Book Description
Hannah thinks tonight’s Passover Seder will be the same as always. Little does she know that this year she will be mysteriously transported into the past where only she knows the horrors that await. ... Read more

Customer Reviews (263)

Brilliantly written
I absolutely could not put this down.I highly recommend it for young readers who are wondering about this event in our history.

Wow...
I used this as a literature circle book for my 6th graders.You could have heard a pin drop whenever it was read silently, and students had a hard time not reading ahead when they needed to stop. It is a traumatic story, but one that needs to be told.It brought up a wealth of questions from students. The Holocaust is a difficult subject, no matter how it is told. As a parent, I will have my children read it, but with guidance so I am there to answer their questions about this horrible event in history.Jane Yolen is truly amazing.

Wonderful book to teach the Holocaust to proto-teens/teens
The protagonist is a typical proto-teen thrust into a disorienting, frightening, Twilight Zone world.In present day New York Hannah opens her apartment door on Passover for Elijah and finds herself transported to 1940s Poland. In a simple manner resurrecting this world through the eyes of Hannah the author teaches her and us about bravery, sacrifice and why we cannot forget.I contributed a copy to my children's school and kept a copy for when my guys are older.

A little bit rough, but still good.
The Devil's Arithmetic was a well-written, interesting novel.It is a great piece of historical fiction.However, it was very emotional and somewhat depressing novel.I would recommend this novel only to someone who is very mature, over 10, and able to handle some very emotional literature.The Devil's Arithmetic is so real, it puts you in shock.

The Devil's Arithmetic
Hannah is a young woman, thirteen years old and a fairly normal sounding teenager. She has no true understanding of her family's culture, or of the memories that are in her blood, ones shares and must not forget. Hannah is reborn into Chaya, as she is taken from a normal, rural life in 1942, into one of the Nazi death camps. We watch as the daily struggles for life transform this teenagers understanding of her world, what it has become and what it was. The glimpses of her true time period, the 1980's, are seen as madness in the camps, but she speaks truth. And she remembers the most important gift of all. Chaya gives up her life for Hannah's ancestor, Rivka, so she may escape to live her life. I enjoyed the family future and past connections; it made the book at that more personal since the readers become so close to her extended family, all in both versions of time. The deep emotions this book brings to the surface would take a careful working, well versed teacher. But this book is told in a way that is an accurate, as well as age appropriate way of explaining, in first person, some of the atrocities that humans can do to one another. On page 163, where Hannah is back in her own time and explains to Aunt Eva what the numbers on her arm mean, I almost started crying. What a powerful way to end the book. "J18202. J is for Jew. And 1 because you were alone, alone of the 8who had been in your family, though 2 was the actual number of them alive..."

... Read more

Book 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 (13)

"Nature is written in the language of mathematics" (Galileo)
I picked this book up because the premise is very interesting, and one of the book jacket reviewers--an academic who is known in the modelling world--called it "a must-read for anyone serious interested in the role of models in ... science and policy."

I was very disappointed. I think critiques of modelling are useful and instructive, whether or not you believe in the approach or not (though few scientists believe it is really useless). But the critiques should be both sound and constructive, and this book provides neither.

Math is a language, for sure, but it is the least ambiguous language we humans have, and is the easiest means by which we can understand complex phenomena. I agree with the authors that qualitative knowledge is essential in science, but I think their premise fails by not more closely evaluating the postive aspects of modelling.

One may find probably the best critique of ecological modelling in Charles Hall's classic 1988 paper, "An assessment of several of the historically most influential theoretical models used in ecology and of the data provided in their support." (One may find it readily on the web.) Instead of getting this book, just read Hall's paper--you'll be better off on both counts.

It's About Models
The first author is a retired professor of geology and a particular expert on beaches.He's a scientist's scientist, and clearly an opinionated and occasionally irascible guy.This book is a bit of a tirade in places but it's full of real examples, good data, and thought provoking stories.I enjoyed it a lot.The main theme is that the natural world is too complicated a place for quantitative models to work well, and that when politics is involved they can lead to really bad decisions.The majority of examples are drawn from cases where earth sciences meet human activities - sea level rise, beach erosion and "nourishment", hydrology of abandoned pit mines, storage of nuclear waste.Closely related are discussions of fishery management and invasive species.For the most part the book is well researched.The writing is clear - the book is an easy read and never boring.
Quantitative models are decried throughout the book, and the suggestion is made that what is reasonable is "qualitative" modelling.The distinction isn't really developed until the last chapter where some good examples are to be found.Still, the distinction isn't as crisp as I'd like - perhaps it is a qualitative difference and not a quantitative one!Another positive suggestion is that incrementalism is a generally better approach to interacting with the complexities of nature than the brittle approaches that arise from an overly numerate engineering mentality.In other words, instead of using quantitative models to plan enormous, long-term projects, try something on a small scale, observe the results, and go from there.
I came away with considerably more knowledge of the topics discussed.I was already a convert to the basic themes - that we tend to overestimate what we know, to trust numbers more than we should, that political processes often interact with science in ways that are inimical to both good decisions and greater knowledge.Several times I thought of Eisenhower's dictum that plans are generally useless but planning is essential.Perhaps that captures best the distinction Pilkey is trying to make about qualitative models.
Unlike some of the other reviewers, I was not offended by the political implications of anything Pilkey asserts.I didn't see it as either pro or anti global warming in any political sense.No hidden agendas here, it's really about modelling.Recommended.

