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

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Cambridge Mathematics Direct provides everything needed to plan, teach and assess primary mathematics, in line with the recommendations of the National Numeracy Strategy. Each year is divided into 3 strands: Numbers and the Number System, Calculations, and Measures, Shape, Space and Handling Data.Each strand provides coverage of Problem Solving objectives. Numbers and the Numbers System 1 Teacher's Handbook provides comprehensive coverage of the Year 1 learning objectives for this strand of the Framework. It is organised into lesson plans, following the recommended structure of the daily maths lesson. These provide oral and mental starter activities, direct teaching and differentiated pupil activities, and a plenary session for short term assessment. Lessons also provide suggestions for homework, a model for classroom organisation and a full equipment list. The Handbook also provides a bank of alternative ideas for the oral and mental starter, and guidance on using the materials. ... Read more

Product Description
Cambridge Mathematics Direct is a structured set of maths resources for primary schools.It provides everything needed to plan, teach and assess primary mathematics, in line with the recommendations of the National Numeracy Strategy. Each year is divided into 3 strands: Numbers and the Number System, Calculations, and Measures, Shape, Space and Handling Data. CMD 2 Numbers and the Number System Activity Sheets provide practice in key mathematical concepts and skills.All Activity Sheets are linked to lessons in the CMD 2 Numbers Teacher's Handbook.Activities can be differentiated according to children's varying abilities and space for noting children's progress is included on individual sheets. ... Read more

Product Description
Cambridge Mathematics Direct provides everything needed to plan, teach and assess primary mathematics, in line with the recommendations of the National Numeracy Strategy. Each year is divided into 3 strands: Numbers and the Number System, Calculations, and Measures, Shape, Space and Handling Data.Each strand provides coverage of Problem Solving objectives. Numbers and the Numbers System 2 Teacher's Handbook provides comprehensive coverage of the Year 2 learning objectives for this strand of the Framework. It is organised into lesson plans, following the recommended structure of the daily maths lesson. These provide oral and mental starter activities, direct teaching and differentiated pupil activities, and a plenary session for short term assessment. Lessons also provide suggestions for homework, a model for classroom organisation and a full equipment list. The Handbook also provides a bank of alternative ideas for the oral and mental starter, and guidance on using the materials. ... Read more

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Cambridge Mathematics Direct is a structured set of maths resources for primary schools. It is linked to the Framework for Teaching Mathematics and follows the approach suggested by the National Numeracy Strategy. It provides everything that is needed to plan, teach and assess the Daily Maths Lesson in a simple and manageable way.CMD 3 Numbers and the Number System Teacher's Handbook contains lessons for children aged 7 to 8. Lessons link directly to objectives in the Framework for Teaching Mathematics and follow the approach suggested by the National Numeracy Strategy. The clearly structured lesson plans provide a manageable approach to differentiation and activities are included for children of all abilities. Oral and mental starters and plenary ideas are included for each lesson, together with questions for the teacher to ask, key words and homework suggestions. ... Read more

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This volume contains selected contributions from a very successful meeting on Number Theory and Dynamical Systems held at the University of York in 1987. There are close and surprising connections between number theory and dynamical systems. One emerged last century from the study of the stability of the solar system where problems of small divisors associated with the near resonance of planetary frequencies arose. Previously the question of the stability of the solar system was answered in more general terms by the celebrated KAM theorem, in which the relationship between near resonance (and so Diophantine approximation) and stability is of central importance. Other examples of the connections involve the work of Szemeredi and Furstenberg, and Sprindzuk. As well as containing results on the relationship between number theory and dynamical systems, the book also includes some more speculative and exploratory work which should stimulate interest in different approaches to old problems. ... Read more

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Fundamental arithmetic operations support virtually all of the engineering, scientific, and financial computations required for practical applications, from cryptography, to financial planning, to rocket science. This comprehensive reference provides researchers with the thorough understanding of number representations that is a necessary foundation for designing efficient arithmetic algorithms. Using the elementary foundations of radix number systems as a basis for arithmetic, the authors develop and compare alternative algorithms for the fundamental operations of addition, multiplication, division, and square root with precisely defined roundings. Various finite precision number systems are investigated, with the focus on comparative analysis of practically efficient algorithms for closed arithmetic operations over these systems. Each chapter begins with an introduction to its contents and ends with bibliographic notes and an extensive bibliography. The book may also be used for graduate teaching: problems and exercises are scattered throughout the text and a solutions manual is available for instructors. ... Read more

