Number Theory: Multiplicative and Additive with Factorization and Primality Testing
暫譯: 數論：乘法與加法，包含因式分解與質數測試
Schumer, Peter D.
- 出版商: de Gruyter
- 出版日期: 2025-08-18
- 售價: $3,340
- 貴賓價: 9.5 折 $3,173
- 語言: 英文
- 頁數: 364
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3111578674
- ISBN-13: 9783111578675
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相關分類:
離散數學 Discrete-mathematics
海外代購書籍(需單獨結帳)
相關主題
商品描述
This is a book for an undergraduate number theory course, senior thesis work, graduate level study, or for those wishing to learn about applications of number theory to data encryption and security. With no abstract algebra background required, it covers congruences, the Euclidean algorithm, linear Diophantine equations, the Chinese Remainder Theorem, Mobius inversion formula, Pythagorean triplets, perfect numbers and amicable pairs, Law of Quadratic Reciprocity, theorems on sums of squares, Farey fractions, periodic continued fractions, best rational approximations, and Pell's equation. Results are applied to factoring and primality testing including those for Mersenne and Fermat primes, probabilistic primality tests, Pollard's rho and p-1 factorization algorithms, and others. Also an introduction to cryptology with a full discussion of the RSA algorithm, discrete logarithms, and digital signatures.
Chapters on analytic number theory including the Riemann zeta function, average orders of the lattice and divisor functions, Chebyshev's theorems, and Bertrand's Postulate. A chapter introduces additive number theory with discussion of Waring's Problem, the pentagonal number theorem for partitions, and Schnirelmann density.
商品描述(中文翻譯)
這是一本針對本科生數論課程、高年級論文研究、研究生階段學習，或希望了解數論在數據加密和安全性應用的讀者所編寫的書籍。該書不需要抽象代數背景，涵蓋了同餘、歐幾里得算法、線性迪奧範廷方程、中國餘數定理、莫比烏斯反演公式、畢氏三元組、完全數和友好數對、二次互反律、平方和定理、法雷分數、周期連分數、最佳有理近似以及佩爾方程。結果應用於因式分解和質數測試，包括梅森質數和費馬質數的測試、隨機質數測試、波拉德的 rho 和 p-1 因式分解算法等。此外，還介紹了密碼學，全面討論 RSA 算法、離散對數和數位簽名。
本書還包括分析數論的章節，內容涵蓋黎曼 ζ 函數、格子和除數函數的平均階、切比雪夫定理以及伯特蘭猜想。還有一章介紹加法數論，討論了瓦林問題、分割的五邊形數定理和施尼雷爾曼密度。
作者簡介
Peter D. Schumer is the John C. Baldwin Professor of Mathematics and Natural Philosophy at Middlebury College. He received his B.S and M.S. degrees from Rensselaer Polytechnic Institute and his Ph.D. from University of Maryland. He has held research and teaching positions at UC Berkeley, Stanford, UC San Diego, San Jose State U, and at Doshisha U, Keio U, and ICU in Japan. His main areas of interest are number theory and the history of mathematics. His courses vary from calculus, linear algebra, and the mathematics of games and puzzles to combinatorics, complex analysis, and advanced number theory. He has directed more than fifty senior projects and theses in related areas. His scholarly work has appeared in Mathematika, Journal of Number Theory, Math Horizons, College Mathematics Journal, and elsewhere. He has published two books, Introduction to Number Theory (PWS, 1996) and Mathematical Journeys (Wiley, 2004). His book Fractions - A Sliver of the Story will be release this year (OUP, 2024). He has also written articles for general audiences on when humans first began to count and the origins of the letter x in algebra. He is a recipient of the Trevor Evans Award from the MAA on an article about the mathematician Paul Erdos (2000). He also teaches courses on the game of go and its cultural significance and has been awarded the national Teacher of the Year award from the American Go Association (2021).
作者簡介(中文翻譯)
彼得·D·舒默（Peter D. Schumer）是米德爾伯里學院（Middlebury College）約翰·C·鮑德溫（John C. Baldwin）數學與自然哲學教授。他在倫斯勒理工學院（Rensselaer Polytechnic Institute）獲得學士和碩士學位，並在馬里蘭大學（University of Maryland）獲得博士學位。他曾在加州大學伯克利分校（UC Berkeley）、史丹佛大學（Stanford）、加州大學聖地牙哥分校（UC San Diego）、聖荷西州立大學（San Jose State U）以及日本的同志社大學（Doshisha U）、慶應義塾大學（Keio U）和國際基督教大學（ICU）擔任研究和教學職位。他的主要研究領域包括數論和數學史。他的課程涵蓋微積分、線性代數、遊戲與謎題的數學、組合數學、複變分析和高級數論等。他指導了五十多個相關領域的高年級專案和論文。他的學術作品發表於《Mathematika》、《Journal of Number Theory》、《Math Horizons》、《College Mathematics Journal》等期刊。他出版了兩本書，分別是《數論導論》（Introduction to Number Theory，PWS，1996）和《數學之旅》（Mathematical Journeys，Wiley，2004）。他的書《分數 - 故事的一小部分》（Fractions - A Sliver of the Story）將於今年出版（OUP，2024）。他還為一般讀者撰寫了有關人類何時開始計數以及代數中字母x的起源的文章。他因撰寫有關數學家保羅·厄爾德什（Paul Erdos）的文章而獲得MAA的特雷弗·埃文斯獎（Trevor Evans Award，2000）。他還教授圍棋及其文化意義的課程，並於2021年獲得美國圍棋協會（American Go Association）頒發的全國年度教師獎。
