A Computational Introduction to Number Theory and Algebra
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 > Computing and Information Technology > Computer science > Mathematical theory of computation > A Computational Introduction to Number Theory and Algebra
A Computational Introduction to Number Theory and Algebra

A Computational Introduction to Number Theory and Algebra


     0     
5
4
3
2
1



Out of Stock


Notify me when this book is in stock
X
About the Book

Number theory and algebra play an increasingly significant role in computing and communications, as evidenced by the striking applications of these subjects to such fields as cryptography and coding theory. This introductory book emphasises algorithms and applications, such as cryptography and error correcting codes, and is accessible to a broad audience. The mathematical prerequisites are minimal: nothing beyond material in a typical undergraduate course in calculus is presumed, other than some experience in doing proofs - everything else is developed from scratch. Thus the book can serve several purposes. It can be used as a reference and for self-study by readers who want to learn the mathematical foundations of modern cryptography. It is also ideal as a textbook for introductory courses in number theory and algebra, especially those geared towards computer science students.

Table of Contents:
Preface; Preliminaries; 1. Basic properties of the integers; 2. Congruences; 3. Computing with large integers; 4. Euclid's algorithm; 5. The distribution of primes; 6. Finite and discrete probability distributions; 7. Probabilistic algorithms; 8. Abelian groups; 9. Rings; 10. Probabilistic primality testing; 11. Finding generators and discrete logarithms in Zp*; 12. Quadratic residues and quadratic reciprocity; 13. Computational problems related to quadratic residues; 14. Modules and vector spaces; 15. Matrices; 16. Subexponential-time discrete logarithms and factoring; 17. More rings; 18. Polynomial arithmetic and applications; 19. Linearly generated sequences and applications; 20. Finite fields; 21. Algorithms for finite fields; 22. Deterministic primality testing; Appendix: some useful facts; Bibliography; Index of notation; Index.

About the Author :
Victor Shoup is Associate Professor at The Courant Institute of Mathematical Sciences at New York University.

Review :
"This is an outstanding and well-written book whose aim is to introduce the reader to a broad range of material -- ranging from basic to relatively advanced -- without requiring any prior knowledge on the part of the reader other than calculus and mathematical maturity. That the book succeeds at this goal is quite an accomplishment! ...this book is a must-read for anyone interested in computational number theory or algebra and especially applications of the latter to cryptography. I would not hesitate, though, to recommend this book even to students 'only' interested in the algebra itself (and not the computational aspects thereof); especially for computer science majors, this book is one of the best available introductions to that subject." SIGACT News As computer science students have very likely not previously mastered probability theory, linear algebra, or basic abstract algebra, Shoup packages crash courses in each. Despite taking time for so many basics, Shoup climaxes with careful treatment of the late-breaking, ingenious, polynomial-time deterministic primality test of Agrawal, Kayal, and Saxena. Apart from number theory, one could easily build a fine discrete mathematics course on this book. Highly recommended. Choice


Best Sellers


Product Details
  • ISBN-13: 9780521851541
  • Publisher: Cambridge University Press
  • Publisher Imprint: Cambridge University Press
  • Height: 255 mm
  • No of Pages: 534
  • Returnable: N
  • Returnable: N
  • Weight: 1217 gr
  • ISBN-10: 0521851548
  • Publisher Date: 28 Apr 2005
  • Binding: Hardback
  • Language: English
  • Returnable: N
  • Returnable: N
  • Spine Width: 40 mm
  • Width: 179 mm


Similar Products

Add Photo
Add Photo

Customer Reviews

REVIEWS      0     
Click Here To Be The First to Review this Product
A Computational Introduction to Number Theory and Algebra
Cambridge University Press -
A Computational Introduction to Number Theory and Algebra
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.

A Computational Introduction to Number Theory and Algebra

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!