have a sense." ... Read more

Product Description
Mott Media has Republished the Version of Ray's Arithmetic from the late 1870's and early 1880's!Extends work in the four operations to higher numbers and begins fractions, measurements, ratio and percentage. Can be used with many children through grades 3 and 4. ... Read more

Product Description
The number of English arithmetics before the sixteenth century is very small. This is hardly to be wondered at, as no one requiring to use even the simplest operations of the art up to the middle of the fifteenth century was likely to be ignorant of Latin, in which language there were several treatises in a considerable number of manuscripts, as shown by the quantity of them still in existence. Until modern commerce was fairly well established, few persons required more arithmetic than addition and subtraction, and even in the thirteenth century, scientific treatises addressed to advanced students contemplated the likelihood of their not being able to do simple division. On the other hand, the study of astronomy necessitated, from its earliest days as a science, considerable skill and accuracy in computation, not only in the calculation of astronomical tables but in their use, a knowledge of which latter was fairly common from the thirteenth to the sixteenth centuries. ... Read more

Product Description
This book is meant to be an introductory text, albeit at an upper graduate level. The main prerequisite for reading this book is some familiarity with the basic theory of elliptic curves as described, for example, in the first volume. Numerous exercises have been included at the end of each chapter. A list of comments and citations for the exercises will be found at the end of the book. ... Read more

Customer Reviews (1)

The most fascinating objects in all of mathematics
This book is a continuation of the authors earlier book on elliptic curves, which was also an excellent book, and treats the more specialized topics in elliptic curves. I cannot think of a branch of physics or engineering that has not made use of some facet of the theory of elliptic curves, and they have myriads of applications in other fields also, such as cryptography and financial engineering. The book is very organized, straightforward to read, the author summarizes well his intentions at the beginning of each chapter, and recommends several references for topics left out of the main discussion. Space does not allow a detailed chapter by chapter review, so I will confine my review to the first two chapters, which were of main interest to me. In summary, Chapter 1 discusses how to study elliptic curves by taking a collection of them, each member being isomorphic, and studying the properties of modular functions and differential forms on this collection, now thought of as an algebraic curve, called the moduli space. The famous linear operators, called the Hecke operators, act on the the space of modular forms, and they and their eigenfunctions satisfy the same set of relations. One then attaches the well-known L-series to the modular forms that has very interesting algebraic and analytic properties. In more detail, the author does the following in the chapter. The set of lattices in the complex plane modulo non-zero multiplication L/C* is considered, along with the set of elliptic curves over the complex plane modulo complex isomorphism. These collections are proven to be bijective by showing that L/C* is isomorphic to C by first putting a complex structure on it. This leads to a surjective map from the upper-half plane H to L/C*. Proving this to be injective leads to a bijection from SL2(Z)\H to L/C*. Since the matrix -1 acts trivially on H, one can quotient out +1 and -1 and obtain the modular group. The quotient space modular group\H is a 2-sphere minus a point, but can be made into a Riemann surface by extending the upper half-plane (called H*). The modular curve X(1) = modular group\H* results and is compact and Hausdorff. A complex structure is put on it, making it into a a Riemann surface of genus 0. Meromorphic functions on X(1) are rational functions of the j function, but more interesting functions are defined on X(1), namely the modular functions, such as the Eisenstein series. These considerations lead to a proof of the uniformization theorem for elliptic curves over C. For a given elliptic curve E, a study of the set of all isogenies to E of degree n is the same as that of studying degree n maps from E to other elliptic curves, which is called the dual isogeny, and leads to the Hecke operator. The Hecke operator and the homothety operator both map the divisor group of the lattice to itself, and generate a commutative algebra, called the Hecke algebra. Hecke operators can act on modular forms of weight 2k, and modular forms exist which are simultaneous eigenfunctions for the Hecke operator of weight 2k. It can be proven, but the author does not do so, that the normalized eigenfunctions form a basis for the space of cusp forms of weight 2k. The Fourier coefficients of the eigenfunction have an Euler product decomposition of a Dirichlet series attached to f, called the L-series. In the next chapter, the author considers elliptic curves that have extra endomorphisms, called complex multiplication. The collection of endomorphisms is usually taken to be the real numbers R, or R(K), which is the ring of integers of R tensored with the rational numbers. And, just as in chapter 1, he studies collections of elliptic curves, but here ones with the same endomorphism ring., called ELL(R) in the book. Asking the question of how to construct an elliptic curve with complex multiplication by a particular R(K) leads him to studying the ideal class group of R(K), and this group is shown to act transitively on ELL(R(K)). The author also shows that every elliptic curve with complex multiplication is defined over an algebraic extension of Q. Several interesting examples of ellipti curves with complex multiplication are given. After a brief review of class field theory, the author proves that K(j(E)) is the Hilbert class field H and shows how the Galois group of H/K acts on j(E). The torsion points of E are then used to generate abelian extensions of K, using the Weber function for E/H, thus generalizing the usual cyclotomic extensions of number theory. Very interesting examples are given of these constructions and it is also shown that j(E) is an algebraic integer. Then after a brief review of cyclotomic class field theory, the author proves what he calls the main theorem of complex multiplication, which says that an automorphism of the torsion subgroup is essentially analytic multiplication by an idele of K. This theorem allows one to define a Grossencharacter associated to an elliptic curve with complex multiplication. For such a curve one can then define an L-series and show that it can be expressed as a Hecke L-series with Grossencharacter. ... Read more