Boring
Some of the complaints in other reviews are sound, but I will mention just one. This is a dull book. Longwinded, preachy. And aside from some jargon, there isn't much substance here beyond what you could say in 20 pages.

Great Idea - if only they had taken their own advice
As a systems engineer, I have practical experience in creating, testing, critiquing, and evaluating models that attempt to explain, predict, or illustrate system processes.Any engineer learns early on that regardless of what the model says - Reality Always Wins. Thus I was very interested in this book because of its evident intent to discuss the limitations of modeling as applied to natural processes.

Unfortunately, the authors exhibit a level of bias against any model they don't approve that is so over the top that I was constantly wondering what cheese would be served with the "whine".And then they cap it off by blindly accepting an entire range of dire global warming predictions, which are entirely derived from - you guessed it - models of complex natural processes.I guess if you like the model's answers then it is magically a good model.

I have a hard time accepting what appears to be intellectual dishonesty, so although the book makes some good points, I really can't recommend it. The authors also appear to be particularly upset with certain individuals and organizations in the coastal engineering community, because the animus comes through loud and clear.

If you really want a good book on the limitations of mathematical modeling as applied to the real world, there is a two-volume set called "Reality Rules" that is much better. However, the Reality Rules books are not aimed at the layperson, so be prepared for some real math in these books.

A pivotal work - outstanding
A pivotal work. Wherever one stands on the debate over human caused global warming, this book will raise questions.A well done investigation of mathematic global modeling pitfalls. ... Read more

Book Description
"Everyone take out your spelling books," said Mrs. Jewls."It's time for arithmetic."
Sue is so excited for her first day at Wayside School.But things at Wayside are far from normal-and Sue's teacher, Mrs. Jewls, is completely wacky.She expects the students to add and subtract words!Sue has never heard of anything so ridiculous.She knows adding apples plus oranges is impossible...or is it?Anything can happen at Wayside School.
... Read more

Customer Reviews (15)

It's great
Although this book looks like a kid's book, it is really for teenagers and older.It is full of math puzzles, so if you have a bent for figuring out puzzles, don't let the cover and title put you off.It's not really arithmetic -- it's more logic puzzles.I loved this book, and so did my high school aged kids.

THIS BOOK WILL GIVE YOU A HEADACHE!
This is not a story book.It is a math book.It is too difficult for a young reader.Most adults or older teenagers would probably enjoy it but only if they love math.My 9 year old child said it gave her a headache.My child was given this book at school to read and expected to do the problems in it.Some of the problems required math skills she has not even been introduced too.It is simply too hard for young readers.

Fun, but challenging
As someone who has always been a math person, I loved this book when I was in 4th grade.I was able to do the problems in it and thought it was a fun different approach to learning about math and using logic.I think that this book can be still a fun brain teaser even for adults, as I am one now :).I would say that for many younger Sachar readers this book has a high chance of being over their heads unless they have an adult help them through it, as it has almost an algebraic approach to it.Personally, I think this book is fantastic, but I would not recommend it for anyone looking for just an entertaining story.This is a book of math riddles.

This is not a story
My 10 year-old loves Louis Sachar in general and the Wayside books in particular.After devouring the 3 in the boxed set, he begged for more Wayside School stories.I searched amazon and found this and ordered it and he was so excited when it arrived that he dropped what he was playing and tore upstairs to read it.

He came down in 5 minutes - SO disappointed.He claimed the book 'is not the same'.I took a look and sure enough - it's a book of puzzles.There is no narrative, no story.

Maybe the puzzles are fun - but we were looking for a story.Personally I don't think that the description here made it clear that this is not in fact a story.I wouldn't have ordered this book if I'd realized what it was.

If you're looking for puzzles - go for it.If you're hoping (as we were) for another installment in the Wayside School stories - this is NOT it.

