Product Description
This book presents an up-to-date, unified treatment of research in bounded arithmetic and complexity of propositional logic with emphasis on independence proofs and lower bound proofs.The author discusses the deep connections between logic and complexity theory and lists a number of intriguing open problems.An introduction to the basics of logic and complexity is followed by discussion of important results in propositional proof systems and systems of bounded arithmetic.Then more advanced topics are treated, including polynomial simulations and conservativity results, various witnessing theorems, the translation of bounded formulas (and their proofs) into propositional ones, the method of random partial restrictions and its applications, simple independence proofs, complete systems of partial relations, lower bounds to the size of constant-depth propositional proofs, the approximation method and the method of Boolean valuations, combinatorics and complexity theory within bounded arithmetic, and relations to complexity issues of predicate calculus.Students and researchers in mathematical logic and complexity theory will find his comprehensive treatment an excellent guide to this expanding interdisciplinary area. ... Read more

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Originally published in 1922.This volume from the Cornell University Library's print collections was scanned on an APT BookScan and converted to JPG 2000 format by Kirtas Technologies.All titles scanned cover to cover and pages may include marks notations and other marginalia present in the original volume. ... Read more

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Mott Media has Republished the Version of Ray's Arithmetic from the late 1870's and early 1880's! 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

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The book deals with computer arithmetic in a more general sense than usual. Advanced computer arithmetic requires that all computer approximations of arithmetic operations - in particular those in the usual vector and matrix spaces - differ from the correct result by at most one rounding. The implementation of advanced computer arithmetic by fast hardware is examined in the book. The new expanded computational capability is gained at modest cost. It increases both, the speed of a computation and the accuracy of the computed result. Fast multiple precision arithmetic can be easily provided with it. All this strongly supports the case for implementing advanced computer arithmetic on every CPU. It is also shown in the book that on superscalar processors interval operations can be made as fast as simple floating-point operations with only very modest additional hardware costs. ... Read more

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This book principally concerns the rapidly growing area of what might be termed "Logical Complexity Theory": the study of bounded arithmetic, propositional proof systems, length of proof, and similar themes, and the relations of these topics to computational complexity theory. Issuing from a two-year international collaboration, the book contains articles concerning the existence of the most general unifier, a special case of Kreisel's conjecture on length-of-proof, propositional logic proof size, a new alternating logtime algorithm for boolean formula evaluation and relation to branching programs, interpretability between fragments of arithmetic, feasible interpretability, provability logic, open induction, Herbrand-type theorems, isomorphism between first and second order bounded arithmetics, forcing techniques in bounded arithmetic, andordinal arithmetic in L D o.Also included is an extended abstract of J.P. Ressayre's new approach concerning the model completeness of the theory of real closed expotential fields. Additional features of the book include the transcription and translation of a recently discovered 1956 letter fro Kurt Godel to J. von Neumann, asking about a polynomial time algorithm for the proof in k-symbols of predicate calculus formulas (equivalent to the P-NP question); and an open problem list consisting of seven fundamental and 39 technical questions contributed by many researchers, together with a bibliography of relevant references.This scholarly work will interest mathematical logicians, proof and recursion theorists, and researchers in computational complexity. ... Read more

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Modern Computer Arithmetic focuses on arbitrary-precision algorithms for efficiently performing arithmetic operations such as addition, multiplication and division, and their connections to topics such as modular arithmetic, greatest common divisors, the Fast Fourier Transform (FFT), and the computation of elementary and special functions. Brent and Zimmermann present algorithms that are ready to implement in your favorite language, while keeping a high-level description and avoiding too low-level or machine-dependent details. The book is intended for anyone interested in the design and implementation of efficient high-precision algorithms for computer arithmetic, and more generally efficient multiple-precision numerical algorithms. It may also be used in a graduate course in mathematics or computer science, for which exercises are included. These vary considerably in difficulty, from easy to small research projects, and expand on topics discussed in the text. Solutions are available from the authors. ... Read more

