George Grätzer – författare

Universal Algebra heralded as ". . . the standard reference in a field notorious for the lack of standardization . . .", has become the most authoritative, consistently relied on text in a field with applications in other branches of algebra and other fields such as combinatorics, geometry, and computer science.Each chapter is followed by an extensive list of exercises and problems. The "state of the art" account also includes new appendices (with contributions from B. Jónsson, R. Quackenbush, W. Taylor, and G. Wenzel) and a well selected additional bibliography of over 1250 papers and books which makes this an indispensable new edition for students, faculty, and workers in the field."This book will certainly be, in the years to come, the basic reference to the subject." The American Mathematical Monthly (First Edition)"In this reviewer's opinion [the author] has more than succeeded in his aim. The problems at the end of each chapter are well-chosen; there are more than 650 of them. The book is especially suitable for self-study, as the author frequently provides ample explanation not only of what he is proving, but also of how and why he is proving it. As a reference work for the specialist or a text for the student, the book is highly recommended." Mathematical Reviews (First Edition)"Since the first day of its appearance in 1968, this book has been the standard reference in universal algebra, and no book since has reached its quality." Journal of Symbolic Logic (Second Edition)

Math Into LaTeX is for the mathematician, physicist, engineer, scientist, or technical typist who needs to quickly learn how to write and typeset articles and books containing mathematical formulas, and requires a thorough reference book on all aspects of LaTeX and the AMS packages (the enhancements to LaTeX by the American Mathematical Society).Key features of Math Into LaTeX: A simple, example-based, visual approach - A quick introduction (Part I) allowing readers to type their first articles in only a few hours - Sample articles to demonstrate the basic structure of LaTeX and AMS articles - Useful appendices containing mathematical and text symbol tables and information on how to convert from older versions- A new chapter in the fourth edition, "A Visual Introduction to MikTeX," an open source implementation of TeX and LaTeX for Windows operating systems- Another new chapter describing amsrefs, a simpler method for formatting references that incorporates and replaces BibTeX data- This edition also integrates a major revision to the amsart document class, along with updated examples

Are you in a hurry? A friend received a letter from the American Mathematical Society (AMS) inform­ ing him that his paper had been accepted for publication in the Proceedings of the AMS. If he submitted it as a lt-TEX document, it would be published in 20 weeks­ any other format would take almost a year before the appearance in print of the article. The friend had It-T EX installed on his computer on Friday, borrowed the manu­ script of this book, and mailed a It-T EX version of his article to the AMS on Monday. First Steps in YI'EX is for the mathematician, physicist, engineer, scientist, or technical typist who needs to quickly learn how to write and typeset articles con­ taining mathematical formulas. A quick introduction to E\TE)C and the AMS enhancements is provided so that you will be ready to prepare your first article (such as the sample articles on pages 53-54 and 67-69) in only a few hours. Specific topics can be found in the table of contents, the Quick Finder, or the index. While the index is Jt.TEX -oriented, the Quick Finder lists the main topics using terminology common to wordprocessing applications. For example, to find out how to italicize text, look under italics in the Quick Finder. Setting the stage Watch someone type a mathematical article in I!lfE)C. You will see how to • Type the document using a text editor to create a Jt.TE)C source file.

The congruences of a lattice form the congruence lattice.  Over the last several decades, the study of congruence lattices has established itself as a large and important field with a great number of interesting and deep results, as well as many open problems.  Written by one of the leading experts in lattice theory, this text provides a self-contained introduction to congruences of finite lattices and presents the major results of the last 90 years.  It features the author’s signature “Proof-by-Picture” method, which is used to convey the ideas behind formal proofs in a visual, more intuitive manner. Key features include:an insightful discussion of techniques to construct "nice" finite lattices with given congruence lattices and "nice" congruence-preserving extensionscomplete proofs, an extensive bibliography and index, and over 180 illustrationsadditional chapters covering new results of the lastseven years, increasing the size of this edition to 430 pages, 360 statements, and 262 referencesThis text is appropriate for a one-semester graduate course in lattice theory, and it will also serve as a valuable reference for researchers studying lattices. Reviews of previous editions:“[This] monograph…is an exceptional work in lattice theory, like all the contributions by this author. The way this book is written makes it extremely interesting for the specialists in the field but also for the students in lattice theory.  — Cosmin Pelea, Studia Universitatis Babes-Bolyai Mathematica LII (1), 2007 "The book is self-contained, with many detailed proofs presented that can be followed step-by-step. I believe that this book is a much-needed tool for any mathematician wishing a gentle introduction to the field of congruences representations of finite lattices, with emphasis on the more 'geometric' aspects."   — Mathematical Reviews