Mind twisting fun
Louis Sachar is at his best.This book is packed with Mathmatical mind benders.And yesEARS + EARS = SWEAR does add up, just do the math Wayside Style. We gave this book to our Mother as a Mother's Day Gift.She is a highschool Math teacher and she loves it. ... Read more

Book Description
Everybody uses arithmetic on virtually a daily basis, and this book serves as a handy brush-up for general readers while it also helps students master basic skills that they need before moving up to high-school-level math and beyond. It reviews addition, subtraction, multiplication, and division, then moves on to calculating with fractions, decimals, and percentages. A concluding chapter reviews units of measurement and word problems. Chapters are filled with short practice exercises, all of which are answered at the back of the book. The book features many tables, charts, and line illustrations. Barron's Easy Way books introduce a variety of academic and practical subjects to students and general readers in clear, understandable language. Ideal as self-teaching manuals for readers interested in learning a new career-related skill, these books have also found widespread classroom use as supplementary texts and brush-up test-preparation guides. Subject heads and key phrases that need to be learned are set in a second color. ... Read more

Customer Reviews (7)

LOVE IT; ITS MY MATH BIBLE
I am an idiot when it comeS to this type of math. I used to hate it and would have panic attackS in class when asked to go to the fronT of the class. Now, I'm the first one to rasing my hand! This book has changed my life lol. Its sounds cheesy but it's true. GET IT!

Great Help
This is the book that my daughter's tutor recommended. My daughter has a hard time remembering the steps to solve math problems. My tutor recommended this book vs. math worksheets because no matter how many worksheets my daughter does to practice, she will have a hard time remembering the steps. This book, on the other hand, gives examples that she can follow and refer back to. It makes her more independent because she can pull the book out and find the concept she's working on and see the steps outlined. I've reviewed and purchased dozens of math books and practice books, and this one is the best.

Satisfied
I got this book to help my 5th grader who is weak at math. This book has been very helpful in getting her to understand and it also gives her extra practice. I like the test that go along with each section. I would recommend this book to anyone needing help in basic math.

I PASSED THE TEST AND GOT THE JOB!
I work for a major corporation that requires employees who apply for other jobs within the company, to take and pass the "Universal Test Battery".A part of this exam is arithmetic, including addition, subtraction, division, multiplication and percentages.I am a 54 year old who has been using a calulator for 30+ years!This book is indeed a 'workbook' that reviews all arithmetic and clearly explains the problems and how to do them all the way to sucess!

I couldn't ask for a better book!!!
I bought the second edition of this book several years ago when our company (USWest) was closing departments and we knew we would have to start testing for job title changes. It was one of the most helpful purchases I have ever made! I retired, and now I'm going into real estate. Naturally the real estate classes (and the state test) have lots of math and math problems. As they say...what you don't use you lose!!! There were several of us in the classes who were having a difficult time with the math problems and formulas. This book was once again a life saver. At first glance one would think it's too simple...more for children than adults, but it isn't. Mr. Williams makes math super simple for any age!!!

The first few chapters are basic math...addition, subtraction, multiplication, division, Roman numerals, etc.

Chapters 6-8 are fractions...changing improper to mixed numbers...subtracting, multiplying and dividing fractions...unlike denominators, etc.

Chapters 10-13 cover decimals...comparing, rounding off, adding, subtracting, multiplying mixed decimals.

Chapter 14 covers percents...changing percents to decimals, to fractions, and finding the percent of a number.

Chapter 15 covers measurement.

There are pre-tests to see if you need to study the chapter, word problems, practice examples, and practice tests after every section.

I recommend this book for everyone...young people who find math difficult, as an invaluable aid for parents of school age children, for anyone who is making a career change and is faced with job testing, and for those...like myself...who have been out of school for years and need a brush up on math skills. The price is minimal!!!

Thank you, Edward Williams, for writing this book. Thank you for the difference it has made it my life!!! ... Read more

Product Description
Attributed to Iamblichus (4th cent. AD), The Theology of Arithmetic is about the mystical, mathmatical and cosmological symbolism of the first ten numbers. Its is the longest work on number symbolism to survive from the ancient world, and Robin Waterfield's careful translation contains helpful footnotes, an extensive glossary, bibliography, and foreword by Keith Critchlow. Never before translated from ancient Greek, this important sourcework is indispensable for anyone intereted in Pythagorean though, Neoplatonism, or the symbolism of Numbers. ... Read more

Customer Reviews (3)

The Holy Grail
The most valuable book I ever found on Pythagorean number philosophy, highly recommended, good luck at ever finding it in print!!!!

You cannot IMAGINE how excellent this book is. I'm stunned
When I bought this book, I presumed I was buying a remotely dry and dull book of late Neoplatonic praddle on numbers. However it turns out this book is a copy of a copy of a copy by Iambblichus all the way back to Pythagoras himself (although this isn't proven).

