Numbers and Functions


Book Description

New mathematics often comes about by probing what is already known. Mathematicians will change the parameters in a familiar calculation or explore the essential ingredients of a classic proof. Almost magically, new ideas emerge from this process. This book examines elementary functions, such as those encountered in calculus courses, from this point of view of experimental mathematics. The focus is on exploring the connections between these functions and topics in number theory and combinatorics. There is also an emphasis throughout the book on how current mathematical software can be used to discover and interesting properties of these functions. The book provides a transition between elementary mathematics and more advanced topics, trying to make this transition as smooth as possible. Many topics occur in the book, but they are all part of a bigger picture of mathematics. By delving into a variety of them, the reader will develop this broad view. The large collection of problems is an essential part of the book. The problems vary from routine verifications of facts used in the text to the exploration of open questions. Book jacket.










Problems in Applied Mathematics


Book Description

A compilation of 380 of SIAM Review's most interesting problems dating back to the journal's inception in 1959.




New Theories for Chemistry


Book Description

Many new developments, related to the interpretation and importance of symmetry relationships, quantum mechanics, general relativity, field theory and mathematics have occurred in the second half of the 20th century without having a visible impact on chemical thinking. By re-examining basic theories, The New Theories for Chemistry aims to introduce a new understanding of old concepts, such as electron spin, The Periodic Table and electronegativity. The book focuses on the new mathematical concepts that enable the exploration of interactions between particles, waves and fields within a chemical context, and is packed with examples to support its arguments. The author adopts a practical approach and topics are arranged sequentially, from the mathematical basis through to general concepts. An essential reference source, this book is suitable for physicists, theoretical and physical chemists, as well as students and researchers working in the field. - Re-examines basic theories, such as electronegativity and electron spin, and introduces new theory - Full of practical experiments and examples - Is an excellent single reference source




Series and Products in the Development of Mathematics: Volume 2


Book Description

This is the second volume of a two-volume work that traces the development of series and products from 1380 to 2000 by presenting and explaining the interconnected concepts and results of hundreds of unsung as well as celebrated mathematicians. Some chapters deal with the work of primarily one mathematician on a pivotal topic, and other chapters chronicle the progress over time of a given topic. This updated second edition of Sources in the Development of Mathematics adds extensive context, detail, and primary source material, with many sections rewritten to more clearly reveal the significance of key developments and arguments. Volume 1, accessible even to advanced undergraduate students, discusses the development of the methods in series and products that do not employ complex analytic methods or sophisticated machinery. Volume 2 examines more recent results, including deBranges' resolution of Bieberbach's conjecture and Nevanlinna's theory of meromorphic functions.




Nature


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Calendar


Book Description




ELECTROMAGNETISM Volume 2 —Applications


Book Description

This book is a sequel to Electromagnetism: Theory (Volume I). It has been updated to cover some additional aspects of theory and nearly all modern applications. The semi-historical approach is unchanged, but further historical comments have been introduced at various places in the book to give a better insight into the development of the subject as well as to make the study more interesting and palatable to the students. • Emphasis on practical aspects of wave guidance and radiation • Sections on analysis of cylindrical dielectric waveguide (e.g. of optical fibres) in Chapters 18 and 22 • Tensor formulation of Maxwell’s Stresses • Extension of Principle of Duality to time varying field problems as well as to non electrical systems • Extrapolation of the method of images from partially embedded conduction current elements to discontinuous current elements with displacement currents in antennae problems • Explanation of the physical basis of the mechanism of electromagnetic radiation • Analysis of wave polarization including complete and partial polarization • Effects of finite geometrical dimensions of the conducting media on the skin-effect phenomenon • Types of apertures in receiving antennae The book is designed to serve as a core text for students of electrical engineering. Besides, it will be useful to postgraduate physics students as well as research engineers and design and development engineers in industries.




Convexity and Graph Theory


Book Description

Among the participants discussing recent trends in their respective fields and in areas of common interest in these proceedings are such world-famous geometers as H.S.M. Coxeter, L. Danzer, D.G. Larman and J.M. Wills, and equally famous graph-theorists B. Bollobás, P. Erdös and F. Harary. In addition to new results in both geometry and graph theory, this work includes articles involving both of these two fields, for instance ``Convexity, Graph Theory and Non-Negative Matrices'', ``Weakly Saturated Graphs are Rigid'', and many more. The volume covers a broad spectrum of topics in graph theory, geometry, convexity, and combinatorics. The book closes with a number of abstracts and a collection of open problems raised during the conference.