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Programming for Mathematicians
Aimed at teaching mathematics students how to program using their knowledge of mathematics, the entire books emphasis is on "how to think" when programming. Three methods for constructing an algorithm or a program are used: manipulation and enrichment of existing code; use of recurrent sequences; deferral of code writing, in order to deal with one difficulty at a time. Many theorems are mathematically proved and programmed, and the text concludes with an explanation of how a compiler works and how to compile "by hand" little programs. Intended for anyone who thinks mathematically and wants to program and play with mathematics.
A Beginner’s Book of TEX
The last two decades have witnessed a revolution in the realm of typography, with the virtual disappearance of hot-lead typesetting in favor of the so-called digital typesetting. The principle behind the new technology is simple: imagine a very fine mesh superimposed on a sheet of paper. Digital typesetting consists in darkening the appropriate pixels (tiny squares) of this mesh, in patterns corresponding to each character and symbol of the text being set. The actual darkening is done by some printing device, say a laser printer or phototypesetter, which must be told exactly where the ink should go. Since the mesh is very fine-the dashes surrounding this sentence are some six pixels thick, and more than 200 pixels long-the printer can only be controlled by a computer program, which takes a "high-level" description of the page in terms of text, fonts, and formatting commands, and digests all of that into "low-level" commands for the printer. TEX is such a program, created by Donald E. Knuth, a computer scientist at Stanford University.
Math into LATEX
It is indeed a lucky author who is given the opportunity to completely rewrite a book barely a year after its publication. Writing about software affords such op portunities (especially if the original edition sold out), since the author is shooting at a moving target. u\TEX and AMS-u\TEX improved dramatically with the release of the new stan dard IbTEX (called u\TEX2) in June of1994 and the revision of AMS-u\TEX (ver f sion 1.2) in February ofl995. The change in AMS-u\TEX is profound. u\TEX2 f made it possible for AMS-IbTEX to join the u\TEX world. One of the main points of the present book is to make this clear. This book introduces u\TEX as a tool for mathematical typesetting, and treats AMS-u\TEX as a set of enhancements to the standard u\TEX, to be used in conjunction with hundreds of other u\TEX 2f enhancements. I am not a TEX expert. Learning the mysteries of the system has given me great respect for those who crafted it: Donald Knuth, Leslie Lamport, Michael Spivak, and others did the original work; David Carlisle, Michael J. Downes, David M. Jones, Frank Mittelbach, Rainer Schopf, and many others built on the work of these pioneers to create the new u\TEX and AMS-LATEX.
Spinning Tops
Since the time of Lagrange and Euler, it has been well known that an understanding of algebraic curves can illuminate the picture of rigid bodies provided by classical mechanics. A modern view of the role played by algebraic geometry has been established iby many mathematicians. This book presents some of these techniques, which fall within the orbit of finite dimensional integrable systems. The main body of the text presents a rich assortment of methods and ideas from algebraic geometry prompted by classical mechanics, whilst in appendices the general, abstract theory is described. The methods are given a topological application to the study of Liouville tori and their bifurcations. The book is based on courses for graduate students given by the author at Strasbourg University but the wealth of original ideas will make it also appeal to researchers.
Algebraic Number Theory
This introduction to algebraic number theory discusses the classical concepts from the viewpoint of Arakelov theory. The treatment of class theory is particularly rich in illustrating complements, offering hints for further study, and providing concrete examples. It is the most up-to-date, systematic, and theoretically comprehensive textbook on algebraic number field theory available.
Hamiltonian Systems and Their Integrability
"This book presents some modern techniques in the theory of integrable systems viewed as variations on the theme of action-angle coordinates. These techniques include analytical methods coming from the Galois theory of differential equations, as well as more classical algebro-geometric methods related to Lax equations. This book would be suitable for a graduate course in Hamiltonian systems."--BOOK JACKET.
More Math Into 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 Course A detailed exposition of multiline math formu...
Text and Math Into LaTeX
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; the new Appendix C, introduces the reader to ChatGPT.
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