Boolean Algebra

★全球暢銷書《持續買進》作者最新續作！★ ★6大階層完整布局、一生受用的「財富階梯」★ 你的理財方法，適合現在的人生階段和口袋深度嗎？ 資料科學家╱投資專家二刀流尼克．馬朱利， 為想在財富階梯穩步向上的你，量身打造—— 當下最合適的賺錢、存錢、花錢、投資方法！ 「能將理財寫得如此引人入勝的作家並不多，馬朱利正是其一。在本書中，他的生花妙筆不僅描繪出在財富階梯穩步向上的路徑，也道出其中可能令人卻步的成本。我高度推薦這本佳作。」 ――威廉．伯恩斯坦（William Bernstein），《投資金律》（The Four Pillars of Investing）作者 「對金錢的看法，會隨人生階段而改變。我是在反覆試錯中才學會這件事，而你，只需要讀這本精彩的書就夠了。」 ――史考特．蓋洛威（Scott Galloway），《蓋洛威教授的人生財富課》（The Algebra of Wealth）作者 為什麼有些理財專家說「省錢才是致富關鍵」，有些卻說「別再省一杯拿鐵錢，去創業吧！」愈聽愈困惑，到底誰說的才對？ 《財富階梯》給你的答案出人意料：問題從來不在於這些建議誰對誰錯，而是你現在位在財富的哪個階段！更精確地說是別把別人的答案，套在自己的階段，那就像健身教練給相撲選手和馬拉松選手開同一份菜單，不但沒用，還有害處。 資料科學家╱投資專家二刀流尼克．馬朱利，他的日常就是與龐大的金融數據，繼分析了近百年股市數據所寫的《持續買進》，這一次，他深入挖掘聯準會的「消費者財務調查」（SCF）以及密西根大學長達五十多年的「收入動態追蹤調查」（PSID）等龐大資料庫，將財富像階梯一樣劃分為六個階層，找出真正能在每個層級致富的客觀規律，掌握其規則、風險和機會。請讀者看看自己是站在哪一階，該如何在這座階梯穩步向上―― 【攀登財富階梯：每一階都有各自的最優策略】 ＿▃▄▅▆第1階：淨資產（資產減負債）你是勉強餬口的「月光族」，這個階段的關鍵字是「生存」。一個偶發的厄運會被放大，一次生病或車禍就可能讓你陷入背上鉅額債務。 進階策略：最常見的錯誤建議就是「記帳」和「省錢」，因為第1階問題不在於花費，而在於收入！ 你要採取極端手段：不管是打零工、做兩份工作、向親友求援，還是拚命學習一項免學費的技能（高額學貸是場豪賭！），目標只有一個：提高收入並建立緊急資金。 ＿▂▃▄▅▆第2階： 1萬～10萬美元 你在

This book has been designed for a first course on digital design for engineering and computer science students. It offers an extensive introduction on fundamental theories, from Boolean algebra and bi

This book has been designed for a first course on digital design for engineering and computer science students. It offers an extensive introduction on fundamental theories, from Boolean algebra and bi

This book is a comprehensive guide to qualitative comparative analysis (QCA) using R. Using Boolean algebra to implement principles of comparison used by scholars engaged in the qualitative study of

Now with new introductory material, Charles Ragin’s The Comparative Method proposes a synthetic new strategy, based on an application of Boolean algebra that, by combining the strengths of both qualit

Beginning with the fundamentals such as logic families, number systems, Boolean algebra and logic gates, and combinational circuits, the book proceeds on to cover the applied aspects like sequential l

Written by prominent experts in the field, this monograph provides the first comprehensive, unified presentation of the structural, algorithmic and applied aspects of the theory of Boolean functions. The book focuses on algebraic representations of Boolean functions, especially disjunctive and conjunctive normal form representations. This framework looks at the fundamental elements of the theory (Boolean equations and satisfiability problems, prime implicants and associated short representations, dualization), an in-depth study of special classes of Boolean functions (quadratic, Horn, shellable, regular, threshold, read-once functions and their characterization by functional equations) and two fruitful generalizations of the concept of Boolean functions (partially defined functions and pseudo-Boolean functions). Several topics are presented here in book form for the first time. Because of the depth and breadth and its emphasis on algorithms and applications, this monograph will have sp

This collection of papers presents a series of in-depth examinations of a variety of advanced topics related to Boolean functions and expressions. The chapters are written by some of the most prominent experts in their respective fields and cover topics ranging from algebra and propositional logic to learning theory, cryptography, computational complexity, electrical engineering, and reliability theory. Beyond the diversity of the questions raised and investigated in different chapters, a remarkable feature of the collection is the common thread created by the fundamental language, concepts, models, and tools provided by Boolean theory. Many readers will be surprised to discover the countless links between seemingly remote topics discussed in various chapters of the book. This text will help them draw on such connections to further their understanding of their own scientific discipline and to explore new avenues for research.

