Tale of Discrete Mathematics, A: A Journey Through Logic, Reasoning, Structures and Graph Theory
Khoury, Joseph
- 出版商: World Scientific Pub
- 出版日期: 2024-04-09
- 售價: $5,880
- 貴賓價: 9.5 折 $5,586
- 語言: 英文
- 頁數: 820
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 9811285780
- ISBN-13: 9789811285783
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商品描述
Topics covered in Discrete Mathematics have become essential tools in many areas of studies in recent years. This is primarily due to the revolution in technology, communications, and cyber security. The book treats major themes in a typical introductory modern Discrete Mathematics course: Propositional and predicate logic, proof techniques, set theory (including Boolean algebra, functions and relations), introduction to number theory, combinatorics and graph theory.An accessible, precise, and comprehensive approach is adopted in the treatment of each topic. The ability of abstract thinking and the art of writing valid arguments are emphasized through detailed proof of (almost) every result. Developing the ability to think abstractly and roguishly is key in any areas of science, information technology and engineering. Every result presented in the book is followed by examples and applications to consolidate its comprehension. The hope is that the reader ends up developing both the abstract reasoning as well as acquiring practical skills.All efforts are made to write the book at a level accessible to first-year students and to present each topic in a way that facilitates self-directed learning. Each chapter starts with basic concepts of the subject at hand and progresses gradually to cover more ground on the subject. Chapters are divided into sections and subsections to facilitate readings. Each section ends with its own carefully chosen set of practice exercises to reenforce comprehension and to challenge and stimulate readers.As an introduction to Discrete Mathematics, the book is written with the smallest set of prerequisites possible. Familiarity with basic mathematical concepts (usually acquired in high school) is sufficient for most chapters. However, some mathematical maturity comes in handy to grasp some harder concepts presented in the book.
商品描述(中文翻譯)
離散數學所涵蓋的主題在近年來已成為許多研究領域的重要工具。這主要是由於科技、通訊和網路安全的革命。這本書探討了典型的現代離散數學入門課程中的主要主題:命題邏輯和謂詞邏輯、證明技術、集合論(包括布林代數、函數和關係)、數論入門、組合數學和圖論。每個主題的處理採用可接近、精確且全面的方法。透過對(幾乎)每個結果的詳細證明,強調抽象思維的能力和撰寫有效論證的藝術。發展抽象思考和靈活應變的能力是科學、資訊科技和工程領域的關鍵。本書中每個結果後面都附有例子和應用,以鞏固理解。希望讀者能夠同時發展抽象推理能力和獲得實用技能。
本書努力以適合一年級學生的水平撰寫,並以促進自我導向學習的方式呈現每個主題。每章從該主題的基本概念開始,逐步深入以涵蓋更多內容。章節被劃分為小節,以便於閱讀。每個小節結尾都有精心挑選的練習題,以加強理解並挑戰和激勵讀者。
作為離散數學的入門書籍,本書以最少的先備知識為前提撰寫。對基本數學概念的熟悉(通常在高中時期獲得)對於大多數章節來說已足夠。然而,某些數學成熟度對於理解書中提出的一些較難概念是有幫助的。