The content of this book is an ABSOLUTE MUST TOOL in the comprehension of Plato, and , my favorite, Plotinus, the logical and numerical philosophical Emanation model (of Plato and Neoplatonists) as expressed in this book is mind blowing. I myself find that 99.9% of the many 1000s of books I've bought get a quick glance and are ditched on the shelf SOON afterwards. I've read the "Theology of Arithmetic" now more than 8 times!

I forward, and rightly so, that this book is in fact an INDESPENSIBLE tool to grasping the logical and numerical ontological expression-model of Pythagoras and Plato/Plotinus in their philosophy of Emanation and necessity in their illuminating the werks (eklampsis/emanation) of the One, the Divine. What's better, is the pithiness of this book is astounding, with main content around 120 pages, its incredibly condensed and packed with revelations and connections leading to insights into Plato's ontology "by" numbers that I never could have made without THIS book.

As per Plotinus in 5.1.1 and his "mystery" world TOLMA as the primordial cause of the "souls descent", I found the answer of this 1500 year-old philosophical-contention mystery SOLVED by means of this very book, "Theology of Arithmetic"

Personally, I find the subtitle of this book should be: "THE KEY TO UNDERSTANDING THE NUMBER ONTOLOGY OF ALL OF PYTHAGOREANISM, PLATONISM AND NEOPLATONISM".

My copy of this book is so underlined and highlighted, I'm buying another copy of it.

Lot's of Little Treasures
I'm not sure if the books' material or the editor's notes are more useful.The book itself is attributed to Iamblichus but it is not really known whether he actually wrote this particular text.The author does note that the book seems to be more of a compilation of material by Anatonlius and Nicomachus.I actually wondered at many points if this text was written by a student (i.e. student notes from lectures at Plato's academy).None-the-less if you are looking for materials on Pythagorean philosophy, this book is for you.It covers the symbolism attributed to the first ten numbers (the monad through the decad) as well as touching on subjects like Plato's lambda and the Geometric, Arithmetic and Harmonic means.If you have the Pythagorean Sourcebook by Guthrie or Jesus Christ, Sun of God by Fidieler this book will complement those two works nicely (esp. Appendix II of the former).Also, Rene Schwaller's Study of Numbers seems to derive a lot of inspiration from either this text or one like it.Keith Critchlow, who wrote Islamic Patterns, introduces this book and extrapolates on Plato's Lambda in a very interesting way.Also the glossary in the back of this book, explaining Platonic/Pythagorean notions of numbers (perfect, over-perfect, even-odd, etc.) was enlightening.With so many gems of Pythagorean knowledge in such a small space (i.e. less than a hundred pages) - the book definately deserves 5 stars. ... Read more

Customer Reviews (3)

Teach First Grade Math With Games Instead of Workbooks
If you are looking for a better way to teach children math in the early grades, you must read this book.

In Young Children Reinvent Arithmetric, Professor Constance Kamii takes you on a journey of discovery as she works withteacher Georgia DeClark in her first grade classroom. Together they work through the first grade math curriculum finding games and real life situations that will assist students in developing the mathematical thinking skills that underlie the curriculum goals.

The book begins with background information on Piaget's Theory of number, demonstrating how children develop logical-mathematical thinking by interacting with the world and each other. In Part Two the goals and objectives of the curriculum are explained. In Part Three the activities used to teach the children are explained in great detail so that teachers will understand how to use them in their own classrooms. In Part 4 The teacher tells her story. Part Five provides the program evaluation with the research and testing that was done. The children in DeClark's classroom are compared to children in a classroom using traditional teaching methods.

Constance Kamii has been transforming the Constructivist Theory of the origins of thinking by Jean Piaget into practical activities for teaching for decades. Her work is so important in these days of standardized testing and NCLB.
Nancy Illing author of SPARKS Ignite Imagination

Kamii shows how children think
It's helpful to have at least a passing acquaintance with Jean Piaget's theories before reading this book, but it's not necessary.Kamii shows inso many many ways that the thought life of young children is different fromour own. Not only should this be required reading for all Kindergartenthrough second grade teachers, but also for those politicians and politicalpundits whose back to basics (and did we ever really leave the basics?)approach to curriculum simply makes life miserable for these poor kids.(because what they think are the basics aren't really the true basics ofthought)

One interesting aspect of the book is that it was in partco-written with a primary school teacher who tries out some of Kamii'sideas in her own classroom. She is initially skeptical that Kamii knowswhat she's talking about, but later realizes the truth of it whenconfronted with the evidence of her own senses.

After you read this book,you'll never see a kid do a problem like 5 + 1 or 16 + 7 with the same eyesagain.

