Bøker av George Gratzer

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. The easy-to-read guide focuses on helping the writer avoid common English mistakes in mathematical writing. With just a few minutes of engaging, light reading each day, the reader will learn to create clearer, more readable, math texts.The book covers 23 crucial topics, ranging from correct article and preposition usage to proper usage of dashes, conjunctions, and prepositions. It also addresses the construction of direct sentences, effective introductory phrases for formulas, and more. As a bonus to the reader, ¿Practice makes perfect¿ exercises relating to each topic are freely accessible on this book¿s Springer website.Appendix A gives a quick tutorial on grammatical terms and constructs. Appendix B looks at ChatGPT and the positive aspects of its powerful capabilities. Additionally, Paul Halmos¿s article on ¿How to write mathematics¿ is included in Appendix C. It deals with the mathematical aspects of writing.

For more than 30 years, this comprehensive manual has been the standard introduction and complete reference for writing articles and books containing mathematical formulas. This sixth edition uses a slightly changed title, Text and Math into LaTeX, to emphasize the importance of text in mathematical/scientific composition. Sections that contained commands no longer much needed (such as \includeonly) and the introductory sections to PDF (now ubiquitous) have been omitted. Many sections are now enhanced with discussion of new and useful packages. An occasional encouragement for the reader to consult ChatGPT for confirmation on various points illustrates the positive relationship between ChatGPT and LaTeX.The new Chapter 17 describes recent developments that enhance, or replace, BibTeX and the new Appendix C, introduces the reader to ChatGPT.Key features: An example-based, visual approach and agentle 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 formulasA detailed approach to creating illustrationsExtras are provided on SpringerLink for the following chapters: 1, 2, 3, 4, 6, 7, 10, 11, 13, 14, 15, 16, 17, 18 and Appendices A, BExtras for Appendices A & B can be found in Extras for Chapter 18.

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

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

Practical LaTeX

"Gratzer's 'General Lattice Theory' has become the lattice theorist's bible. Now we have the second edition, in which the old testament is augmented by a new testament. The new testament gospel is provided by leading and acknowledged experts in their fields.

This outstanding text is written in clear language and enhanced with many exercises, diagrams, and proofs. It discusses historical developments and future directions and provides an extensive bibliography and references. 1971 edition.