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| fixed length control field |
nam a22 4500 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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231129b xxu||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9783030081300 |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
510 |
| Item number |
GRI |
| 100 ## - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Grigorieva, Ellina |
| 245 ## - TITLE STATEMENT |
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| Title |
Methods of Solving Number Theory Problems |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Name of publisher, distributor, etc |
Birkhauser, |
| Date of publication, distribution, etc |
2018 |
| Place of publication, distribution, etc |
Cham : |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
xxi, 391 p. ; |
| Other physical details |
ill., |
| Dimensions |
23 cm |
| 365 ## - TRADE PRICE |
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| Price amount |
49.99 |
| Price type code |
EUR |
| Unit of pricing |
91.70 |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes index. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc |
Through its engaging and unusual problems, this book demonstrates methods of reasoning necessary for learning number theory. Every technique is followed by problems (as well as detailed hints and solutions) that apply theorems immediately, so readers can solve a variety of abstract problems in a systematic, creative manner. New solutions often require the ingenious use of earlier mathematical concepts - not the memorization of formulas and facts. Questions also often permit experimental numeric validation or visual interpretation to encourage the combined use of deductive and intuitive thinking. The first chapter of the book covers topics like even and odd numbers, divisibility, prime, perfect, figurate numbers, and introduces congruence. The next chapter works with representations of natural numbers in different bases, as well as the theory of continued fractions, quadratic irrationalities, and also explores different methods of proofs. The third chapter is dedicated to solving unusual factorial and exponential equations, Diophantine equations, introduces Pell's equations and how they connect algebra and geometry. Chapter 4 reviews Pythagorean triples and their relation to algebraic geometry, representation of a number as the sum of squares or cubes of other numbers, quadratic residuals, and interesting word problems. Appendices provide a historic overview of number theory and its main developments from ancient cultures to the modern day. Drawing from cases collected by an accomplished female mathematician, Methods in Solving Number Theory Problems is designed as a self-study guide or supplementary textbook for a one-semester course in introductory number theory. It can also be used to prepare for mathematical Olympiads. Elementary algebra, arithmetic and some calculus knowledge are the only prerequisites. Number theory gives precise proofs and theorems of an irreproachable rigor and sharpens analytical thinking, which makes this book perfect for anyone looking to build their mathematical confidence. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Pythagorean triples |
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Pell’s equation |
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| Topical term or geographic name as entry element |
Legendre symbol |
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| Topical term or geographic name as entry element |
Jacobi symbol |
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| Topical term or geographic name as entry element |
Fermat’s Little Theorem |
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| Topical term or geographic name as entry element |
Diophantine equations |
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| Topical term or geographic name as entry element |
Catalan number |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
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| Item type |
Books |