Bøger af 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

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.

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 a fine work for students, instructors, and researchers 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)

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

Manche beginnen den Tag mit Gymnastik, um den Korper zu entrosten und beweglich zu halten. Leider kummern sich aber nur wenige um das Training ihres Gehirns, also des Organs, das uns zum Menschen macht. Dieses Buch versorgt Sie mit Denksportaufgaben und hilft Ihnen beim ganzjahrigen Hirnjogging. Angesprochen sindSchler ab 14 Jahren, die ihren Verstand durch geeignetes Training schrfen mchten, Erwachsene, denen das Lsen von Kreuzwortrtseln nicht reicht, ltere Menschen, die geistig fit bleiben mchten. Sie alle werden sehen, dass sich Ihr Denkorgan beim Lsen der Aufgaben entschlackt und flexibler wird. Lesen Sie jede Woche einige Rtsel, denken Sie darber nach und versuchen Sie sich an den Lsungen. Das schrft das Denkvermgen und Sie werden an jedem Schritt Ihre Freude haben. Sollten Sie die Aufgabe nicht innerhalb von ein bis zwei Tagen lsen, dann sehen Sie in den Hinweisen nach und versuchen, damit weiter zu kommen. Es ist ein groes Erlebnis, wenn man nach Stunden oder Tagen des Kampfes sagen kann: Heureka, ich hab's gefunden!"e; Stimmen zum Buch: Dieses Buch war eine meiner Lieblingslektren als Mittel- und Oberstufen-Schler. Es ist von einem fhrenden Mathematiker in einem angenehmen Stil geschrieben und enthlt sehr interessante Rtsel und mathematische Probleme, die mit groer Sorgfalt angeordnet sind. Lszl Lovsz, Prsident der International Mathematical Union und Verfasser von Combinatorial Problems and Exercises"e;.

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 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 "e;diamond sections'', many written by leading specialists in these fields, provide a brief glimpse into special topics beyond the basics. "e;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 Grtzer'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."e;Bulletin of the American Mathematical Society"e;Grtzer's book General Lattice Theory has become the lattice theorist's bible."e; Mathematical Reviews

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.