A First Journey Through Logic
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A First Journey Through Logic
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Author : Martin Hils
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-09-11
A First Journey Through Logic written by Martin Hils and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-11 with Mathematics categories.
The aim of this book is to present mathematical logic to students who are interested in what this field is but have no intention of specializing in it. The point of view is to treat logic on an equal footing to any other topic in the mathematical curriculum. The book starts with a presentation of naive set theory, the theory of sets that mathematicians use on a daily basis. Each subsequent chapter presents one of the main areas of mathematical logic: first order logic and formal proofs, model theory, recursion theory, Gödel's incompleteness theorem, and, finally, the axiomatic set theory. Each chapter includes several interesting highlights—outside of logic when possible—either in the main text, or as exercises or appendices. Exercises are an essential component of the book, and a good number of them are designed to provide an opening to additional topics of interest.
Tale Of Discrete Mathematics A A Journey Through Logic Reasoning Structures And Graph Theory
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Author : Joseph Khoury
language : en
Publisher: World Scientific
Release Date : 2024-03-19
Tale Of Discrete Mathematics A A Journey Through Logic Reasoning Structures And Graph Theory written by Joseph Khoury and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-19 with Mathematics categories.
Topics covered in Discrete Mathematics have become essential tools in many areas of studies in recent years. This is primarily due to the revolution in technology, communications, and cyber security. The book treats major themes in a typical introductory modern Discrete Mathematics course: Propositional and predicate logic, proof techniques, set theory (including Boolean algebra, functions and relations), introduction to number theory, combinatorics and graph theory.An accessible, precise, and comprehensive approach is adopted in the treatment of each topic. The ability of abstract thinking and the art of writing valid arguments are emphasized through detailed proof of (almost) every result. Developing the ability to think abstractly and roguishly is key in any areas of science, information technology and engineering. Every result presented in the book is followed by examples and applications to consolidate its comprehension. The hope is that the reader ends up developing both the abstract reasoning as well as acquiring practical skills.All efforts are made to write the book at a level accessible to first-year students and to present each topic in a way that facilitates self-directed learning. Each chapter starts with basic concepts of the subject at hand and progresses gradually to cover more ground on the subject. Chapters are divided into sections and subsections to facilitate readings. Each section ends with its own carefully chosen set of practice exercises to reenforce comprehension and to challenge and stimulate readers.As an introduction to Discrete Mathematics, the book is written with the smallest set of prerequisites possible. Familiarity with basic mathematical concepts (usually acquired in high school) is sufficient for most chapters. However, some mathematical maturity comes in handy to grasp some harder concepts presented in the book.
Analysis And Linear Algebra The Singular Value Decomposition And Applications
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Author : James Bisgard
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-10-19
Analysis And Linear Algebra The Singular Value Decomposition And Applications written by James Bisgard and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-19 with Education categories.
This book provides an elementary analytically inclined journey to a fundamental result of linear algebra: the Singular Value Decomposition (SVD). SVD is a workhorse in many applications of linear algebra to data science. Four important applications relevant to data science are considered throughout the book: determining the subspace that “best” approximates a given set (dimension reduction of a data set); finding the “best” lower rank approximation of a given matrix (compression and general approximation problems); the Moore-Penrose pseudo-inverse (relevant to solving least squares problems); and the orthogonal Procrustes problem (finding the orthogonal transformation that most closely transforms a given collection to a given configuration), as well as its orientation-preserving version. The point of view throughout is analytic. Readers are assumed to have had a rigorous introduction to sequences and continuity. These are generalized and applied to linear algebraic ideas. Along the way to the SVD, several important results relevant to a wide variety of fields (including random matrices and spectral graph theory) are explored: the Spectral Theorem; minimax characterizations of eigenvalues; and eigenvalue inequalities. By combining analytic and linear algebraic ideas, readers see seemingly disparate areas interacting in beautiful and applicable ways.
Journey Through The Bhagavad Gita A Modern Commentary With Word To Word Sanskrit English Translation
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Author : GK Marballi
language : en
Publisher: Lulu.com
Release Date : 2013
Journey Through The Bhagavad Gita A Modern Commentary With Word To Word Sanskrit English Translation written by GK Marballi and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Religion categories.
