17 Lectures on Fermat Numbers
Book 1
Book 2
Book 3
Book 1
Book 2
Book 3
Book 1
Book 2
Book 3
Book 1
Book 2
Book 3
Home > Mathematics and Science Textbooks > Mathematics > Number theory > 17 Lectures on Fermat Numbers: From Number Theory to Geometry(CMS Books in Mathematics)
17 Lectures on Fermat Numbers: From Number Theory to Geometry(CMS Books in Mathematics)

17 Lectures on Fermat Numbers: From Number Theory to Geometry(CMS Books in Mathematics)


     0     
5
4
3
2
1



Available


X
About the Book

French mathematician Pierre de Fermat became most well known for his pioneering work in the area of number theory. His work with numbers has been attracting the attention of amateur and professional mathematicians for over 350 years. This book was written in honor of the 400th anniversary of his birth and is based on a series of lectures given by the authors. The purpose of this book is to provide readers with an overview of the many properties of Fermat numbers and to demonstrate their numerous appearances and applications in areas such as number theory, probability theory, geometry, and signal processing. This book introduces a general mathematical audience to basic mathematical ideas and algebraic methods connected with the Fermat numbers and will provide invaluable reading for the amateur and professional alike.

Table of Contents:
1. Introduction.- 2. Fundamentals of Number Theory.- 3. Basic Properties of Fermat Numbers.- 4. The Most Beautiful Theorems on Fermat Numbers.- 5. Primality of Fermat Numbers.- 6. Divisibility of Fermat Numbers.- 7. Factors of Fermat Numbers.- 8. Connection of Fermat Numbers with Pascal’s Triangle.- 9. Miscellaneous Results.- 10. The Irrationality of the Sum of Some Reciprocals.- 11. Fermat Primes and a Diophantine Equation.- 12. Fermat’s Little Theorem, Pseudoprimes, and Superpseudoprimes.- 13. Generalizations of Fermat Numbers.- 14. Open Problems.- 15. Fermat Number Transform and Other Applications.- 16. The Proof of Gauss’s Theorem.- 17. Euclidean Construction of the Regular Heptadecagon.- A. Tables of Fermat Numbers and Their Prime Factors.- B. Mersenne Numbers.- C. Remembrance of Pierre de Fermat.- References.- Web Site Sources.- Name Index.

Review :
From the reviews: CANADIAN MATHEMATICAL SOCIETY NOTES "It is certainly satisfying for the reader to have almost everything that is known on a particular subject collected in one place. Also, it contributes to a sense of mathematics as a unified subject to see several different areas enter, often in unexpected ways…I can…recommend it to number-theorists and other mathematicians alike; everybody will find useful and interesting information in it. In the classroom, this book might be suitable for undergraduate projects or supplementary readings in a number theory, algebra, or history of mathematics course. It will also be accessible to bright high school students and interested amateurs. In fact, Fermat’s name in the title may attract such readers, and they will find a well written, interesting, and mathematically sound book…"   M. Krizek; F. L. Luca; and L. Somer 17 Lectures on Fermat Numbers From Number Theory to Geometry "The authors have brought together a wealth of material involving the Fermat numbers . . . amateurs and high-school students should also be able to profitably read this well-written book."—MATHEMATICAL REVIEWS "This admirable book contains what must be everything that is worth knowing about Fermat numbers. … It contains a wealth of fascinating results … . The Foreword, by Alena Šolcová, is an excellent account of Fermat’s life and works. … The authors, and the series editors, Jonathan and Peter Borwein, deserve credit and praise for producing what will be the definitive work on the subject for many years to come." (Dudley Underwood, Math DL, May, 2005) "This book was written in celebration of the 400th anniversary of the birth of Pierre de Fermat … . The clear writing style and the evident enthusiasm of the authors make this book a pleasure to read or to dip into. It is not a text book, but might well inspirestudents at any levels, and it succeeds in making what is potentially a dry and abstract topic fresh and full of connections. It would be a valuable addition to any library." (Alison Wolff, The Australian Mathematical Society Gazette, Vol. 31 (3), 2004) "The book is very interesting and well written – an enjoyable and very thorough collection of all the knowledge on Fermat numbers that have been accumulated during the centuries. … Those who are interested in the history of mathematics will find answers for many questions concerning the history of Fermat numbers. This is an excellent book that can be recommended to all those interested in Fermat numbers or generally in number theory." (László Megyesi, Acta Scientiarium Mathematicarum, Vol. 69, 2003) "In this book the authors have brought together a wealth of material involving the Fermat numbers … . amateurs and high-school students should also be able to profitably read this well-written book. … It has 71 illustrations in total, an extensive list of references and a good subject and name index." (Pieter Moree, Mathematical Reviews, 2002 i) "It is certainly satisfying for the reader to have almost everything that is known on a particular subject collected in one place. … The bibliography, with more than 350 entries, is very complete and contributes to the value of the book as reference, as do the extensive name and subject indexes. … I can … recommend it to number-theorists and other mathematicians alike; everybody will find useful and interesting information in it. … a well written, interesting, and mathematically sound book … ." (CMS Notes, Vol. 34 (8), 2002) "Pierre de Fermat was born just over four hundred years ago, and this book is in part a celebration of his quatercentenary. … A pleasing feature of the exposition is that as many results as possible are illustrated pictorially. … The text is copiously illustrated with both photographs and excellentdiagrams, and I can recommend the book as a whole to anyone who wants to venture into this treasure-trove of somewhat arcane number theory." (Gerry Leversha, The Mathematical Gazette, Vol. 87 (509), 2003) "The purpose of this book is to provide readers with an overview of the many properties of Fermat numbers and to demonstrate their numerous appearances and applications … . This book introduces a general mathematical audience to basic mathematical ideas and algebraic methods connected with the Fermat numbers and provides invaluable reading for amateurs and professionals alike." (L’Enseignement Mathématique, Vol. 48 (1-2), 2002)


