Essential Discrete Mathematics for Computer Science

Todd Feil, Joan Krone

  • 出版商: Prentice Hall
  • 出版日期: 2002-11-24
  • 售價: $532
  • 語言: 英文
  • 頁數: 216
  • 裝訂: Paperback
  • ISBN: 0130186619
  • ISBN-13: 9780130186614
  • 相關分類: Computer-Science
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商品描述

For freshman/sophomore one-semester introductory courses in discrete math that include intermediate programming for computer science and mathematics students.

This brief introduction to the mathematics of computer science prepares students for the math they will encounter in later courses. With applications that are specific to computer science, this text helps students develop reasoning skills and provides them with an early introduction to fundamental mathematics necessary for future math and computer science courses.

Table of Contents

0. Notes on Proofs.

Propositional Logic. Implication. Direct Proof. The Contrapositive. Proof by Contradiction. If And Only If.


1. Sets.

What Are Sets? New Sets from Old. Properties of Sets. A Paradox. Large Collection of Sets.


2. Functions and Relations.

Exponential and Log Functions. Floor and Ceiling Functions. Relations.


3. Boolean Algebra.

Propositional Logic. Sets. Boolean Algebras. Some Boolean Algebra Theorems. Switching Circuits. Storing Numbers in a Digital Computer. Circuitry to Add.


4. Natural Numbers and Induction.

Well-ordering and Mathematical Induction. Well-ordering Implies Mathematical Induction. The Peano Axioms.


5. Number Theory.

The Division Theorem. Greatest Common Divisors. Primes. Modular Arithmetic. A Cryptological Example. Modular Multiplication and Division. More Cryptology. Fermat's Little Theorem. Fast Exponentiation. Euler's Theorem. RSA Encryption.


6. Recursion.

Binary Search. Euclid's Algorithm. Tower of Hanoi.


7. Solving Recurrences.
8. Counting.

The Rules of Sum and Product. Permutations. Combinations. Calculation Considerations. The Binomial Theorem. Applications of Counting to Probability.


9. Matrices.

Matrix Operations. Systems of Equations. The Determinant. Gaussian Elimination. Computing Multiplicative Inverses. Encryption Revisited.


10. Graphs.

Euler Circuits and Tours. Symbols and Terms for Graphs. A Return to Euler Circuits. Minimal Spanning Tree. Some Programming Considerations.


Solutions.
Index.

商品描述(中文翻譯)

適用於計算機科學和數學學生的新生/二年級一學期離散數學入門課程的簡要介紹。這本關於計算機科學數學的簡介為學生們在後續課程中遇到的數學做好準備。這本教材具有特定於計算機科學的應用,幫助學生發展推理能力,並提供他們對未來數學和計算機科學課程所需的基礎數學的早期介紹。

目錄
0. 關於證明的注意事項。
命題邏輯。蘊含。直接證明。反命題。反證法。當且僅當。
1. 集合。
什麼是集合?從舊集合中創建新集合。集合的性質。一個悖論。大量的集合。
2. 函數和關係。
指數和對數函數。地板和天花板函數。關係。
3. 布爾代數。
命題邏輯。集合。布爾代數。一些布爾代數定理。開關電路。在數字計算機中存儲數字。加法電路。
4. 自然數和歸納法。
良序性和數學歸納法。良序性意味著數學歸納法。皮亞諾公理。
5. 數論。
除法定理。最大公因數。質數。模算術。一個密碼學的例子。模乘法和除法。更多密碼學。費馬小定理。快速冪運算。歐拉定理。RSA加密。
6. 遞迴。
二分搜索。歐幾里得算法。漢諾塔。
7. 解遞迴式。
8. 計數。
求和和乘積的規則。排列。組合。計算注意事項。二項定理。計數應用於概率。
9. 矩陣。
矩陣運算。方程組。行列式。高斯消去法。計算乘法逆元。重新加密。
10. 圖。
歐拉迴路和遊歷。圖的符號和術語。再回到歐拉迴路。最小生成樹。一些編程注意事項。

解答。
索引。