The congruences of a lattice form the congruence lattice.  Over the last several decades, the study of congruence lattices has established itself as a large and important field with a great number of interesting and deep results, as well as many open problems.  Written by one of the leading experts in lattice theory, this text provides a self-contained introduction to congruences of finite lattices and presents the major results of the last 90 years.  It features the author’s signature “Proof-by-Picture” method, which is used to convey the ideas behind formal proofs in a visual, more intuitive manner. Key features include:an insightful discussion of techniques to construct "nice" finite lattices with given congruence lattices and "nice" congruence-preserving extensionscomplete proofs, an extensive bibliography and index, and over 180 illustrationsadditional chapters covering new results of the lastseven years, increasing the size of this edition to 430 pages, 360 statements, and 262 referencesThis text is appropriate for a one-semester graduate course in lattice theory, and it will also serve as a valuable reference for researchers studying lattices. Reviews of previous editions:“[This] monograph…is an exceptional work in lattice theory, like all the contributions by this author. The way this book is written makes it extremely interesting for the specialists in the field but also for the students in lattice theory.  — Cosmin Pelea, Studia Universitatis Babes-Bolyai Mathematica LII (1), 2007 "The book is self-contained, with many detailed proofs presented that can be followed step-by-step. I believe that this book is a much-needed tool for any mathematician wishing a gentle introduction to the field of congruences representations of finite lattices, with emphasis on the more 'geometric' aspects."   — Mathematical Reviews

This colorful and concise little book is uniquely tailored for those who write mathematical texts at any level and are eager to improve their English writing skills.

Part III is Important and also contains six topics addressing common issues that help to master the art of polishing a writing piece even further.

This book provides a clear and accessible introduction to lattice theory for graduate students, researchers, and mathematically mature readers new to the subject. Emphasizing ideas over technical detail, it presents the central concepts and results of lattice theory while avoiding long or intricate proofs.Diagrams play a central role throughout the text, supporting intuition and visual understanding.  Carefully chosen examples clarify definitions and theorems, and optional exercises at the end of each chapter allow readers to deepen their understanding or explore further topics.Part I develops the foundations of lattice theory, including ordered sets, lattices, homomorphisms, ideals, and congruences.  Part II examines some important classes of lattices: distributive, semimodular, modular, and complemented modular lattices.  Particular attention is paid to finite congruence lattices.  Part III focuses on free lattices, among the most intricate and conceptually rich areas of the theory.  Part IV concludes with a brief presentation of several deep and elegant results.A glossary and a detailed index make the book suitable both for first study and for reference.

Large Language Models (LLMs) are reshaping how people write, communicate, and conduct research. ChatGPT, one of the most widely used tools in OpenAI’s GPT series, can serve as a practical assistant when used thoughtfully and responsibly. ChatGPT for Math is a concise, hands-on guide to applying ChatGPT in mathematical work. It shows how to clarify arguments, debug proofs, generate diagrams, support LaTeX workflows, and improve both research writing and teaching materials. The book emphasizes a disciplined approach: ChatGPT is treated as an assistant, not an oracle, and its limitations are addressed openly. Each chapter includes carefully designed exercises to help readers build skill, judgment, and confidence in using ChatGPT effectively.

George Grätzer started writing about LaTeX in 1992. His successful and widely used Math into LaTeX, now in its sixth edition, has long served as a standard reference for mathematical typesetting. Now he extends this tradition by presenting a structured approach to learning LaTeX with the assistance of ChatGPT.The reader is guided in formulating effective queries, interpreting generated output, and assessing correctness. ChatGPT is treated as an assistant whose usefulness depends on informed and critical use. This book offers a concise and accessible introduction to LaTeX, organized around principles that support reliable document preparation. It is intended for students, researchers, and authors who wish to incorporate contemporary AI tools into their LaTeX workflow while maintaining high standards of accuracy and presentation.

This book started with Lattice Theory, First Concepts, in 1971. Then came General Lattice Theory, First Edition, in 1978, and the Second Edition twenty years later. Since the publication of the first edition in 1978, General Lattice Theory has become the authoritative introduction to lattice theory for graduate students and the standard reference for researchers. The First Edition set out to introduce and survey lattice theory. Some 12,000 papers have been published in the field since then; so Lattice Theory: Foundation focuses on introducing the field, laying the foundation for special topics and applications. Lattice Theory: Foundation, based on the previous three books, covers the fundamental concepts and results. The main topics are distributivity, congruences, constructions, modularity and semimodularity, varieties, and free products. The chapter on constructions is new, all the other chapters are revised and expanded versions from the earlier volumes. Almost 40 “diamond sections’’, many written by leading specialists in these fields, provide a brief glimpse into special topics beyond the basics. “Lattice theory has come a long way... For those who appreciate lattice theory, or who are curious about its techniques and intriguing internal problems, Professor Grätzer's lucid new book provides a most valuable guide to many recent developments. Even a cursory reading should provide those few who may still believe that lattice theory is superficial or naive, with convincing evidence of its technical depth and sophistication.” Bulletin of the American Mathematical Society “Grätzer’s book General Lattice Theory has become the lattice theorist’s bible.” Mathematical Reviews