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Based on the constructivist Jean Piaget's theories on how children develop logico-mathematical thinking, this text describes and develops a programme for teaching arithmetic to young primary school children. The authors provide a theoretical foundation and an explanation of goals and objectives. ... 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

Product Description
Obtain better system performance, lower energy consumption, and avoid hand-coding arithmetic functions with this concise guide to automated optimization techniques for hardware and software design. High-level compiler optimizations and high-speed architectures for implementing FIR filters are covered, which can improve performance in communications, signal processing, computer graphics, and cryptography. Clearly explained algorithms and illustrative examples throughout make it easy to understand the techniques and write software for their implementation. Background information on the synthesis of arithmetic expressions and computer arithmetic is also included, making the book ideal for newcomers to the subject. This is an invaluable resource for researchers, professionals, and graduate students working in system level design and automation, compilers, and VLSI CAD. ... Read more

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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 (11)

Great Arithmetic Review for Adults Going Back to School ! ! !
**** 4 Stars !!! A great review of grade school Arithmetic for Adults who have been out of school for many years. I bought this book to keep me out of Remedial classes when I return to Community College, and I can say, with no reservations, that Barron's has really come through with this excellant review of Arithmetic, I originally learned 40 years ago. Buy It! Peace ;-)

More like a 3.5...
As soon as you jump into this book, it already assumes something about you; you know the material, because you've been taught it before, you've just forgotten it. And yes, this is true in my case. I bought it to brush up on my very basic math before taking the Accuplacer test (C'mon, everyone forgets how to do percentages and long division) standard at my college and it helped immensely.

So why did I rate it 3 stars?

For a few reasons... The biggest one being what I said above, it's fully confident that you've been taught this stuff so it only lightly touches on what needs to be done. The sample problems before each chapter section are sometimes incomplete and confusing. It does a good job in telling you what needs to be done but there's never any information regarding WHY it needs to be done. Because it assumes what it does, it never explains things in depth. Yeah, This isn't a book mathematical theory, but helping someone better understand why they're taking the steps they're taking when solving a problem is crucial in helping someone understand the material.

One last issue I wasn't expecting on a book like this was something most math books are notorious for, but found it to be rampant in this book. It gives you something like 2 or 3 generous examples and maybe 12+ problems to solve on each section. The thing is, it throws problems at you that weren't touched on by any of the examples. The luxury of having a tutor or teacher explain these to you aren't available to the people this book is meant for. The only fully solved problems are the chapter tests, the others just list the answers.

In the end though, with the help of this book and Schaum's Outlines of Elementary Algebra, I was able to take the Accuplacer, allowing me to skip a few semester's worth of Math Classes. And regardless of everything I've said, this is still one of the better cram books I've worked with up to this point. I would still recommend it to anyone wanting to brush up on their basic math, I'd just warn them to be cautious about it.

Excellent for teaching numeracy to ESL and ABE adult literacy students
Numeracy is a neglected part of adult literacy tutoring. It's no longer enough simply to teach people how to use words--they also need to understand basic numbers, along with financial literacy and basic computer skills. This book really starts at the beginning--a shepherd counting his sheep, one by one, making notches on a stick--a tally. And moves forward from there. I purchased 5 copies for my ESL adult students and myself, and will probably buy more in the future.

Study guide
I bought this book for my nephew. He not only found it easy to pick up and read but learned a great deal about basic math skills and tricks.