Teaching Number Concepts in Young Children
I am a Kindergarten teacher and would recommend this book to teachers and parents looking for a good resource to teach children number concepts.Kamii not only discusses number concepts and problem solving, she alsogives lots of easy to make games to make learning these things fun. Wonderful book! ... Read more

Customer Reviews (2)

A Homeschool Classic...should be read by everyone
Ruth Beechick is a comforting voice of confidence to new homeschoolers and math-phobics.She made me feel equipped and prepared to introduce math skills to my children.This book is worth every penny and more for the fun ideas, using basic household items, and the wise counsel.You would have to dig through volumes to get this kind of quality information, otherwise.

Worth if for "Modes of Thinking" chapter alone
The explanation of the 3 modes of thinking about arithmetic is excellent.By far the clearest I have ever seen, and makes sense with what I have seen.I has already helped me understand my child's approach to math.Although kids now seem to learn more and faster than before, so this book may no longer cover K - 3rd grade (unless you are home schooling and hold the pace). It is well worth more than the ... price.28 pages.clearly written. ... Read more

Book Description

The bestselling guide updated and expanded for today's mathphobes

Written by two pioneers of the concept of math anxiety and how to overcome it, Arithmetic and Algebra Again has helped tens of thousands of people conquer their irrational fear of math.

This revised and expanded second edition of the perennial bestseller:

Customer Reviews (4)

exactly what I needed
I received the book in a timely fashion as well as in great condition. Thanks for being reliable!

For us math challenged peeps!
I am back to school after how many years and was half panicking when I was told I would have not one but TWO math classes.This book is one of the texts.It is easy to follow and quite thorough.Out of the 6 books I need for these classes, so far I understand this one the best.

Outstanding for people who struggle with math
I had to prepare for a test for certification in middle school math and was terrified. I hadn't studied algebra or statistics in over 20 years.I ordered several books online and got more at the public library, and this was the ONLY book written in a way that allowed for effective self teaching.The other reviewer said it best, the language they use to explain concepts is the key.I wanted a book that talked to me like I was 6 years old.It needed a bit more on geometry, other than that is was an excellent study guide.Great for Praxis preparation.

What I've been looking for....
This is a very well-thought-out book. I've looked at many many math books, looking for one with good, clear explanations. This one is deceptive - at first glance it looks just like any other math book, but this is what I was looking for. For example, the explanation of why we invert and multiply when we divide fractions is clear and understandable - few other math books even bother to try to explain why or how this works, but this book does and does it well. Another wonderful thing about this book is that the authors are aware that words used in math can be confusing - they take the time to explain, for example, why we often use the word "of" when multiplying fractions (1/6 of 3/4) instead of saying "times" (1/6 times 3/4).

The explanations in this book are excellent (and that is what I was looking for) and they always show every step of a solution, so it is easy to follow along. They also use visual explanations, again making sure to show every step.

The focus in this book is on relating the math to practical life - this also really aids understanding.

There are lots of exercises to practice with - and answers are provided for all of them.

The best thing about this book is the "tone" of the authors. They write in an easy-to-understand, clear way. The book doesn't seem to have been written in "mathese" another language, but in normal English for normal people. It gives the feeling of being written by people who are caring and helpful and want the reader to understand - as opposed to most math textbooks that seem to be written more to impress other math educators than for real people who aren't used to math-style writing.

The book covers all the usual topics of arithmetic and goes up through elementary algebra.

Even though the intended market for this book is adults or college students who have already been through years of math, much of which they've forgotten, I recommend it also for homeschoolers. This inexpensive book can take the place of purchasing curriculum for years. It also can be used as a reference for finding good explanations and examples of specific topics - it has an excellent table of contents and index. ... Read more

Customer Reviews (1)

A very moving account of the realities of the Second World War in Eastern Europe
It continues to astound me that there are people who deny The Holocaust. In some sense I can understand it because it is so difficult to believe that such a thing could have been done as a part of official state policy. Nevertheless, the documentation is so overwhelming that the people who deny it look like pathetic fools.
This story describes the events in one of the camps, but from a unique perspective. Hannah is a young girl living in New Rochelle, New York in modern times. She is with her family and they are going to a Passover service at the home of her elderly relatives that survived the camps. Hannah is a bit rebellious, growing tired of the rituals and wishing she were elsewhere.
Everything changes when Hannah opens the door as a symbolic gesture to let the Prophet Elijah into their home to take part in the ceremony. Suddenly, she is now Chaya, a Jewish girl in Eastern Europe during the Second World War. Shortly after she arrives, the Jews in their shtetl are rounded up, packed into railroad cars and shipped off to a death camp. Her life then becomes a daily challenge to survive.
Like all the others in the camp Chaya is now being slowly worked and starved to death, looking over at the smoke rising from the crematoriums and knowing what it means. Her "time" at the camp ends when she is with four friends and a guard comes over and says he must select three of them to be killed. After all, he has a daily quota that must be filled.
Suddenly, she is Hannah once more and she looks at her Aunt Eva and she can explain the meaning of the tattoo on Eva's arm. Furthermore, she recognizes her Aunt Eva and Grandpa Will as people she knew in the camp. This realization changes her outlook on her Jewish heritage as she now has firsthand knowledge of what took place.
This book is very moving and descriptive of those terrible times. The perspective is always that of a young girl, although she grows up very fast once she arrives at the camps. It should be required reading for all middle school children. While some may object to the depictions of brutality, the history of the human race is not pretty, and the best way to avoid the ugliness is to understand the consequences.
... Read more

