Discrete Mathematics: Combinatorics, Counting, Proofs, Recurrences, Solutions
暫譯: 離散數學：組合學、計數、證明、遞迴、解法

Hower, Walter

Discrete Mathematics: Combinatorics, Counting, Proofs, Recurrences, Solutions
  • 出版商: de Gruyter
  • 出版日期: 2025-07-21
  • 售價: $1,930
  • 貴賓價: 9.5 折 $1,834
  • 語言: 英文
  • 頁數: 134
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3111206432
  • ISBN-13: 9783111206431
  • 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

Discrete Mathematics presents the material in an easily accessible manner. Beside the usual content (expanded a little bit), a special writing style is used.

We start with the natural numbers, function and relations, as well as the powerset lattice. The second chapter illustrates set theory with its laws and the Generalized Continuum Hypothesis. Chapter 3 delivers Boolean Algebra, with the double exponential formula for the # different boolean functions. The next chapter covers the induction, direct, and indirect proof. Chapter 5 presents combinatorics: Rules of sum, product, quotient, the pigeonhole principle, in/exclusion, permutation and binomial coefficient, plus Stirling numbers of 1st and 2nd kind as well as the Bell number; additionally, the recurrence relation with back- and forward reasoning is offered. We conclude with general and conditional probability, incl. the Monty Hall problem.

Discrete Mathematics presents the material in a lively fashion, including topics which are usually not presented. Providing an annex with questions and solutions it offers the chance to the readers worldwide to grasp the subject in this handy and clearly arranged treatise.

商品描述(中文翻譯)

離散數學以易於理解的方式呈現材料。除了通常的內容（稍微擴展了一些），還使用了特殊的寫作風格。

我們從自然數、函數和關係開始，以及冪集格。第二章說明了集合論及其定律和廣義連續體假設。第三章介紹布爾代數，並提供了不同布爾函數的雙指數公式。接下來的章節涵蓋了數學歸納法、直接證明和間接證明。第五章介紹組合數學：和、積、商的規則，鴿巢原理、包含/排除原則、排列和二項係數，以及第一類和第二類的斯特林數，還有貝爾數；此外，還提供了帶有回推和前推推理的遞迴關係。我們以一般和條件概率作結，包括蒙提霍爾問題。

離散數學以生動的方式呈現材料，包括通常不會介紹的主題。提供附錄，包含問題和解答，讓全球讀者有機會在這本方便且清晰安排的論文中掌握這一主題。

作者簡介

Walter Hower was born into a farming family. After Kindergarten and primary as well as secondary school he attended the high school - and enjoyed his favourite subject Mathematics. After his military period as air force NATO soldier he studied Computer Science (including the minor Economics) - with the main focus on Artificial Intelligence - at the University of Kaiserslautern, with a really heavy pillar on Mathematics (incl. Mathematik für Informatiker II [Prof. Dr. Heinz Lüneburg]). Already at that time he thought about the need or an alternative to present this difficult material - the inspiration for this book.

Under supervision of Prof. PhD Jörg Siekmann he obtained the university (master) degree "Diplom-Informatiker". Later on, he worked as research assistant under the guidance of Prof. Dr. W. Bibel and as PhD candidate in the group of Prof. Dr. Manfred Rosendahl, where he obtained the degree "Dr. rer. nat." for his doctoral thesis "On constraint satisfaction and computer-aided layout design". Immediately afterwards, Dr. Hower accepted the offer by Prof. PhD Jim Bowen to head a research group at University College Cork, National University of Ireland, where he invigorates an expert team on Constraint Processing - which finally evolved into the famous Cork Constraint Computation Centre. After a period in research labs and business companies, since more than 20 years the author now works as professor for Computer Science and Fundamentals of Mathematics; he can be reached as follows:

Albstadt-Sigmaringen University, Fakultät Informatik, Poststr. 6, D-72458 Albstadt-Ebingen, hower@hs-albsig.de.

Prof. Dr. Hower received the Teaching Prize 2006 of the state Baden-Württemberg and germany-wide the 3rd place Professor of the Year in Engineering / Computer Science in 2009.

Scientific activities include:

A Lattice-based Constraint Formalism, First Australian Knowledge Engineering Congress, Workshop on AI & Creativity, Melbourne, Australia, March 14/15, 1989;

The Relaxation of Unsolvable CSPs - General Problem Formulation and Specific Illustration in the Scheduling Domain, IJCAI-89 Workshop on Constraint Processing, Detroit, USA, August 20, 1989;

Parallel global constraint satisfaction, IJCAI-91 Workshop on Parallel Processing for Artificial Intelligence (PPAI-91), Darling Harbour, Sydney, New South Wales, Australia, August 24/25, 1991;

Notes on complexity issues within constraint satisfaction, In IJCAI-93 Workshop on Knowledge-based Production Planning, Scheduling and Control, pp. 179-186, Chambéry, Savoie, France, August 29, 1993 (co-author);

Constraint Processing - Part I/II, Department of Mathematics and Computing Science, The University of the South Pacific, Suva, Fiji, March 29/30, 1994;