Product Description

Floating-point arithmetic is by far the most widely used way of implementing real-number arithmetic on modern computers. Although the basic principles of floating-point arithmetic can be explained in a short amount of time, making such an arithmetic reliable and portable, yet fast, is a very difficult task. From the 1960s to the early 1980s, many different arithmetics were developed, but their implementation varied widely from one machine to another, making it difficult for nonexperts to design, learn, and use the required algorithms. As a result, floating-point arithmetic is far from being exploited to its full potential.

This handbook aims to provide a complete overview of modern floating-point arithmetic, including a detailed treatment of the newly revised (IEEE 754-2008) standard for floating-point arithmetic. Presented throughout are algorithms for implementing floating-point arithmetic as well as algorithms that use floating-point arithmetic. So that the techniques presented can be put directly into practice in actual coding or design, they are illustrated, whenever possible, by a corresponding program.

Key topics and features include:

* Presentation of the history and basic concepts of floating-point arithmetic and various aspects of the past and current standards

* Development of smart and nontrivial algorithms, and algorithmic possibilities induced by the availability of a fused multiply-add (fma) instruction, e.g., correctly rounded software division and square roots

* Implementation of floating-point arithmetic, either in software—on an integer processor—or hardware, and a discussion of issues related to compilers and languages

* Coverage of several recent advances related to elementary functions: correct rounding of these functions and computation of very accurate approximations under constraints

* Extensions of floating-point arithmetic such as certification, verification, and big precision

Handbook of Floating-Point Arithmetic is designed for programmers of numerical applications, compiler designers, programmers of floating-point algorithms, designers of arithmetic operators, and more generally, students and researchers in numerical analysis who wish to better understand a tool used in their daily work and research.

Customer Reviews (1)

an encylopedia on floating-point arithmetic
If the accuracy of the book matches it's scope and content, it is likely to be the standard reference on the subject of floating-point.

The table of contents does not indicate the full extent of the book. Written much in the Knuth style and contains similar information density. ... Read more

Product Description
This book is a general introduction to the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part introduces basic objects such as schemes, morphisms, base change, local properties (normality, regularity, Zariski's Main Theorem). This is followed by the more global aspect: coherent sheaves and a finiteness theorem for their cohomology groups. Then follows a chapter on sheaves of differentials, dualizing sheaves, and grothendieck's duality theory. The first part ends with the theorem of Riemann-Roch and its application to the study of smooth projective curves over a field. Singular curves are treated through a detailed study of the Picard group. The second part starts with blowing-ups and desingularization (embedded or not) of fibered surfaces over a Dedekind ring that leads on to intersection theory on arithmetic surfaces. Castelnuovo's criterion is proved and also the existence of the minimal regular model. This leads to the study of reduction of algebraic curves. The case of elliptic curves is studied in detail. The book concludes with the fundamental theorem of stable reduction of Deligne-Mumford. The book is essentially self-contained, including the necessary material on commutative algebra. The prerequisites are therefore few, and the book should suit a graduate student. It contains many examples and nearly 600 exercises. ... Read more

Customer Reviews (2)

Algebraic Geometry and Arithmetic
This book together with Matsumura on Commutative Algebra and Hartschone on Algebraic Geometry is an excellent book to learn the subject. I am really enjoying it.