Mathematics for Electrical Engineering and Computing embraces many applications of modern mathematics, such as Boolean Algebra and Sets and Functions, and also teaches both discrete and continuous sys

Written by the founder of symbolic logic (and Boolean algebra), this classic treatise on the calculus of finite differences offers a thorough discussion of the basic principles of the subject, coverin

Boolean algebras have historically played a special role in the development of the theory of general or "universal" algebraic systems, providing important links between algebra and analysis, set theor

In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts of groups, sets, subsets, topology, Boolean algebra, and other mathematical subjects. 200 illu

By considering the size of the logical network needed to perform a given computational task, the intrinsic difficulty of that task can be examined. Boolean function complexity, the combinatorial study of such networks, is a subject that started back in the 1950s and has today become one of the most challenging and vigorous areas of theoretical computer science. The papers in this book stem from the London Mathematical Society Symposium on Boolean Function Complexity held at Durham University in July 1990. The range of topics covered will be of interest to the newcomer to the field as well as the expert, and overall the papers are representative of the research presented at the Symposium. Anyone with an interest in Boolean Function complexity will find that this book is a necessary purchase.

Boolean functions are essential to systems for secure and reliable communication. This comprehensive survey of Boolean functions for cryptography and coding covers the whole domain and all important results, building on the author's influential articles with additional topics and recent results. A useful resource for researchers and graduate students, the book balances detailed discussions of properties and parameters with examples of various types of cryptographic attacks that motivate the consideration of these parameters. It provides all the necessary background on mathematics, cryptography, and coding, and an overview on recent applications, such as side channel attacks on smart cards, cloud computing through fully homomorphic encryption, and local pseudo-random generators. The result is a complete and accessible text on the state of the art in single and multiple output Boolean functions that illustrates the interaction between mathematics, computer science, and telecommunications

This book focuses on the different representations and cryptographic properties of Booleans functions, presents constructions of Boolean functions with some good cryptographic properties. More specifi

This book represents a significant step towards bridging the areas of Boolean satisfiability and constraint satisfaction by providing theoretical explanations for why SAT-solvers are efficient on cert

Boolean circuit complexity is the combinatorics of computer science and involves many intriguing problems that are easy to state and explain, even for the layman. This book is a comprehensive descrip

Boolean functions are the building blocks of symmetric cryptographic systems. Symmetrical cryptographic algorithms are fundamental tools in the design of all types of digital security systems (i.e. co

This book is an informal, although systematic presentation of lectures given by the authors on Boolean algebras, intended for advanced undergraduates and beginning graduate students. In a bold and ref

A central problem in the design of programming systems is to provide methods for verifying that computer code performs to specification. This book presents a rigorous foundation for defining Boolean categories, in which the relationship between specification and behaviour can be explored. Boolean categories provide a rich interface between program constructs and techniques familiar from algebra, for instance matrix- or ideal-theoretic methods. The book's distinction is that the approach relies on only a single program construct (the first-order theory of categories), the others being derived mathematically from four axioms. Development of these axioms (which are obeyed by an abundance of program paradigms) yields Boolean algebras of 'predicates', loop-free constructs, and a calculus of partial and total correctness which is shown to be the standard one of Hoare, Dijkstra, Pratt, and Kozen. The book is based in part on courses taught by the author, and will appeal to graduate students a

The second volume continues the course of study started in Volume 1, but may be used independently by those already possessing an elementary knowledge of the subject. A summary of basic group theory is followed by accounts of group homomorphisms, rings, fields and integral domains. The related concepts of an invariant subgroup and an ideal in a ring are brought in and the reader introduced to vector spaces and Boolean algebra. The theorems behind the abstract work and the reasons for their importance are discussed in greater detail than is usual at this level. The book is intended both for those who, educated in traditional mathematics, wish to know something about modern algebra and also for those already familiar with the elements of the subject who wish to study further. Fresh ideas and structures are introduced gradually and in a simpler manner, with concrete examples and much more informal discussion. There are many graded exercises, including some worked examples. This book is th

The Boolean network (BN) is a mathematical model of genetic networks and other biological networks. Although extensive studies have been done on BNs from a viewpoint of complex systems, not so many st

For courses in Intermediate and College Algebra. Intermediate through College Algebra: A Streamlined Experience College Algebra with Intermediate Algebra: A Blended Course is an innovative new p