Book Description
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

Book Description
Serre's A Course in Arithmetic is a concentrated, modern introduction to basically three areas of number theory, quadratic forms, Dirichlet's density theorem, and modular forms. The first edition was very well accepted and is now one of the leading introductory texts on the advanced undergraduate or beginning graduate level.
From the reviews: "... The book is carefully written - in particular very much self-contained. As was the intention of the author, it is easily accessible to graduate or even undergraduate students, yet even the advanced mathematician will enjoy reading it. The last chapter, more difficult for the beginner, is an introduction to contemporary problems." American Scientist ... Read more

Customer Reviews (4)

not to be confused with an "arithmetic" book
In french, "arithmétique" means elementary study of rational numbers... You will not learn how to add or substract rational numbers here. An easy book to begin with this kind of maths is Andrew's: number theory (from Dover): well explained with a lot of examples...I guess that the author meant something like: "arithmetic of quadratic forms..." The truth is contained in the book's introduction: the text is made of lessons given to second-year "normaliens" from the "rue d'Ulm": those were (and still are) among the most gifted mathematic students in France; (post-graduate level...) therefore any reader without a really sharp mind and a very good level of knowledge in algebra will hardly grasp anything from the book which is really demanding; in the first ten pages, you will find a study of finite fields aimed at proving the celebrated "law of quadratic reciprocity"; it is already well beyond classical elementary arithmetic as it was taught in "classe terminale" thirty years ago and furthermore nowdays.
Then it tackles with p-adic fields, entire quadratic forms and then Dirichlet Theorem on primes in arithmetic sequences in a mere 20 pages (to set things up, this theorem is not proven in Hardy an Wright's: "introduction to the theory of numbers" because it is not an elementary theorem as mathematicians go since any proof of it requires use of advanced complex variable methods...) and at last modular forms; as you can expect, everything in the book is connected; so it looks like (it is...) an impressive piece of mathematics; it is a daunting but not impossible task to go through the whole book; let say that such hard work is rewarding and the chapter on modular forms is really a fascinating one ( and a first step towards Wiles' proof of Fermat's last theorem albeit so many more steps have to be climbed to achieve that precise aim...) ; moreover, the chapters using "analytic methods" can be read independantly; "un tour de force".

Breathtaking
Serre's work could best be summarized in one word - Elegance.
The book comprises of two distinct parts.
The first one is the 'algebraic' part. Serre's goal in this section is to give a complete classification of the quadratic forms over the rationals. As preliminaries to reaching this goal, he introduces the reader to quadratic reciprocity, p-adic fields and the Hilbert Symbol. After these three, he spends the next chapter detailing the properties of quadratic forms over Q and Q_p (the p-adic field). The reason to work over Q_p is the Hasse-Minkowski Theorem (which says that if you have a quadratic form, it has solutions in Q if and only if it has solutions in Q_p). Using Hensels Lemma, checking for solutions in Q_p is (almost) as easy as checking for solutions in Z/pZ. After doing that, he spends yet another chapter talking about the quadratic forms over the integers. (Note: the classification goal is already achieved in previous chapter).
The second half of the book is the 'analytic' one. The first chapter in this section gives a complete proof of Dirichlet's theorem while the second one studies the properties of modular forms (these are good!)
Due to the extreme elegance, the book is sometimes hard to read. This might sound like a paradox, but it's not and I'll explain why. The book takes some effort to read because it's terse and it often takes a while to figure out why something is 'obvious'. However, once you see it all, you'll realize that a great mind was guiding you through the pursuit. The choice of topics is just right to achieve the goals that the author sets out for himself. Also, I'd rather think for myself and read a smaller book than be given a huge fat tome where the author details his own thought process.
This book was my first foray into number theory and I absolutely enjoyed it. If you're considering reading it, I wish you joy in your pursuits.