Very good exposition
Liu's book has two distinct parts to it. The first 7 chapters combine to give a wonderful exposition of the language of schemes; the other chapters are of a specialised nature and concentrate on arithmetic curves. I will talk about the former. (So when I say "this book", I am only referring to the first 7 chapters)

The book starts off with a chapter on some topics in basic commutative algebra - localisation, flatness and completion. Once this is done, the stage is set to introduce schemes in the next chapter and prove their basic properties. Chapter 3 talks about morphisms of schemes and base change. Chapter 4 continues with a discussion of morphisms and also presents some results about some special types of schemes (normal, regular). It culminates with a proof of Zariski's main theorem.The next chapter takes up sheaf cohomology and is followed up with a chapter on differential calculus on schemes (Kahler differentials, duality theory). Lastly, chapter 7 takes up divisors, proves the Riemann Roch theorem and culminates with some applications to curves.

At a first glance, this would basically look like Hartshorne - the most popular book for an introduction to schemes. However, there are few differences which I will point out. Firstly, Hartshorne emphasizes geometric applications and, as such, uses algebraically closed fields freely. Liu, on the other hand, does not hesistate to give arithmetic applications whenever possible and, therefore, tries to relax the hypotheses on the base field whenever possible. Secondly, Liu is much more readable than Hartshorne which, in its supreme elegance, is a tad dense for a first reading. Unlike Hartshorne, a majority of important results are not presented in the exercises (though many are!). Moreover, unlike Harshorne, this book develops all the necessary commutative algebra along the way (chapter 1,2 of Atiyah-Macdonald should be good enough to read this book). Coming back to the geometry, Hartshorne's chapter 4,5 form an excellent resource for classical geometric applications for theory of schemes. Moreover, chapter 1 presents a very readable and scheme-free account of classical algebraic geometry (pre-Grothendieck) in the language of varieties. Liu's book, however, does not emphasize classical or geometric applications and is not the best place to start if one wishes to learn about varieties.

In the current literature on algebraic geometry, there is a noticeable void. Namely, on one hand, we have Grothendieck's "Elements" (EGA) which present all results about schemes and sheaf cohomology in utmost generality, prove everything with excruciating detail, and are almost unreadable as texts (they're a great references). On the other hand, we have Hartshorne which is basically a beautiful summary of EGA along with geometric applications, but is quite hard to read for an introduction. The book under review is not as concise as Hartshorne's book, presents arithmetic applications and is more readable in a reasonable amount of time than EGA.

In conclusion, this book should be an invaluable resource to anyone who wishes to learn about schemes, especially with arithmetic applications in mind. For those inclined towards geometry, an account of schemes from this book coupled with applications from another book (like Hartshorne) would be a good combination. ... Read more

Product Description
Mott Media has Republished the Version of Ray's Arithmetic from the late 1870's and early 1880's!Contains answers for problems in these elementary level books: Primary, Intellectual, and Practical Arithmetic. ... Read more

Customer Reviews (1)

Excellent
We purchased the set, which was quite an expense for us and were pleasantly suprised to see the parent/teachers guide included. The product desciption could have been much clearer.The books seem to be just what we were looking for.Basic but with high expectations.We can do the work orally or written.My daughter now asks for these math books more than workbooks/worksheets which I think were too busy and distracting for her.I think the story problems are excellent and though the language is antiquated our homeschooler finds that an interesting charm rather than a problem. ... Read more

Product Description
Foundations of mathematics is the study of the most basic concepts and logical structure of mathematics, with an eye to the unity of human knowledge. Almost all of the problems studied in this book are motivated by an overriding foundational question: What are the appropriate axioms for mathematics? Through a series of case studies, these axioms are examined to prove particular theorems in core mathematical areas such as algebra, analysis, and topology, focusing on the language of second-order arithmetic, the weakest language rich enough to express and develop the bulk of mathematics.In many cases, if a mathematical theorem is proved from appropriately weak set existence axioms, then the axioms will be logically equivalent to the theorem. Furthermore, only a few specific set existence axioms arise repeatedly in this context, which in turn correspond to classical foundational programs. This is the theme of reverse mathematics, which dominates the first half of the book. The second part focuses on models of these and other subsystems of second-order arithmetic. Additional results are presented in an appendix. ... Read more

Customer Reviews (1)

2 steps backward, 1 step forward for academic printing
[This review is for the paperback edition.]