The Bhagavad Gita contains the essence and analysis of the Vedas and the Upanishads - ancient Indian spiritual texts that are at the heart of Indian spiritual tradition. It presents us with a solution for completely eradicating sorrow from our lives. This book is a straightforward, modern, and simple explanation and commentary of the Bhagavad Gita. Each shloka (verse) is explained in detail. A summary of each chapter is also included. No prior background in Indian scriptures or Vedanta is required. Serious students of the Gita will also appreciate the word-to-word Sanskrit-to-English translation of each verse. About The Author GK Marballi works in the technology industry and is presently based in New York City. He received his bachelors degree in commerce from the University of Mumbai, and his MBA from Harvard Business School.
An Invitation To Pursuit Evasion Games And Graph Theory
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Author : Anthony Bonato
language : en
Publisher: American Mathematical Society
Release Date : 2022-06-16
An Invitation To Pursuit Evasion Games And Graph Theory written by Anthony Bonato and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-16 with Mathematics categories.
Graphs measure interactions between objects such as friendship links on Twitter, transactions between Bitcoin users, and the flow of energy in a food chain. While graphs statically represent interacting systems, they may also be used to model dynamic interactions. For example, imagine an invisible evader loose on a graph, leaving only behind breadcrumb clues to their whereabouts. You set out with pursuers of your own, seeking out the evader's location. Would you be able to detect their location? If so, then how many resources are needed for detection, and how fast can that happen? These basic-seeming questions point towards the broad conceptual framework of pursuit-evasion games played on graphs. Central to pursuit-evasion games on graphs is the idea of optimizing certain parameters, whether they are the cop number, burning number, or localization number, for example. This book would be excellent for a second course in graph theory at the undergraduate or graduate level. It surveys different areas in graph searching and highlights many fascinating topics intersecting classical graph theory, geometry, and combinatorial designs. Each chapter ends with approximately twenty exercises and five larger scale projects.
An Introduction To Symmetric Functions And Their Combinatorics
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Author : Eric S. Egge
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-11-18
An Introduction To Symmetric Functions And Their Combinatorics written by Eric S. Egge and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-18 with Education categories.
This book is a reader-friendly introduction to the theory of symmetric functions, and it includes fundamental topics such as the monomial, elementary, homogeneous, and Schur function bases; the skew Schur functions; the Jacobi–Trudi identities; the involution ω ω; the Hall inner product; Cauchy's formula; the RSK correspondence and how to implement it with both insertion and growth diagrams; the Pieri rules; the Murnaghan–Nakayama rule; Knuth equivalence; jeu de taquin; and the Littlewood–Richardson rule. The book also includes glimpses of recent developments and active areas of research, including Grothendieck polynomials, dual stable Grothendieck polynomials, Stanley's chromatic symmetric function, and Stanley's chromatic tree conjecture. Written in a conversational style, the book contains many motivating and illustrative examples. Whenever possible it takes a combinatorial approach, using bijections, involutions, and combinatorial ideas to prove algebraic results. The prerequisites for this book are minimal—familiarity with linear algebra, partitions, and generating functions is all one needs to get started. This makes the book accessible to a wide array of undergraduates interested in combinatorics.
Galois Theory For Beginners A Historical Perspective Second Edition
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Author : Jörg Bewersdorff
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-07-15
Galois Theory For Beginners A Historical Perspective Second Edition written by Jörg Bewersdorff and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-15 with Education categories.
Galois theory is the culmination of a centuries-long search for a solution to the classical problem of solving algebraic equations by radicals. In this book, Bewersdorff follows the historical development of the theory, emphasizing concrete examples along the way. As a result, many mathematical abstractions are now seen as the natural consequence of particular investigations. Few prerequisites are needed beyond general college mathematics, since the necessary ideas and properties of groups and fields are provided as needed. Results in Galois theory are formulated first in a concrete, elementary way, then in the modern form. Each chapter begins with a simple question that gives the reader an idea of the nature and difficulty of what lies ahead. The applications of the theory to geometric constructions, including the ancient problems of squaring the circle, duplicating the cube, and trisecting the angle, and the construction of regular n n-gons are also presented. This new edition contains an additional chapter as well as twenty facsimiles of milestones of classical algebra. It is suitable for undergraduates and graduate students, as well as teachers and mathematicians seeking a historical and stimulating perspective on the field.