This self-contained monograph explores a new theory centered around boolean representations of simplicial complexes leading to a class of complexes and featuring matroids as central to the theory. The

In this new text, Steven Givant—the author of several acclaimed books, including works co-authored with Paul Halmos and Alfred Tarski—develops three theories of duality for Boolean algebras with opera

Boolean functions are perhaps the most basic objects of study in theoretical computer science. They also arise in other areas of mathematics, including combinatorics, statistical physics, and mathematical social choice. The field of analysis of Boolean functions seeks to understand them via their Fourier transform and other analytic methods. This text gives a thorough overview of the field, beginning with the most basic definitions and proceeding to advanced topics such as hypercontractivity and isoperimetry. Each chapter includes a 'highlight application' such as Arrow's theorem from economics, the Goldreich–Levin algorithm from cryptography/learning theory, Håstad's NP-hardness of approximation results, and 'sharp threshold' theorems for random graph properties. The book includes roughly 450 exercises and can be used as the basis of a one-semester graduate course. It should appeal to advanced undergraduates, graduate students and researchers in computer science theory and related mat

This book brings to bear a body of logic synthesis techniques, in order to contribute to the analysis and control of Boolean Networks (BN) for modeling genetic diseases such as cancer. The authors pro

This book provides an overview of automatic test pattern generation (ATPG) and introduces novel techniques to complement classical ATPG, based on Boolean Satisfiability (SAT). A fast and highly fault

This third edition, now available in paperback, is a follow up to the author's classic Boolean-Valued Models and Independence Proofs in Set Theory. It provides an exposition of some of the most import

In Semimodular Lattices: Theory and Applications Manfred Stern uses successive generalizations of distributive and modular lattices to outline the development of semimodular lattices from Boolean algebras. He focuses on the important theory of semimodularity, its many ramifications, and its applications in discrete mathematics, combinatorics, and algebra. The book surveys and analyzes Garrett Birkhoff's concept of semimodularity and the various related concepts in lattice theory, and it presents theoretical results as well as applications in discrete mathematics group theory and universal algebra. The author also deals with lattices that are 'close' to semimodularity or can be combined with semimodularity, e.g. supersolvable, admissible, consistent, strong, and balanced lattices. Researchers in lattice theory, discrete mathematics, combinatorics, and algebra will find this book invaluable.

Self-taught mathematician and father of Boolean algebra, George Boole (1815–1864) published A Treatise on the Calculus of Finite Differences in 1860 as a sequel to his Treatise on Differential Equations (1859). Both books became instant classics that were used as textbooks for many years and eventually became the basis for our contemporary digital computer systems. The book discusses direct theories of finite differences and integration, linear equations, variations of a constant, and equations of partial and mixed differences. Boole also includes exercises for daring students to ponder, and also supplies answers. Long a proponent of positioning logic firmly in the camp of mathematics rather than philosophy, Boole was instrumental in developing a notational system that allowed logical statements to be symbolically represented by algebraic equations. One of history's most insightful mathematicians, Boole is compelling reading for today's student of logic and Boolean thinking.

In Test Pattern Generation using Boolean Proof Engines, we give an introduction to ATPG. The basic concept and classical ATPG algorithms are reviewed. Then, the formulation as a SAT problem is conside

Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books

Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Advanced Algebra includ

An investigation of the logical flexibility principles needed for a formal semantic account of coordination, plurality, and scope in natural language. Since the early work of Montague, Boolean seman

In Semimodular Lattices: Theory and Applications Manfred Stern uses successive generalizations of distributive and modular lattices to outline the development of semimodular lattices from Boolean algebras. He focuses on the important theory of semimodularity, its many ramifications, and its applications in discrete mathematics, combinatorics, and algebra. The book surveys and analyzes Garrett Birkhoff's concept of semimodularity and the various related concepts in lattice theory, and it presents theoretical results as well as applications in discrete mathematics group theory and universal algebra. The author also deals with lattices that are 'close' to semimodularity or can be combined with semimodularity, e.g. supersolvable, admissible, consistent, strong, and balanced lattices. Researchers in lattice theory, discrete mathematics, combinatorics, and algebra will find this book invaluable.

Learning pre-algebra has never been so easy or so painless Barron's Painless Pre-algebra provides comprehensive review and practice in an easy, step-by-step format. Inside you'll find: Clear examples

Based on the recommendations of the Linear Algebra Curriculum Study Group, this introduction to linear algebra offers a matrix-oriented approach with more emphasis on problem solving and applications.

This new edition in Barron's Easy Way Series contains everything students need to prepare for an algebra class. Algebra: The Easy Way provides key content review and practice exercises to help stu