With over 100 million users in its first few months and growing exponentially, ChatGPT has revolutionized how we think and work. From creative writing to customer support, and from education to healthcare, it has sparked a global transformation. But how can you and your business unlock its full potential? Mastering ChatGPT: Prompts and Beyond offers practical guidance to help you maximize ChatGPT’s capabilities. This comprehensive guide delves into the core of ChatGPT, presenting actionable insights, real-world case studies, engaging exercises, and proven strategies. Learn how to craft impactful prompts, overcome ChatGPT’s limitations, and tailor its features to your specific goals. From sparking creative breakthroughs to revolutionizing business strategies, this book’s expert guidance on mastering ChatGPT will transform the way you engage with AI and unlock its full potential. Packed with examples of ChatGPT’s applications in customer support, education, healthcare, and beyond, Mastering ChatGPT: Prompts and Beyond paints a vivid picture of an AI-powered future—and equips you to be part of it.

No detailed description available for "General Lattice Theory".

George Grätzer's Lattice Theory: Foundation is his third book on lattice theory (General Lattice Theory, 1978, second edition, 1998). Congruence Lattices of Infinite Lattices and Beyond includes four chapters by Friedrich Wehrung and George Grätzer.

Practical LaTeX

For over two decades, this comprehensive manual has been the standard introduction and complete reference for writing articles and books containing mathematical formulas. If the reader requires a streamlined approach to learning LaTeX for composing everyday documents, Grätzer’s © 2014 Practical LaTeX may also be a good choice.In this carefully revised fifth edition, the Short Course has been brought up to date and reflects a modern and practical approach to LaTeX usage. New chapters have been added on illustrations and how to use LaTeX on an iPad.Key features:An example-based, visual approach and a gentle introduction with the Short CourseA detailed exposition of multiline math formulas with a Visual GuideA unified approach to TeX, LaTeX, and the AMS enhancementsA quick introduction to creating presentations with formulasFrom earlier reviews:Grätzer’s book is a solution. —European Mathematical Society NewsletterThere are several LaTeX guides, but this one wins hands down for the elegance of its approach and breadth of coverage.—Amazon.com, Best of 2000, Editor’s choiceA novice reader will be able to learn the most essential features of LaTeX sufficient to begin typesetting papers within a few hours of time… An experienced TeX user, on the other hand, will find a systematic and detailed discussion of LaTeX features.—Report on Mathematical PhysicsA very helpful and useful tool for all scientists and engineers.   —Review of Astronomical Tools

George Grätzer's Lattice Theory: Foundation is his third book on lattice theory (General Lattice Theory, 1978, second edition, 1998).

This is a self-contained exposition by one of the leading experts in lattice theory, George Grätzer, presenting the major results of the last 70 years on congruence lattices of finite lattices, featuring the author's signature Proof-by-Picture method.Key features:* Insightful discussion of techniques to construct "nice" finite lattices with given congruence lattices and "nice" congruence-preserving extensions* Contains complete proofs, an extensive bibliography and index, and over 140 illustrations* This new edition includes two new parts on Planar Semimodular Lattices and The Order of Principle Congruences, covering the research of the last 10 yearsThe book is appropriate for a one-semester graduate course in lattice theory, and it is a practical reference for researchers studying lattices.Reviews of the first edition:"There exist a lot of interesting results in this area of lattice theory, and some of them are presented inthis book. [This] monograph…is an exceptional work in lattice theory, like all the contributions by this author. … The way this book is written makes it extremely interesting for the specialists in the field but also for the students in lattice theory. Moreover, the author provides a series of companion lectures which help the reader to approach the Proof-by-Picture sections." (Cosmin Pelea, Studia Universitatis Babes-Bolyai Mathematica, Vol. LII (1), 2007)  "The book is self-contained, with many detailed proofs presented that can be followed step-by-step. [I]n addition to giving the full formal details of the proofs, the author chooses a somehow more pedagogical way that he calls Proof-by-Picture, somehow related to the combinatorial (as opposed to algebraic) nature of many of the presented results. I believe that this book is a much-needed tool for any mathematician wishing a gentle introduction to the field of congruences representations offinite lattices, with emphasis on the more 'geometric' aspects."   —Mathematical Reviews

In this present edition, the work has been significantly updated and expanded. It contains an extensive new bibliography of 530 items and has been supplemented by eight appendices authored by an exceptional group of experts. The first appendix, written by the author, briefly reviews developments in lattice theory, specifically, the major results of the last 20 years and solutions of the problems proposed in the first edition. The other subjects concern distributive lattices and duality (Brian A. Davey and Hilary A. Priestley), continuous geometries (Friedrich Wehrung), projective lattice geometries (Marcus Greferath and Stefan E. Schmidt), varieties (Peter Jipsen and Henry Rose), free lattices (Ralph Freese), formal concept analysis (Bernhard Ganter and Rudolf Wille), and congruence lattices (Thomas Schmidt in collaboration with the author).