Very Demanding
The book is divided into two parts -- algebraic and analytic. I've only worked through the analytic part. Anything by Serre is worth its weight in gold and this book is no exception; everything Serre covers is of the utmost importance. But Serre's style is extremely condensed and spare, and he makes no concessions to the reader in terms of motivation or examples. I can't digest more than half a page of Serre a day; however if one wants to understand the structure of a theory, Serre is ideal.

I worked through "A Course in Arithmetic" over a decade back. As I recall I covered Riemann's zeta function and the Prime Number Theorem, the proof of Dirichlet's theorem on primes in arithmetical progressions using group characters in the context of arithmetical functions, and some of the basic theory of modular functions. All of this material is also covered in Apostol's two books on analytic number theory ("Introduction to Analytic Number Theory", and "Dirichlet Series and Modular Functions in Number Theory"); Apostol goes further than Serre in the analytic part -- which is only to be expected since he is devoting two whole texts to the subject.

A sheer delight
This short book on number theory by one of the giants of 20th centurymathematics is delightful to read. Its length motivates one to finish thebook, and it is packed full of interesting results. Most of the theorydiscussed in the book has wide-ranging applications, such as cryptographyand dynamical systems. The last chapter of the book is the best and coversthe subject of modular forms, including theta functions, Hecke operators,and general modular functions. If you want to understand the Wiles proof ofFermat's last theorem, start with this book. ... Read more

Book 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 theory of elliptic curves in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. The book begins with a brief discussion of the necessary algebro-geometric results, and proceeds with an exposition of the geometry of elliptic curves, the formal group of an elliptic curve, elliptic curves over finite fields, the complex numbers, local fields, and global fields. The last two chapters deal with integral and rational points, including Siegel's theorem and explicit computations for the curve Y^2 = X^3 + DX. The book contains three appendices: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and a third appendix giving 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. ... Read more

Book Description

KEY MESSAGE: Integrated Arithmetic and Basic Algebra, Fourth Edition, integrates arithmetic and algebra to allow students to see the big picture of math. Rather than separating these two subjects, this text helps students recognize algebra as a natural extension of arithmetic. As a result, students see how concepts are interrelated and are better prepared for future courses.

KEY TOPICS: Adding and Subtracting Integers and Polynomials; Laws of Exponents, Products and Quotients of Integers and Polynomials; Linear Equations and Inequalities; Graphing Linear Equations and Inequalities; Factors, Divisors, and Factoring; Multiplication and Division of Rational Numbers and Expressions; Addition and Subtraction of Rational Numbers and Expressions; Ratios, Percents, and Applications; Systems of Linear Equations; Roots and Radicals; Solving Quadratic Equations

MARKET: For all readers interested in algebra and basic algebra.

Book Description
A crucial step in getting a civil service job is a great score on the entry-level civil service exam. Basic math and English usage are two skill areas where many test-takers could use the most help. Detailed subject review and up-to-date practice material make this self-tutorial the first choice for job seekers looking for work with federal, state, local, and municipal governments. ... Read more

Customer Reviews (1)

Good study Guide
Great study guide, I bought this for my wife who was taking the civil service Administrative Analyst position.She went from getting 69% to a 90% passing score!However, getting through the politics of the organization is a whole different matter...

Otherwise from that, its an excellent study guide. ... Read more

Product Description
Mott Media has Republished the Version of Ray's Arithmetic from the late 1870's and early 1880's!Ray's Arithmetics teach arithmetic in an orderly fashion, starting from rules and principles, building knowledge piece by piece, leading pupils from simple to complex. From the very first pages, Ray's Arithmetics incorporate what has become the scourge of today's math students - story problems. Students must READ simple sentences which pose real life problems, decide whether to add, subtract, multiply or divide, and finally arrive at the answer - sometimes mentally - sometimes in writing.Ray's Arithmetics students learn arithmetic, increase their reading comprehension skills, and learn to think rather than plod through page after page of addition or subtraction problems with a one-line direction at the top of each page. A student raised on Ray's will not even know he should be fearful of "story problems" because from day one every problem is posed in a sentence format.Most early work is to be done with real objects such as fruit, counting blocks, or marbles. Later it is to be done in the head with mental images of the objects. When children are ready to think symbolically, they gradually drop their use of objects and images and learn to compute quickly with digits. Thus the child is carefully led through three growth states in arithmetic: 1) the manipulative stage, 2) the mental image stage, 3) the abstract stage.Over 120 million copies were sold in American education's golden age. Many millions of children used these Arithmetics in the generations that produced Edison, Bell, and Ford. Now it's your turn. ... Read more

Customer Reviews (2)

great price - great education
I love this series.It's practical, productive, and, most of all, interesting - it keeps my children's interest.I have natural mathematicians and struggling ones in our homeschooling family, but this suits all of them equally.Math is no longer avoided by the ones that find math challenging.The natural development of the mind is addressed by this unique but "old-fashioned" style.The parent's guide offers clear instructions to assist the learning schedule and process.

