Effective Theories in Programming Practice

Set theory, logic, discrete mathematics, and fundamental algorithms (along with their correctness and complexity analysis) will always remain useful for computing professionals and need to be understood by students who want to succeed. This textbook explains a number of those fundamental algorithms to programming students in a concise, yet precise, manner. The book includes the background material needed to understand the explanations and to develop such explanations for other algorithms. The author demonstrates that clarity and simplicity are achieved not by avoiding formalism, but by using it properly.

The book is self-contained, assuming only a background in high school mathematics and elementary program writing skills. It does not assume familiarity with any specific programming language. Starting with basic concepts of sets, functions, relations, logic, and proof techniques including induction, the necessary mathematical framework for reasoning about the correctness, termination and efficiency of programs is introduced with examples at each stage. The book contains the systematic development, from appropriate theories, of a variety of fundamental algorithms related to search, sorting, matching, graph-related problems, recursive programming methodology and dynamic programming techniques, culminating in parallel recursive structures.

集合論、邏輯、離散數學和基礎演算法（以及它們的正確性和複雜性分析）對於計算專業人士來說始終是有用的，並且需要學生們理解這些概念才能成功。本教科書以簡潔而精確的方式向程式設計學生解釋了一些基礎演算法。該書包含了理解這些解釋以及為其他演算法開發解釋所需的背景材料。作者證明了清晰和簡潔不是通過避免形式主義來實現的，而是通過正確使用形式主義來實現的。

本書是自成體系的，只需具備高中數學和基礎程式撰寫技能即可。它不假設讀者熟悉任何特定的程式語言。從集合、函數、關係、邏輯和證明技巧（包括歸納法）的基本概念開始，逐步介紹了關於程式正確性、終止性和效率的數學框架，並提供了每個階段的示例。本書從相關理論中系統地發展了各種與搜索、排序、匹配、圖形相關問題、遞迴程式設計方法和動態規劃技巧相關的基礎演算法，最終達到並行遞迴結構的高潮。