On an improvement of a global algorithm for the NP-complete constraint satisfaction problem, International Computer Science Institute, Berkeley, California, USA, June 21, 1996;

Computational Complexity in Constraint-based Combinatorial Auctions, INFORMATIK 2008, 38. Jahrestagung der Gesellschaft für Informatik, München, September 8-13, 2008 (co-author);

https: //educ.ethz.ch/content/dam/ethz/special-interest/dual/educeth-dam/documents/Unterrichtsmaterialien/informatik/Recurrence%20Relations%20and%20Induction%20Proofs/educETH_WHo.pdf", Zürich, Switzerland, 2008;

Boolean Algebra and Probability Theory, EU Erasmus guest professor, Angers, France, November 2008;

Reviewer for the Engineering and Physical Sciences Research Council, UK, 1996.

His research interests are combinatorial optimization as well as cooperative and non-cooperative game theory.

A lively insight into presentations of the author (on the identical cardinality of N with just the natural even numbers as well as on the funny Monty Hall problem) could be possible - although in German - via https: //www.youtube.com/watch?v=zeCCMOHVS3w.

作者簡介(中文翻譯)

沃爾特·霍威（Walter Hower）出生於一個農民家庭。在幼稚園、小學及中學之後，他進入了高中，並享受他最喜愛的科目——數學。在服完空軍北約士兵的兵役後，他在凱瑟斯勞滕大學（University of Kaiserslautern）學習計算機科學（包括輔修經濟學），主要專注於人工智慧，並在數學方面有著非常扎實的基礎（包括計算機科學的數學 II [海因茨·呂內堡教授]）。早在那時，他就思考如何以替代的方式呈現這些困難的材料，這成為了本書的靈感來源。

在約爾格·西克曼教授（Prof. PhD Jörg Siekmann）的指導下，他獲得了大學（碩士）學位「Diplom-Informatiker」。之後，他在W·比貝爾教授（Prof. Dr. W. Bibel）的指導下擔任研究助理，並在曼弗雷德·羅森達爾教授（Prof. Dr. Manfred Rosendahl）的團隊中作為博士候選人，獲得了「Dr. rer. nat.」學位，論文題目為「關於約束滿足和計算機輔助佈局設計」。隨後，霍威博士接受了吉姆·鮑文教授（Prof. PhD Jim Bowen）的邀請，負責愛爾蘭國立大學科克大學（University College Cork）的一個研究小組，並在那裡激勵了一個專注於約束處理的專家團隊，最終發展成著名的科克約束計算中心（Cork Constraint Computation Centre）。經過一段時間在研究實驗室和商業公司的工作後，作者現在已經在計算機科學和數學基礎方面擔任教授超過20年；他的聯絡方式如下：

阿爾布施塔特-西格馬林根大學（Albstadt-Sigmaringen University），計算機科學系，郵政地址：Poststr. 6, D-72458 Albstadt-Ebingen，電子郵件：hower@hs-albsig.de。

霍威教授（Prof. Dr. Hower）於2006年獲得巴登-符騰堡州的教學獎，並在2009年獲得全德工程/計算機科學年度教授第三名。

他的科學活動包括：

基於格的約束形式主義，第一屆澳大利亞知識工程大會，人工智慧與創造力研討會，澳大利亞墨爾本，1989年3月14/15日；

不可解的約束滿足問題的放鬆——一般問題表述及在排程領域的具體說明，IJCAI-89約束處理研討會，美國底特律，1989年8月20日；

平行全局約束滿足，IJCAI-91人工智慧平行處理研討會（PPAI-91），澳大利亞新南威爾士州悉尼達令港，1991年8月24/25日；

關於約束滿足中的複雜性問題的筆記，收錄於IJCAI-93知識基礎生產計劃、排程與控制研討會，頁179-186，法國尚貝里，1993年8月29日（共同作者）；

約束處理 - 第一部分/第二部分，南太平洋大學數學與計算科學系，斐濟蘇瓦，1994年3月29/30日；

關於NP完全約束滿足問題的全局算法改進，國際計算機科學研究所，美國加州伯克利，1996年6月21日；

基於約束的組合拍賣中的計算複雜性，INFORMATIK 2008，德國計算機學會第38屆年會，慕尼黑，2008年9月8-13日（共同作者）；

https://educ.ethz.ch/content/dam/ethz/special-interest/dual/educeth-dam/documents/Unterrichtsmaterialien/informatik/Recurrence%20Relations%20and%20Induction%20Proofs/educETH_WHo.pdf，瑞士蘇黎世，2008年；

布爾代數與概率論，歐盟伊拉斯謨客座教授，法國昂熱，2008年11月；

英國工程與物理科學研究委員會的審稿人，1996年。

他的研究興趣包括組合優化以及合作與非合作博弈論。

關於作者的演講（關於N與自然偶數的相同基數以及有趣的蒙提霍爾問題）可以通過以下鏈接獲得生動的見解——雖然是德語的——https://www.youtube.com/watch?v=zeCCMOHVS3w。

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