Methods of solving number theory problems / (Record no. 66237)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 03187nam a22001817a 4500 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 210305b2010 ||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9783319909141 |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 512.7 GRI-E |
| 100 ## - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Grigorieva, Ellina |
| 245 ## - TITLE STATEMENT | |
| Title | Methods of solving number theory problems / |
| Statement of responsibility, etc. | Ellina Grigorieva |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication, distribution, etc. | Switzerland |
| Name of publisher, distributor, etc. | Springer International Publishing |
| Date of publication, distribution, etc. | 2010 |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 391 p. |
| 500 ## - GENERAL NOTE | |
| General note | 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. <br/><br/>The first chapter starts with simple topics like even and odd numbers, divisibility, and prime numbers and helps the reader to solve quite complex, Olympiad-type problems right away. It also covers properties of the perfect, amicable, and figurate numbers and introduces congruence. The next chapter begins with the Euclidean algorithm, explores the representations of integer numbers in different bases, and examines continued fractions, quadratic irrationalities, and the Lagrange Theorem. The last section of Chapter Two is an exploration of different methods of proofs. The third chapter is dedicated to solving Diophantine linear and nonlinear equations and includes different methods of solving Fermat’s (Pell’s) equations. It also covers Fermat’s factorization techniques and methods of solving challenging problems involving exponent and factorials. Chapter Four reviews the Pythagorean triple and quadruple and emphasizes their connection with geometry, trigonometry, algebraic geometry, and stereographic projection. A special case of Waring’s problem as a representation of a number by the sum of the squares or cubes of other numbers is covered, as well as quadratic residuals, Legendre and Jacobi symbols, and interesting word problems related to the properties of numbers. Appendices provide a historic overview of number theory and its main developments from the ancient cultures in Greece, Babylon, and Egypt to the modern day. <br/><br/>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 | |
| Topical term or geographic name as entry element | Number theory |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Logic, Symbolic and mathematical |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Mathematics |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Mathematics--Study and teaching |
| 952 ## - LOCATION AND ITEM INFORMATION (KOHA) | |
| Withdrawn status | |
| Lost status | Source of classification or shelving scheme | Damaged status | Not for loan | Collection code | Home library | Current library | Shelving location | Date acquired | Total Checkouts | Full call number | Barcode | Checked out | Date last seen | Date last checked out | Price effective from | Koha item type |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Dewey Decimal Classification | 510 | BITS Pilani Hyderabad | BITS Pilani Hyderabad | General Stack (For lending) | 05/03/2021 | 3 | 512.7 GRI-E | 41851 | 27/10/2022 | 13/10/2022 | 13/10/2022 | 05/03/2021 | Books |