The best texts for the best price
Ray's Arithmetics offers the best of all I liked about other popular homeschooling programs (and more) at a fraction of their cost. The lessons are sensible andpractical, and they will take us through the eighthgrade, from learning to count and read numbers to doing college-levelbusiness math. The teacher's guide, which is written by RuthBeechick,provides an outline and tips on teaching each grade level. Hereis her entry for the chapter on Grade 2 : "Teaching Second Grade - ATypical Day - A Typical Week's Schedule - Planning Guide - ProgressRecord- Testing Second Graders - Test Schecule - Unit Tests - Answer Key for UnitTests."She offers outlines for fitting lessons into a 36-week year.She also includes a chapter on interesting projects and games that helpteach everything from counting to geometry and measures. Thebooks are compact and well-made, so they will fit on my already-crowdedbookshelf and they will last through all our children. This eight-book setis perfect for parents who are not impressed with bells and whistles andslick packaging: Ray's Arithmetics look old-fashioned, inside and out. Theexercises are practical word problems written using 19th-century prices andsituations, which is charming and could be used to enhance a unit study onthat era. Ruth Beechick recommends taking care in the eighth-grade yearto strengthen any weaknesses that are apparent before going on to algebra,probability, navigation, and so on.I'm excited about learning alongwith the children. I see many things in these books that I wish Iunderstood, but never was taught, not even in college. When we're finished,the children and I will KNOW math, and I will no longer feel helpless whenit comes to our insurance and investments. I highly recommend Ray'sArithmetics. ... Read more

Product Description
Grades 7-9.Essentially a complete teacher's manual for the book, this LitPlan Teacher Pack includes lesosn plans and reproducible resource materials for The Devil's Arithmetic.It includes:20 Daily LessonsShort answer study questionsMultiple choice quiz questionsVocabulary worksheets for each reading assignment3 detailed writing assignmentsIndividual and group activitiesCritical thinking discussion questions5 unit tests (2 short answer, 2 multiple choice, 1 advanced)Evaluation formsReview puzzles & gamesBulletin board ideasReproducible student materialsAnd more!A Note About A Few Of The Many Different Assignments Included:There are three writing assignments in this unit, each with the purpose of informing, persuading, or expressing personal opinions. The detailed writing assignment sheets guide students through the assignments. The first assignment is to inform: students write a composition about one of the background topics assigned in Lesson One. The second assignment gives students the opportunity to express personal opinions: students will keep a diary throughout the reading of the novel. The third assignment is to persuade: students pretend to be Hannah (Chaya) in the camp when the commandant comes and sees Reuven limping out of the camp hospital. Her objective is to convince Breuer not to choose Reuven. Uses:These materials are geared for whole class use but are very easily adaped for independent study work, lit circles or book groups, home school use, or tutoring.If you have never taught this book before, this manual will give you a great foundation of materials on a variety of levels.If you have taught this book before, you might like to know that veteran teachers have told us they have found our LitPlan Teacher Pack manuals to be different from many other materials they have seen--and very helpful. ... Read more

Product Description
Mott Media has Republished the Version of Ray's Arithmetic from the late 1870's and early 1880's!This book introduces the four operations of addition, subtraction, multiplication, and division, along with counting and other basic skills. It can be used to guide your teaching for about two years - through grades 1 and 2. It goes farther than the average second grade course, but with Ray's mental system many second graders are able to do this work. ... Read more

Product Description

This book, intended for research mathematicians, proves the duality theorems that have come to play an increasingly important role in number theory and arithmetic geometry, for example, in the proof of Fermat's Last Theorem.

Reviews of the first edition
The book deals with duality theorems in Galois, étale and flat cohomology, for local and global fields, as well as the corresponding rings of integers. Also covered are results about cohomological dimension, finiteness and Euler-Poincaré characteristics. It can serve as a good general reference for these questions.
Mathematical Reviews, Gerd Faltings.

… However, much of this work [by Tate, Artin, Verdier, and others] was never published in details. The main purpose of the book under review is to offer a selfcontained and systematic treatment of these developments.
Zentralblatt MATH, L. Badescu.

Book 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

Book Description
Nothing strikes fear into the hearts of math students more than word problems. In How to Solve Word Problems in Arithmetic, noted math teacher Phyllis Pullman defangs the dreaded word problem for 5th through 8th grade-level arithmetic students by emphasizing the mechanics and grammar of problem-solving, and focusing on problems involving arithmetic skills, area, percent, basic geometry, measurement, and statistics. ... Read more