The LLL Algorithm

This book is devoted to five main principles of algorithm design: divide and conquer, greedy algorithms, thinning, dynamic programming, and exhaustive search. These principles are presented using Haskell, a purely functional language, leading to simpler explanations and shorter programs than would be obtained with imperative languages. Carefully selected examples, both new and standard, reveal the commonalities and highlight the differences between algorithms. The algorithm developments use equational reasoning where applicable, clarifying the applicability conditions and correctness arguments. Every chapter concludes with exercises (nearly 300 in total), each with complete answers, allowing the reader to consolidate their understanding and apply the techniques to a range of problems. The book serves students (both undergraduate and postgraduate), researchers, teachers, and professionals who want to know more about what goes into a good algorithm and how such algorithms can be expresse

榮獲美國出版人協會（Association of American Publishers）電腦資訊科學最佳書籍獎電腦網路技術無所不在：每天，我們從海量的資訊中搜尋到所要的資訊、我們上傳照片到臉書上、我們運用公鑰加密來傳送私人資訊例如信用卡號碼等等、我們使用數位簽章來確認所造訪的網站的真偽……這本書介紹了讓電腦網路世界得以運作，塑造今日人類生活的九種最重要的演算法（algorithm）。作者挑選這九大演算法的標準是：1.每天會被一般電腦使用者用到的演算法。2.必須能解決現實世界的具體問題。3.主要是與資訊科學理論有關的演算法。4. 美、簡潔、優雅。本書所介紹的九大演算法是：搜尋引擎的索引（search engine indexing）、網頁排序（page rank）、公鑰加密（public-key cryptography）、錯誤更正碼（error-correcting codes）、模式辨識（pattern recognition，如手寫辨識、聲音辨識、人臉辨識等等）、資料壓縮（data compression）、資料庫（databases）、數位簽章（digital signature），以及一種如果存在的話將會很了不起的偉大演算法，並探討電腦能力的極限。作者將我們日常生活會用到的電腦功能背後的道理，以淺顯易懂的方式介紹，不具備資訊科學的背景也可以了解。而且令人驚喜的是，每一種演算法，都是一個解決問題的創意與線索，也讓我們得以一窺近代數學家、資訊科學家的努力探索成果。面對越來越科技化的現代生活與職場挑戰，這些基本原理和概念值得我們去了解、吸收，為未來世界做好準備。媒體好評：「這是一本很容易讀的書，介紹了一些很重要的演算法。最重要的是，這本書傳達了一種神奇——不光是指科技的成就，而是使得電腦發揮神奇功能的美麗科學。」Andreas Trabesinger，《自然物理學》(Nature Physics) 「這本書寫得非常好……風格相當平易近人，適合廣大讀者閱讀。」John Gilbey，《泰晤士報高等教育專刊》(Times Higher Education) 「作者讓讀者有一種發動機的感覺，這台發動機為網路世界提供動力……本書讓讀者體會真實世界，開始看到這些演算法在你我周遭活跳跳。」Kevin Slavin，《新科學家》(New Scientist

MATCHES THE LATEST EXAM Let us supplement your AP classroom experience with this easy-to-follow study guide The immensely popular 5 Steps to a 5: AP Computer Science A guide has been updated for the 2021-22 school year and now contains: 3 full-length practice exams that reflect the latest examComprehensive overview of the AP Computer Science A exam formatHundreds of practice exercises with thorough answer explanationsTwo full sections devoted to algorithm writing and two levels of sample questions for each Java concept (basic and advanced)Proven strategies specific to each section of the test

Based on course-tested material, this rigorous yet accessible graduate textbook covers both fundamental and advanced optimization theory and algorithms. It covers a wide range of numerical methods and topics, including both gradient-based and gradient-free algorithms, multidisciplinary design optimization, and uncertainty, with instruction on how to determine which algorithm should be used for a given application. It also provides an overview of models and how to prepare them for use with numerical optimization, including derivative computation. Over 400 high-quality visualizations and numerous examples facilitate understanding of the theory, and practical tips address common issues encountered in practical engineering design optimization and how to address them. Numerous end-of-chapter homework problems, progressing in difficulty, help put knowledge into practice. Accompanied online by a solutions manual for instructors and source code for problems, this is ideal for a one- or two-sem

Optimization techniques are at the core of data science, including data analysis and machine learning. An understanding of basic optimization techniques and their fundamental properties provides important grounding for students, researchers, and practitioners in these areas. This text covers the fundamentals of optimization algorithms in a compact, self-contained way, focusing on the techniques most relevant to data science. An introductory chapter demonstrates that many standard problems in data science can be formulated as optimization problems. Next, many fundamental methods in optimization are described and analyzed, including: gradient and accelerated gradient methods for unconstrained optimization of smooth (especially convex) functions; the stochastic gradient method, a workhorse algorithm in machine learning; the coordinate descent approach; several key algorithms for constrained optimization problems; algorithms for minimizing nonsmooth functions arising in data science; found

The area of computational cryptography is dedicated to the development of effective methods in algorithmic number theory that improve implementation of cryptosystems or further their cryptanalysis. This book is a tribute to Arjen K. Lenstra, one of the key contributors to the field, on the occasion of his 65th birthday, covering his best-known scientific achievements in the field. Students and security engineers will appreciate this no-nonsense introduction to the hard mathematical problems used in cryptography and on which cybersecurity is built, as well as the overview of recent advances on how to solve these problems from both theoretical and practical applied perspectives. Beginning with polynomials, the book moves on to the celebrated Lenstra–Lenstra–Lovász lattice reduction algorithm, and then progresses to integer factorization and the impact of these methods to the selection of strong cryptographic keys for usage in widely used standards.

In the last few years, Algorithms for Convex Optimization have revolutionized algorithm design, both for discrete and continuous optimization problems. For problems like maximum flow, maximum matching, and submodular function minimization, the fastest algorithms involve essential methods such as gradient descent, mirror descent, interior point methods, and ellipsoid methods. The goal of this self-contained book is to enable researchers and professionals in computer science, data science, and machine learning to gain an in-depth understanding of these algorithms. The text emphasizes how to derive key algorithms for convex optimization from first principles and how to establish precise running time bounds. This modern text explains the success of these algorithms in problems of discrete optimization, as well as how these methods have significantly pushed the state of the art of convex optimization itself.