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Students explore different ways to represent numbers (with manipulatives, dot patterns, and equations); play mathematical games in which they combine and compare numbers; represent patterns with numbers and with manipulatives; work with the counting sequence up to 100; and solve a variety of addition and subtraction problems, including story problems. Suggested pacing: 37 sessions. ... Read more

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This book is one of very few which, address in detail and in-depth, how preservice teachers build important mathematical ideas. A detailed case study of important mathematical learning by five preservice elementary school teachers, who construct powerful mathematical ideas by working through a major influential construction personally. ... Read more

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Originally published in 1891.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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Customer Reviews (1)

A good history of the different notations for numbers
Counting is the point of origin of all mathematics, and it can be done in many ways. There are the trivial differences in the names of the numbers, and the more significant ones concerning the base and the notation used to abbreviate the names of the numbers. For example, the words "twenty one" are but one name for 21, which means two tens and one one. In base twenty, this would be one twenty and one one. We tend to think of the base ten as a mathematical law, but that is largely an anatomical accident. Humans have ten fingers and that is the origin of the base 10.
Depending on the circumstances, other bases are more natural than 10. For example, base 2 is more natural for computers, base 12 is more natural for some areas of commerce due to the larger number of factors and base 360 works very well for astronomical computations. Smeltzer takes us through the historical and cultural records of the different bases used by humans and when bases other than ten make more sense. It is an excellent demonstration of how humans have tightened up the notation used for numbers and the abstractions that have developed over centuries.
We use the representation of numbers and the symbols for arithmetic operations routinely and rarely realize that they developed over centuries. I believe all students of mathematics, especially those who are on track to teach elementary and middle school mathematics, should know the history of the development of these notations. This readable book is an excellent way to learn the fundamentals of number representation and how those notations developed over time. ... Read more

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“A lively new book . . . [that] readers will enjoy sprinting through.”—Jordan Ellenberg, New York Times Book ReviewWhat Lynn Truss did for grammar in Eats, Shoots & Leaves, Andrew Hodges has done for mathematics. In One to Nine, Hodges, one of Britain’s leading biographers and mathematical writers, brings numbers to three-dimensional life in this delightful and illuminating volume, filled with illustrations, which makes even the most challenging math problems accessible to the layman. Starting with the puzzle of defining unity, and ending with the recurring nines of infinite decimals, Hodges tells a story that takes in quantum physics, cosmology, climate change, and the origin of the computer. Hodges has written a classic work, at once playful but also satisfyingly instructional, which will be ideal for the math aficionado and the Sudoku addict, as well as the life of the party. 40 illustrations ... Read more

Customer Reviews (10)

Good bed time reading . . .
I have the basic education to digest this book and I'm of the same 'vintage' as the author so I can see his mind set.This book should never have made it past the editor's desk.It's a good start but it needs serious work with respect to organization etc.
It's more like the author's conversation with himself - that's it - it reads like a blog!!Except it isn't one so I cannot blast the author when he gets too full of himself or wanders hopelessly far from his premise (which is often hard to determine.)
The book is an entertaining read, though, in small chunks, as bed time reading.

It's been a long time since it took me as long to finish a book as this one is taking!

A largely unreadable random walk
I love books about math.Eli Maor's book "e": The Story of a Number (Princeton Science Library) is one of my favorite of all time on any subject.

This book by Hodges is incoherent crap, which he tries to pass off as erudite rumination.It comes across more as senile rambling that does little to offer an exploration of its supposed topic.Did this book have an editor?Did its author proofread it at all?Or did he simply type it in one sitting and send it directly to the printing press?

I was very excited to see this book on the shelf, since I thought it sounded interesting and promised to add to the relatively small selection of well-written general audience math books.How wrong I was.DO NOT WASTE YOUR TIME.