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! ... Read more

Customer Reviews (1)

Arithmetic 5 work Text Teacher Edition
Great teaching book, would be more helpful if all the problems solution explanations.Sometime had problems with explaining problems in detail, but overall was able to accomplish the task. ... Read more

Product Description
Is the continuum hypothesis still open? If we interpret it as finding the laws of cardinal arithmetic (or exponentiation, since addition and multiplication were classically solved), the hypothesis would be solved by the independence results of Gödel, Cohen, and Easton, with some isolated positive results (like Gavin-Hajnal).Most mathematicians expect that only more independence results remain to be proved.In Cardinal Arithmetic, however, Saharon Shelah offers an alternative view.By redefining the hypothesis, he gets new results for the conventional cardinal arithmetic, finds new applications, extends older methods using normal filters, and proves the existence of Jonsson algebra. Researchers in set theory and related areas of mathematical logic will want to read this provocative new approach to an important topic. ... Read more

Product Description
This scarce antiquarian book is a selection from Kessinger Publishing's Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the world's literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone! ... Read more

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The 18th century was a wealth of knowledge, exploration and rapidly growing technology and expanding record-keeping made possible by advances in the printing press. In its determination to preserve the century of revolution, Gale initiated a revolution of its own: digitization of epic proportions to preserve these invaluable works in the largest archive of its kind. Now for the first time these high-quality digital copies of original 18th century manuscripts are available in print, making them highly accessible to libraries, undergraduate students, and independent scholars.
Western literary study flows out of eighteenth-century works by Alexander Pope, Daniel Defoe, Henry Fielding, Frances Burney, Denis Diderot, Johann Gottfried Herder, Johann Wolfgang von Goethe, and others. Experience the birth of the modern novel, or compare the development of language using dictionaries and grammar discourses.
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The below data was compiled from various identification fields in the bibliographic record of this title. This data is provided as an additional tool in helping to insure edition identification:
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British Library

T084003



London : printed and sold by Henry Kent, 1760. xv,[9],168p.,plate,table : port ; 12° ... Read more

Product Description
Lessons in this book help students strengthen their foundation of fraction knowledge and focus on adding and subtracting fractions.
While the book builds on Teaching Arithmetic: Lessons for Introducing Fractions, Grades 4—5, it remains accessible and appropriate for all students who have had beginning experiences naming, comparing, and ordering fractions.

The Marilyn Burns Fraction Kit, Grades 4—6 is recommended to help implement the lessons in this book.

This book is part of the Teaching Arithmetic, Complete Series.

by Marilyn Burns
232 Pages ... Read more

Customer Reviews (1)

Marilyn Burns is My Hero!
This is a fabulous book well worth the investment.For children who have already had an introduction to fractions, this reviews some basics so that children who didn't get it the first time around have another chance, whilechildren who did get it the first time aren't bored because the ways in which basic fractions are reviewed are interesting and novel.Lots of hands-on activities and problem-solving.After one math class, my students said it was the best math lesson ever because we played games the whole time.It's easy to be a better math teacher with this book. ... Read more

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This book is divided into two parts. The first part is preliminary and consists of algebraic number theory and the theory of semisimple algebras. There are two principal topics: classification of quadratic forms and quadratic Diophantine equations. The second topic is a new framework which contains the investigation of Gauss on the sums of three squares as a special case.To make the bookconcise, the author proves some basic theorems in number theory only in some special cases. However, the book is self-contained when the base field is the rational number field, and the main theorems are statedwith an arbitrary number field as the base field. So the reader familiar with class field theory will be able to learn the arithmetic theory of quadratic forms with no further references. ... Read more

Product Description
The articles in this volume are expanded versions of lectures delivered at the Graduate Summer School and at the Mentoring Program for Women in Mathematics held at the Institute for Advanced Study/Park City Mathematics Institute. The theme of the program was arithmetic algebraic geometry. The choice of lecture topics was heavily influenced by the recent spectacular work of Wiles on modular elliptic curves and Fermat's Last Theorem. The main emphasis of the articles in the volume is on elliptic curves, Galois representations, and modular forms. One lecture series offers an introduction to these objects. The others discuss selected recent results, current research, and open problems and conjectures. The book would be a suitable text for an advanced graduate topics course in arithmetic algebraic geometry. ... Read more