The cliche is that librarians hate books, a saying that is obviously unfair but that many library patrons have found to contain more than a grain of truth.More and more, it seems that academic publishers are none too fond of books themselves.This morning, my copy of Subsystems of Second Order Arithmetic arrived, and I could tell just by the thickness of the package that I'd been stung by an inferior digital reprint again.While Cambridge University Press is certainly no stranger to digital reprints, we used to be able to count on them for two things.First, they used to reserve digital reprinting for their back list, not for books that had just been released.Second, they used to be candid on their website about which editions of which books were digitally reprinted, but Cambridge's webpage for the paperback edition of Subsystems makes no mention of it being a digital reprint.The good news is that Amazon's Lexington, Kentucky, digital printers have finally got their print quality up to that of a $100 personal laser printer.Even with the muddy cover, the mediocre paper, and the Orwellianly-named "perfect binding", we should give them credit for that step forward.

So why haven't I said anything about the content of the book?My perusal of the library's copy and my attendance at talks given by practitioners of Reverse Mathematics suggest to me that it is first rate and, unlike so much stuff done in mathematical logic, of substantial interest to mathematicians in general.But anything more will have to wait for my review of the hardback edition that I'll be ordering today.This digital reprint is being returned.

[5/17/2010 update:The hardback edition (ordered direct from the publisher) arrived today, and (unlike the first printing in our campus library) it's print-on-demand, too.Sigh.Are there any publishers left who care about the craftsmanship of making books?] ... Read more

Customer Reviews (2)

"How to live in the wilderness, with a sixties sensibility."
There are 276 pages in this book, 241 of which tell you where and how to live in the wild. Don't pay any attention to the criticism that this book somehow promotes a by-gone communist or socialist world-view. Some info is dated, of course, but there is still lots of useful information for the back-to-nature set.

Blech!
This is not at all what I'd expected.I'd thought it would be some sort of 70s-era back-to-the-land resource.Instead it's a scatterbrained socialist manifesto (the dedication is to 'Uncle Ho,' i.e. the murderous Ho Chi Ming).Not worth buying or reading, really, expect as a glimpse into a thankfully now-past era. ... Read more

Product Description

Whether you realize it or not, numbers are everywhere--and integral to almost every facet of your life . . . from your next raise in pay to the inevitable rise of inflation, your weekly family budget to your end of the national debt. And as George Shaffner amazingly reveals, there are discerning answers (and a great measure of comfort) in numbers. In The Arithmetic of Life, he applies the basic principles of mathematics--addition, subtraction, multiplication, and division--to some of the most profound and just plain puzzling questions of our time.

Illuminated with anecdotes, humor, and insight, each chapter explains a unique part of life that can be understood only through the magic of numbers. Whether it's an unconventional theory on why more things go wrong than right, a simple calculation of how much it will cost you to smoke for a lifetime, why crime (accumulatively) doesn't pay, or a glimpse into the probability of life after death, this enlightening and lucidly reasoned book will forever change the way you think about numbers--and the world around you. ... Read more

Customer Reviews (2)

Answers Questions At the Rim of Your Thinking.
This excellent book answers several questions that I have always wondered about - but never knew how to approach them.It also provideds support for issues I feel strongly about but did not understand why.It clarifies why some counter intuitive actions may be so effective.Finally it provides support to those of us working with young adults on how and why to take the proper long term actions.He hints at why rapidly finishing high school and college will provide much more income over the long run.

Math is really only a small building block in this book.No advanced math is required, just addition and averaging.The math is a tool - a simple effective one at that- and nothing more.The main focus is providing solutions to issues one feels strongly about but does not have a clue on how to attack them.

This book has also reminded me of a few ways I better improve myself.I stick to the speed limit and no longer tailgate!!!!!

I just wish Mr. Shaffner would write another book!!!!!

Interesting applications of math and statistics
While books on arithmetic certainly aren't for everyone, I found this one to be interesting, and at times fascinating.My favorite chapter, and one that I plan to use at my daughter's school is on how 8th graders can get a job that pays $45/hour."What kind of job is that," I'm sure you ask...The answer, of course, is "Stay in School".Since high school graduates on average make significantly more than dropouts, you can assign that difference an hourly rate for the hours that remain till graduation day.Sometimes interesting, sometimes fascinating, sometimes a bit of a stretch, but for an engineer, math fan, statistician, etc., definitely worth the buy. ... Read more