Best Sellers


Product Details
  • ISBN-13: 9780387953328
  • Publisher: Springer-Verlag New York Inc.
  • Publisher Imprint: Springer-Verlag New York Inc.
  • Height: 235 mm
  • No of Pages: 257
  • Returnable: Y
  • Sub Title: From Number Theory to Geometry
  • ISBN-10: 0387953329
  • Publisher Date: 08 Jan 2002
  • Binding: Hardback
  • Language: English
  • Returnable: Y
  • Series Title: CMS Books in Mathematics
  • Width: 155 mm


Similar Products

Add Photo
Add Photo

Customer Reviews

REVIEWS      0     
Click Here To Be The First to Review this Product
17 Lectures on Fermat Numbers: From Number Theory to Geometry(CMS Books in Mathematics)
Springer-Verlag New York Inc. -
17 Lectures on Fermat Numbers: From Number Theory to Geometry(CMS Books in Mathematics)
Writing guidlines
We want to publish your review, so please:
  • keep your review on the product. Review's that defame author's character will be rejected.
  • Keep your review focused on the product.
  • Avoid writing about customer service. contact us instead if you have issue requiring immediate attention.
  • Refrain from mentioning competitors or the specific price you paid for the product.
  • Do not include any personally identifiable information, such as full names.

17 Lectures on Fermat Numbers: From Number Theory to Geometry(CMS Books in Mathematics)

Required fields are marked with *

Review Title*
Review
    Add Photo Add up to 6 photos
    Would you recommend this product to a friend?
    Tag this Book Read more
    Does your review contain spoilers?
    What type of reader best describes you?
    I agree to the terms & conditions
    You may receive emails regarding this submission. Any emails will include the ability to opt-out of future communications.

    CUSTOMER RATINGS AND REVIEWS AND QUESTIONS AND ANSWERS TERMS OF USE

    These Terms of Use govern your conduct associated with the Customer Ratings and Reviews and/or Questions and Answers service offered by Bookswagon (the "CRR Service").


    By submitting any content to Bookswagon, you guarantee that:
    • You are the sole author and owner of the intellectual property rights in the content;
    • All "moral rights" that you may have in such content have been voluntarily waived by you;
    • All content that you post is accurate;
    • You are at least 13 years old;
    • Use of the content you supply does not violate these Terms of Use and will not cause injury to any person or entity.
    You further agree that you may not submit any content:
    • That is known by you to be false, inaccurate or misleading;
    • That infringes any third party's copyright, patent, trademark, trade secret or other proprietary rights or rights of publicity or privacy;
    • That violates any law, statute, ordinance or regulation (including, but not limited to, those governing, consumer protection, unfair competition, anti-discrimination or false advertising);
    • That is, or may reasonably be considered to be, defamatory, libelous, hateful, racially or religiously biased or offensive, unlawfully threatening or unlawfully harassing to any individual, partnership or corporation;
    • For which you were compensated or granted any consideration by any unapproved third party;
    • That includes any information that references other websites, addresses, email addresses, contact information or phone numbers;
    • That contains any computer viruses, worms or other potentially damaging computer programs or files.
    You agree to indemnify and hold Bookswagon (and its officers, directors, agents, subsidiaries, joint ventures, employees and third-party service providers, including but not limited to Bazaarvoice, Inc.), harmless from all claims, demands, and damages (actual and consequential) of every kind and nature, known and unknown including reasonable attorneys' fees, arising out of a breach of your representations and warranties set forth above, or your violation of any law or the rights of a third party.


    For any content that you submit, you grant Bookswagon a perpetual, irrevocable, royalty-free, transferable right and license to use, copy, modify, delete in its entirety, adapt, publish, translate, create derivative works from and/or sell, transfer, and/or distribute such content and/or incorporate such content into any form, medium or technology throughout the world without compensation to you. Additionally,  Bookswagon may transfer or share any personal information that you submit with its third-party service providers, including but not limited to Bazaarvoice, Inc. in accordance with  Privacy Policy


    All content that you submit may be used at Bookswagon's sole discretion. Bookswagon reserves the right to change, condense, withhold publication, remove or delete any content on Bookswagon's website that Bookswagon deems, in its sole discretion, to violate the content guidelines or any other provision of these Terms of Use.  Bookswagon does not guarantee that you will have any recourse through Bookswagon to edit or delete any content you have submitted. Ratings and written comments are generally posted within two to four business days. However, Bookswagon reserves the right to remove or to refuse to post any submission to the extent authorized by law. You acknowledge that you, not Bookswagon, are responsible for the contents of your submission. None of the content that you submit shall be subject to any obligation of confidence on the part of Bookswagon, its agents, subsidiaries, affiliates, partners or third party service providers (including but not limited to Bazaarvoice, Inc.)and their respective directors, officers and employees.

    Accept

    Fresh on the Shelf


    Inspired by your browsing history


    Your review has been submitted!

    You've already reviewed this product!