Not for the mathematically challenged
Oxford Fellow Andrew Hodges, who wrote the very well received biography, Alan Turing: The Enigma (1992), uses--rather quixotically I might say--the one to nine format to delve into the world of mathematics.His emphasis is on number theory, mathematics as applied to physics, and mathematics as applied to cryptology.The text is difficult, and the puzzles strewn throughout, whether labeled, EASY, GENTLE, TOUGH, HARD, TRICKY or DEADLY, proved mostly too difficult for this non-mathematician.

For those readers versed in number theory, that branch of mathematics in which numbers are explored purely for their own sake without even the dream of a practical application, this book is probably a delight.And for cryptologists it is probably a double delight since Hodges explores in some considerable depth the delicious irony of how pure mathematics became contaminated, as it were, when it was noticed some years ago that the encryption of messages could be facilitated by using very large numbers with unique divisors.While it is easy to multiply two even very large numbers and get a unique result it is enormously difficult to find the unique factors that make up a very large number.

At any rate that is my understanding.And if I have gotten it wrong it is only because I am not much of a mathematician.Which brings me to the central criticism of this book.To put it bluntly I don't think anyone but a mathematician can fully appreciate Andrew Hodges' text.It's that difficult.Additionally, Hodges, who is a physicist as well as a mathematician, brings string and twistor theory into the fray further multiplying the difficulties for the general reader.

But even more off-putting (and this explains some of the negative reviews this book has garnered) is the fact that the book is more than a bit self-indulgent.Hodges's political views are a bit too obvious and gratuitous (although not necessarily disagreeable).He digresses often, sometimes whimsically, sometimes unaccountably.He employs naked jargon, insider allusions, and unexplained references.His subject matter spills over and jumps around from one chapter to another making the "One to Nine" structure seem artificial what with matter pertaining to the number six, for example, appearing in the chapter on the number seven and vice-versa.

I think it's obvious that the sort of book that Hodges has written here must needs another sort of structure, perhaps in three parts, one dealing with encryption, the second with pure number theory, and the third with mathematical physics.He is following to some extent (as he acknowledges) the structure that Constance Reid used so successfully in "From Zero to Infinity" (1956, new edition 2006) in which the chapters were entitled "Zero," "One," "Two,"..."Nine," and then "e" and "Aleph Zero."It's too bad that Hodges didn't emulate Reid's reader friendly prose--and he's a good enough writer to do it--instead of her structure.

Finally I didn't like the fact that the reader has to go to a Website to get the answers to the puzzles!

Why was this published?
This may be the most disappointing book I have ever read.I enjoy math and books about math and, after reading the blurbs on the jacket, I looked forward to reading Hodges' book.However, this book seems to be just his unstructured ramblings with little effort made to actually make it interesting or readable. I took away almost nothing about math from the book; only the writer's political, religious and quasi-scientific beliefs.I gave up after a few chapters.

Waste Neither Your Time Nor Money
One To Nine: The Inner Life of Numbers

The title, One to Nine The Inner Life of Numbers, suggests a book of note.The book, though, appears to be only a mish mash of information from the author's weekly newspaper column in the Observer on mathematical topics.The author indulges himself with comments regarding politics and society and does not appear to know his audience.His text is arrogant and wanders without direction.That is a pity, because the topic should have been an interesting one.Not only is the book poorly written, the book is also poorly typeset. Word spacing is inconsistent which makes the text difficult to read.

When I completed this book, I had to ask myself why I bothered.I found this to be one of the worst books that I have read in the past 60 years.Waste neither your money nor your time on this book.
Not recommended. ... Read more

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Highly computer-oriented text, introducing numerical methods and algorithms along with the applications and conceptual tools.                                                                         Includes homework problems, suggestions for research projects, and open-ended questions at the end of each chapter.                                                                                            Written by our successful author who also wrote Continuous System Modeling, a best-selling Springer book first published in the 1991 (sold about 1500 copies).

