Essential Discrete Mathematics for Computer Science
暫譯: 計算機科學的基本離散數學

Todd Feil, Joan Krone

Essential Discrete Mathematics for Computer Science
  • 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

    • 下單後立即進貨 (約5~7天)

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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)

對於大一/大二的單學期離散數學入門課程，包含計算機科學和數學學生的中級程式設計。

這本簡短的計算機科學數學入門書籍為學生準備了他們在後續課程中將遇到的數學。透過與計算機科學相關的應用，本書幫助學生發展推理能力，並為他們提供必要的基礎數學早期介紹，以便未來的數學和計算機科學課程。

目錄

0. 證明的注意事項。
命題邏輯。蘊涵。直接證明。對偶命題。反證法。當且僅當。

1. 集合。
什麼是集合？從舊集合生成新集合。集合的性質。一個悖論。大量集合的集合。

2. 函數和關係。
指數和對數函數。下取整和上取整函數。關係。

3. 布林代數。
命題邏輯。集合。布林代數。一些布林代數定理。開關電路。在數位計算機中儲存數字。加法電路。

4. 自然數和數學歸納法。
良序性和數學歸納法。良序性暗示數學歸納法。佩亞諾公理。

5. 數論。
除法定理。最大公因數。質數。模運算。一個密碼學範例。模乘法和模除法。更多密碼學。費馬小定理。快速指數運算。歐拉定理。RSA加密。

6. 遞歸。
二分搜尋。歐幾里得算法。漢諾塔。

7. 解遞歸。
8. 計數。
和與積的法則。排列。組合。計算考量。二項式定理。計數在概率中的應用。

9. 矩陣。
矩陣運算。方程組。行列式。高斯消去法。計算乘法逆元。重新探討加密。

10. 圖。
歐拉回路和巡迴。圖的符號和術語。回到歐拉回路。最小生成樹。一些程式設計考量。

解答。
索引。

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