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eBook The Higher Arithmetic epub

by H. Davenport

eBook The Higher Arithmetic epub
  • ISBN: 0521422272
  • Author: H. Davenport
  • Genre: Science
  • Subcategory: Mathematics
  • Language: English
  • Publisher: Cambridge University Press; 6 edition (September 25, 1992)
  • Pages: 217 pages
  • ePUB size: 1342 kb
  • FB2 size 1345 kb
  • Formats docx doc txt lit


The Higher Arithmetic. An Introduction to the Theory of Numbers

The Higher Arithmetic. An Introduction to the Theory of Numbers.

The Higher Arithmetic"'s style of writing is unstructured prose (as opposed to the roof structure) . Davenport chose NOT to write a lemma-theorem-proof kind of book, and the result is a marvelous, eminently readable introduction to the subject.

The Higher Arithmetic"'s style of writing is unstructured prose (as opposed to the roof structure), supposedly rendering the text less rigid and more "friendly", when, in fact, it accomplishes the exact opposite effect: You're never sure where a proof begins and where it ends. This compounds unnecessary intellectual and psychological strains on top of those already naturally present whenever one learns new material.

The rest of the book remains unchanged; The Higher Arithmetic introduces concepts and theorems in a way that does not require the reader to have an in-depth knowledge of the theory of numbers while touching on matters of deep mathematical significance.

Davenport/The Higher Arithmetic. 1 H. Davenport: The Higher Arithmetic: An Introduction to the Theory of Numbers. 5 Cited by. 6 Sources. H.

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late Rouse Ball Professor of Mathematics in the University of Cambridge and Fellow of Trinity College teas granted by Henry VIL in 1534, The University has printed ‘and published continuously since 1584.

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Самая большая электронная читалка рунета. Поиск книг и журналов. The higher arithmetic: An introduction to the theory of numbers (Harold Davenport). 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63. 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126.

The Higher Arithmetic. Davenport, H. Published by Hutchinson University Library, 1962. Used Condition: Good Hardcover. From WookieBooks (Houston, TX, . WookieBooks Inc. 4245 Richmond, Suite 50 Houston, Texas 77027 (888) 514-1055 Tara Grundemeier. List this Seller's Books. Payment Methods accepted by seller.

1992 Cambridge
Comments: (7)
Ubranzac
Anyone familiar with Davenport knows that he was uncommonly brilliant. He is one of the few great mathematicians of the 20th century, I believe, that could take any technical idea and explain it plainly to someone at a bus stop so that at least the essential ideas are in tact. In fact, from reading his work, I think it is apparent that he truly enjoyed setting things down in a very straightforward, clear manner and he had a gift for this.

Now, some comments are in order regarding the use of this text. It is a common trend in math textbooks to present in a theorem-proof style. So naturally students get comfortable with this and it becomes a hindrance when a book does not meet such a format. Davenport's book is not written like this, so if you require the stock format, you will be disappointed. However, the clarity of this text provides an understanding beyond what a stock treatment can if you can go beyond this artificial hurdle.

Andrew Wiles has said that when he wants to review a topic he always picks up Davenport first, then goes to Hardy and Wright. Davenport's book can almost be read like a novel it is so good and clear. But you won't find symbols marking the end of proofs or telling you where they begin. He simply explains as a great teacher would in conversation. Usually, the logical flow is clear enough where you do not need to see "Proof .... QED." Furthermore, this is not an introductory text that a researcher could find nothing of interest in. Despite being elementary of character, it has innovations in development and bears a stamp of Davenport's brilliant mind. Just to provide an example, the section on continued fractions is very original and beautifully done. There is definitely plenty of meat on the bone even for an experienced reader of number theory.
kinder
Another great addition to my library!
Phobism
I've purchased this book based on the rave reviews it's received on Amazon.com, both on this page and elsewhere. I've been greatly disappointed.

This is the eighth edition, and, as such, is low on error count, so if all you're looking for in a math textbook is that it be error-free, this may be the book for you.

If you are looking for a little more than that: say, an interesting, well-motivated and pedagogically sound lecture, you'd be better off looking for it elsewhere, for instance in Jones & Jones' superb "Elementary Number Theory".

"The Higher Arithmetic"'s style of writing is unstructured prose (as opposed to the Definition-Theorem-Proof structure), supposedly rendering the text less rigid and more "friendly", when, in fact, it accomplishes the exact opposite effect: You're never sure where a proof begins and where it ends. This compounds unnecessary intellectual and psychological strains on top of those already naturally present whenever one learns new material.

The unstructured-ness also makes this book quite useless as a work of reference.

The proofs aren't particularly elegant or insightful (in fact, they are quite difficult to follow in some cases, for no good reason).

There's very little in terms of historical background and in terms of interesting applications and recreations.

Finally, the book is uncannily devoid of that geeky sense of humor that embellishes the best of math textbooks (e.g. "in this sense, at least, the prime 2 is very odd!", Jones & Jones, 1998, p. 106).

This book can best be recommended to those who have already studied number theory, and would like a refresher of the main topics an introductory course is likely to include.

P.S.
This review is based on my impressions of the first three chapters (which constitute roughly one third of the book in terms of number of pages). I simply couldn't bear reading any further. I can't preclude the possibility that it gets better down the road.
Stonewing
This book is an AMAZING introduction to the Theory of Numbers. It assumes no previous exposure to the subject, or any technical mathematical knowledge for that matter. Its prose is lucid and the style appealing. Davenport chose NOT to write a lemma-theorem-proof kind of book, and the result is a marvelous, eminently readable introduction to the subject. Its wonderful to read a book where good prose is used to appropiately substitute a massive collection of uninviting symbols. I've also been reading other books on Number Theory, such as Hardy & Wright, but none are as clear as this one.
I found the chapter on quadratic residues (which includes the reciprocity law) to be especially well written. The section on computers and number theory is excelent as well. A concise and coherent discussion of crytography and the RSA system is included here. The organization of the book's chapters is fantastic. Each chapter builds up on results proven in the previous ones, showing well the connections between the different aspects of Number Theory. The exercises of the book range from simple to challenging, but are all accesible to someone willing to put effort into them.
This would be an excelent source for learning number theory for mathematical competition purposes, such as the ASHME, AIME, USAMO, and even for the International Mathematical Olympiad. The book contains much more than what is needed for these competitions, but the olympiad/contest reader will benefit greatly from a study of Davenport's work.
The book can certainly be used for an undergraduate course in Number Theory, though it might need supplementary materials, to cover a semester's worth of work. I know the book has been used in the past in previous editions as the main text for Math 124: Number Theory at Harvard University.
I would also recommend this book to anyone interested in acquanting themselves with Number Theory.
Awesome! There is simply no other word that describes The Higher Arithmetic.
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