Customer Reviews (1)

Frequency Domain Numerical Stability
This book provides an excellent description of many different integration schemes and describes their regions of stability.Understanding numerical stability is a necessity for modeling and simulation engineers.It is possible to simulate an unstable system with simulation results that appear stable.Cellier explains how and why this can happen as well as explaining other pitfalls of simulating continuous systems. ... Read more

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Monte Carlo simulation has become one of the most important tools in all fields of science. Simulation methodology relies on a good source of numbers that appear to be random. These "pseudorandom" numbers must pass statistical tests just as random samples would. Methods for producing pseudorandom numbers and transforming those numbers to simulate samples from various distributions are among the most important topics in statistical computing.

This book surveys techniques of random number generation and the use of random numbers in Monte Carlo simulation. The book covers basic principles, as well as newer methods such as parallel random number generation, nonlinear congruential generators, quasi Monte Carlo methods, and Markov chain Monte Carlo. The best methods for generating random variates from the standard distributions are presented, but also general techniques useful in more complicated models and in novel settings are described. The emphasis throughout the book is on practical methods that work well in current computing environments.

The book includes exercises and can be used as a test or supplementary text for various courses in modern statistics. It could serve as the primary test for a specialized course in statistical computing, or as a supplementary text for a course in computational statistics and other areas of modern statistics that rely on simulation. The book, which covers recent developments in the field, could also serve as a useful reference for practitioners. Although some familiarity with probability and statistics is assumed, the book is accessible to a broad audience.

The second edition is approximately 50% longer than the first edition. It includes advances in methods for parallel random number generation, universal methods for generation of nonuniform variates, perfect sampling, and software for random number generation.

Customer Reviews (4)

Just What I Ordered!!!
My purchase came very quickly and in perfect condition. Thanks so much:) I will definitely order from you guys again!

Great Reference Book !
Very useful book if you plan to use Monte Carlo methods in your work. A timely topic + a highly respected authority in the field + good writing style = a great reference book !

Not good for the beginner
Even though this book contains a lot of things,but you can not konw exactly how to do them from the book.The whole book is something like introduction and result.If you are interested at random number algorithm, this book is OK.The best book of Monte Carlo Methods for the beginner is Basics, Volume 1, Monte Carlo Methods,though this book is quite expensive.

Random number algorithms
Software developers will find this book very useful. It gives a thoroughintroduction to the types of RNGs available (linear congruential, laggedFibonacci, etc.), as well as a thorough analysis of the strengths andweaknesses of each. The math is complete, but not intimidating. Algorithmsare included for sampling from many different types of distributions (Beta,Weibull, etc.). A helpful discussion of generating independent streams ofrandom numbers (i.e., on parallel processors or machines) is included.

Also useful: a chapter on assessing the quality of RNGs, discussions ofGibbs and Latin Hypercube sampling, and bootstrapping.

This book is"non-denominational". Many MC books focus on simulation inparticular fields (such as physics). The focus here is on the science ofrandom numbers itself.

This short book has been extremely helpful in myimplementation of Monte Carlo methods. The first 40 pages are virtually adaily reference for me. Any developer needing assistance and understandingof the types of random number generators available will find this smallbook extremely helpful. ... Read more

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Discrete dynamics is the study of change.In particular, it shows how to translate real world situations into the language of mathematics.With the increase in computational ability and the recent interest in chaos, discrete dynamics has emerged as an important area of mathematical study.This text is the first to provide an elementary introduction to the world of dynamical systems. The aim of the text is to explain both the wide variety of techniques used to study dynamical systems and their many applications in areas ranging from population growth to problems in genetics.This investigation leads to the fruitful concepts of stability, strange attractors, chaos, and fractals.Very little previous mathematical knowledge is assumed and students with an elementary exposure to calculus and linear algebra will be able to follow the text easily.A large number of worked examples and exercises are provided to assist instruction. Throughout, students are encouraged to experiment with models of dynamical systems on computers and explore this fascinating area of mathematics on their own. ... Read more

Customer Reviews (1)

Excellent textbook on chaos!
Although this text lacks the brightly-colored fractals of many other works, the coverage it gives to the mathematics end of things more than makes up for it.It deals very well with the concepts of statistics and dynamic equations that are necessary for the understanding of chaos, presuming very little in the way of mathematical knowledge on the part of the reader.All definitions are clearly delineated, and the answers to the exercises are provided in the back. ... Read more