The Great Prime Number Race
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Author : Roger Plymen
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-08-13
The Great Prime Number Race written by Roger Plymen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-13 with Education categories.
Have you ever wondered about the explicit formulas in analytic number theory? This short book provides a streamlined and rigorous approach to the explicit formulas of Riemann and von Mangoldt. The race between the prime counting function and the logarithmic integral forms a motivating thread through the narrative, which emphasizes the interplay between the oscillatory terms in the Riemann formula and the Skewes number, the least number for which the prime number theorem undercounts the number of primes. Throughout the book, there are scholarly references to the pioneering work of Euler. The book includes a proof of the prime number theorem and outlines a proof of Littlewood's oscillation theorem before finishing with the current best numerical upper bounds on the Skewes number. This book is a unique text that provides all the mathematical background for understanding the Skewes number. Many exercises are included, with hints for solutions. This book is suitable for anyone with a first course in complex analysis. Its engaging style and invigorating point of view will make refreshing reading for advanced undergraduates through research mathematicians.
Random Explorations
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Author : Gregory F. Lawler
language : en
Publisher: American Mathematical Society
Release Date : 2022-12-06
Random Explorations written by Gregory F. Lawler and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-06 with Mathematics categories.
The title “Random Explorations” has two meanings. First, a few topics of advanced probability are deeply explored. Second, there is a recurring theme of analyzing a random object by exploring a random path. This book is an outgrowth of lectures by the author in the University of Chicago Research Experiences for Undergraduate (REU) program in 2020. The idea of the course was to expose advanced undergraduates to ideas in probability research. The book begins with Markov chains with an emphasis on transient or killed chains that have finite Green's function. This function, and its inverse called the Laplacian, is discussed next to relate two objects that arise in statistical physics, the loop-erased random walk (LERW) and the uniform spanning tree (UST). A modern approach is used including loop measures and soups. Understanding these approaches as the system size goes to infinity requires a deep understanding of the simple random walk so that is studied next, followed by a look at the infinite LERW and UST. Another model, the Gaussian free field (GFF), is introduced and related to loop measure. The emphasis in the book is on discrete models, but the final chapter gives an introduction to the continuous objects: Brownian motion, Brownian loop measures and soups, Schramm-Loewner evolution (SLE), and the continuous Gaussian free field. A number of exercises scattered throughout the text will help a serious reader gain better understanding of the material.
The Idea Of Hegel S Science Of Logic
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Author : Stanley Rosen
language : en
Publisher: University of Chicago Press
Release Date : 2024-05-31
The Idea Of Hegel S Science Of Logic written by Stanley Rosen and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-31 with Philosophy categories.
Although Hegel considered Science of Logic essential to his philosophy, it has received scant commentary compared with the other three books he published in his lifetime. Here philosopher Stanley Rosen rescues the Science of Logic from obscurity, arguing that its neglect is responsible for contemporary philosophy's fracture into many different and opposed schools of thought. Through deep and careful analysis, Rosen sheds new light on the precise problems that animate Hegel's overlooked book and their tremendous significance to philosophical conceptions of logic and reason. Rosen's overarching question is how, if at all, rationalism can overcome the split between monism and dualism. Monism—which claims a singular essence for all things—ultimately leads to nihilism, while dualism, which claims multiple, irreducible essences, leads to what Rosen calls "the endless chatter of the history of philosophy." The Science of Logic, he argues, is the fundamental text to offer a new conception of rationalism that might overcome this philosophical split. Leading readers through Hegel's book from beginning to end, Rosen's argument culminates in a masterful chapter on the Idea in Hegel. By fully appreciating the Science of Logic and situating it properly within Hegel's oeuvre, Rosen in turn provides new tools for wrangling with the conceptual puzzles that have brought so many other philosophers to disaster.