Discrete Mathematics with Applications, 5/e (Metric Edition)(Paperback)

本書序言

●Discussion of strings and graphs begins in Chapter 1 and is integrated with applications throughout the text. The handshake theorem, previously in Chapter 12, is now in Chapter 4.
●This title is now available with WebAssign, including innovative new exercise types that guide and assess students' abilities to complete proofs.
●New material was added on binary search trees, cryptographic hash functions, bound variables and scope in mathematics and computer programming, and the use of cryptography for message authentication.
●Sections on quantifier use, the concept of mathematical proof, proof-writing advice, and set theory proofs were revised and expanded based on classroom experience, and new types of exercises were added.
●The sections introducing mathematical induction were reorganized, discussion of structural induction was expanded, and additional applications of induction were provided.
●Explanations for two’s complements and for O-, Ω-, and Θ-Notations were significantly simplified.

本書特色

●Over 500 worked examples in problem-solution format guide students in building a conceptual understanding of how to solve problems. Proof solutions are intuitively developed in two steps, a discussion on how to approach the proof and a summary of the solution, allowing students the choice of faster or more deliberate instruction depending on how well they understand the problem.
●Flexible organization, allowing instructors the ability to mix core and optional topics easily to suit a wide variety of discrete math course syllabi and topic focus.
●Features, definitions, theorems, and exercise types are clearly marked and easily navigable, making the book an excellent reference that students will want to keep and continually refer back to in their later courses.
●A large number of computer science applications are included, both to motivate students and to ease their transition into more advanced computer science courses.
●Epp addresses inherent difficulties in understanding logic and language with very concrete and easy-to-conceptualize examples, an approach that helps students with a variety of backgrounds better comprehend basic mathematical reasoning, and enables them to construct sound mathematical arguments.
●More than 2500 exercises provide ample practice for students, with numerous applied problems covering an impressive array of applications.

本書序言

●本書從第一章開始討論字串和圖形，並將其與應用程序結合在整個文本中。之前在第12章的握手定理現在移到第4章。
●本書現在可與WebAssign一起使用，包括創新的新練習類型，引導和評估學生完成證明的能力。
●新增了關於二元搜索樹、加密哈希函數、數學和計算機編程中的綁定變量和作用域，以及使用加密技術進行消息驗證的內容。
●根據課堂經驗，修訂和擴充了量詞使用、數學證明概念、證明寫作建議和集合論證明的部分，並新增了新類型的練習題。
●重新組織了介紹數學歸納法的部分，擴展了結構歸納的討論，並提供了更多的歸納應用。
●對於二補數、O-、Ω-和Θ-符號的解釋大幅簡化。

本書特色

●超過500個以問題解決格式呈現的實例引導學生建立對如何解決問題的概念理解。證明解答以直觀的方式分為兩步，首先討論如何進行證明，然後總結解答，讓學生可以根據對問題的理解程度選擇更快或更仔細的指導方式。
●靈活的組織方式，使教師能夠輕鬆混合核心和選修主題，以適應各種離散數學課程大綱和主題重點。
●特徵、定義、定理和練習類型清晰標記，易於導航，使本書成為學生優秀的參考資料，他們會想要保留並在以後的課程中不斷參考。
●包含大量計算機科學應用，既能激發學生的興趣，也能幫助他們順利過渡到更高級的計算機科學課程。
●Epp通過非常具體且易於概念化的例子來解釋邏輯和語言的困難，這種方法有助於具有不同背景的學生更好地理解基本的數學推理，並使他們能夠構建合理的數學論證。
●超過2500個練習題為學生提供充足的練習，其中包括大量應用問題，涵蓋了令人印象深刻的應用領域。

1.SPEAKING MATHEMATICALLY.
2.THE LOGIC OF COMPOUND STATEMENTS.
3.THE LOGIC OF QUANTIFIED STATEMENTS.
4.ELEMENTARY NUMBER THEORY AND METHODS OF PROOF.
5.SEQUENCES, MATHEMATICAL INDUCTION, AND RECURSION.
6.SET THEORY.
7.PROPERTIES OF FUNCTIONS.
8.PROPERTIES OF RELATIONS.
9.COUNTING AND PROBABILITY.
10.THEORY OF GRAPHS AND TREES.
11.ANALYSIS ALGORITHM EFFICIENCY.
12.REGULAR EXPRESSIONS AND FINITE-STATE AUTOMATA.
Appendix A Properties of the Real Numbers
Appendix B Solutions and Hints to Selected Exercises

1. 數學口語表達。
2. 複合陳述的邏輯。
3. 量化陳述的邏輯。
4. 初等數論和證明方法。
5. 數列、數學歸納法和遞迴。
6. 集合論。
7. 函數的性質。
8. 關係的性質。
9. 計數和概率。
10. 圖和樹的理論。
11. 分析算法效率。
12. 正則表達式和有限狀態自動機。
附錄A 實數的性質。
附錄B 選擇性練習的解答和提示。