Combinatorial and Algorithmic Mathematics: From Foundation to Optimization (組合與演算法數學:從基礎到優化)

Alzalg, Baha

  • 出版商: Wiley
  • 出版日期: 2024-07-29
  • 售價: $3,940
  • 貴賓價: 9.5$3,743
  • 語言: 英文
  • 頁數: 528
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 1394235941
  • ISBN-13: 9781394235940
  • 相關分類: Algorithms-data-structures
  • 海外代購書籍(需單獨結帳)

相關主題

商品描述

Detailed review of optimization from first principles, supported by rigorous math and computer science explanations and various learning aids

Supported by rigorous math and computer science foundations, Combinatorial and Algorithmic Mathematics: From Foundation to Optimization provides a from-scratch understanding to the field of optimization, discussing 70 algorithms with roughly 220 illustrative examples, 160 nontrivial end-of-chapter exercises with complete solutions to ensure readers can apply appropriate theories, principles, and concepts when required, and Matlab codes that solve some specific problems. This book helps readers to develop mathematical maturity, including skills such as handling increasingly abstract ideas, recognizing mathematical patterns, and generalizing from specific examples to broad concepts.

Starting from first principles of mathematical logic, set-theoretic structures, and analytic and algebraic structures, this book covers both combinatorics and algorithms in separate sections, then brings the material together in a final section on optimization. This book focuses on topics essential for anyone wanting to develop and apply their understanding of optimization to areas such as data structures, algorithms, artificial intelligence, machine learning, data science, computer systems, networks, and computer security.

Combinatorial and Algorithmic Mathematics includes discussion on:

  • Propositional logic and predicate logic, set-theoretic structures such as sets, relations, and functions, and basic analytic and algebraic structures such as sequences, series, subspaces, convex structures, and polyhedra
  • Recurrence-solving techniques, counting methods, permutations, combinations, arrangements of objects and sets, and graph basics and properties
  • Asymptotic notations, techniques for analyzing algorithms, and computational complexity of various algorithms
  • Linear optimization and its geometry and duality, simplex and non-simplex algorithms for linear optimization, second-order cone programming, and semidefinite programming

Combinatorial and Algorithmic Mathematics is an ideal textbook resource on the subject for students studying discrete structures, combinatorics, algorithms, and optimization. It also caters to scientists across diverse disciplines that incorporate algorithms and academics and researchers who wish to better understand some modern optimization methodologies.

商品描述(中文翻譯)

詳細的優化原理回顧,並輔以嚴謹的數學和計算機科學解釋及各種學習輔助工具

在嚴謹的數學和計算機科學基礎支持下,《組合與算法數學:從基礎到優化》提供了對優化領域的從零開始的理解,討論了70種算法,並提供約220個示例、160個非平凡的章末練習題及完整解答,以確保讀者在需要時能夠應用適當的理論、原則和概念,並附有解決某些特定問題的Matlab代碼。本書幫助讀者發展數學成熟度,包括處理越來越抽象的概念、識別數學模式以及從具體示例推廣到廣泛概念的技能。

本書從數學邏輯、集合論結構以及分析和代數結構的基本原理開始,分別涵蓋組合學和算法,然後在最後一部分將材料整合到優化中。本書專注於對任何希望發展並應用其對優化理解的主題,這些主題包括數據結構、算法、人工智慧、機器學習、數據科學、計算機系統、網絡和計算機安全等領域。

《組合與算法數學》包括以下討論:
- 命題邏輯和謂詞邏輯、集合論結構(如集合、關係和函數)以及基本的分析和代數結構(如序列、級數、子空間、凸結構和多面體)
- 遞迴解法技術、計數方法、排列、組合、物件和集合的排列,以及圖的基本知識和性質
- 漸進符號、分析算法的技術以及各種算法的計算複雜度
- 線性優化及其幾何和對偶性、線性優化的單純形和非單純形算法、二次錐規劃和半正定規劃

《組合與算法數學》是學習離散結構、組合學、算法和優化的學生理想教科書資源。它同樣適合於各種學科的科學家,這些學科涉及算法,以及希望更好理解一些現代優化方法的學者和研究人員。

作者簡介

Baha Alzalg is a Professor in the Department of Mathematics at the University of Jordan in Amman, Jordan. He has also held the post of visiting associate professor in the Department of Computer Science and Engineering at the Ohio State University in Columbus, Ohio. His research interests include topics in optimization theory, applications, and algorithms, with an emphasis on interior-point methods for cone programming.

作者簡介(中文翻譯)

Baha Alzalg 是約旦安曼約旦大學數學系的教授。他曾擔任俄亥俄州立大學計算機科學與工程系的訪問副教授。他的研究興趣包括優化理論、應用及演算法,特別強調用於錐規劃的內點法。