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Categorical Foundations
Publisher Description
Educational Interfaces between Mathematics and Industry
This book is the “Study Book” of ICMI-Study no. 20, which was run in cooperation with the International Congress on Industry and Applied Mathematics (ICIAM). The editors were the co-chairs of the study (Damlamian, Straesser) and the organiser of the Study Conference (Rodrigues). The text contains a comprehensive report on the findings of the Study Conference, original plenary presentations of the Study Conference, reports on the Working Groups and selected papers from all over world. This content was selected by the editors as especially pertinent to the study each individual chapter represents a significant contribution to current research.
Raising Public Awareness of Mathematics
This collective book aims to encourage and inspire actions directed towards raising public awareness of the importance of mathematical sciences for our contemporary society in a cultural and historical perspective. Mathematical societies, in Europe and around the world, can find ideas, blueprints and suggestions for activities – including concerted actions with other international organizations – directed towards raising public awareness of science, technology and other fields where mathematics plays a strong role. The material is divided into four parts: • National experiences • Exhibitions / mathematical museums • Popularization activities • Popularization: why and how?
New Frontiers in Crustacean Biology
This work contains the Proceedings of The Crustacean Society Summer Meeting in Tokyo, Japan, in 2009, organized by Carcinological Society of Japan and The Crustacean Society. The presentations by internationally leading carcinologists represent major reviews of all areas of crustacean research.
New Perspectives in Algebra, Topology and Categories
This book provides an introduction to some key subjects in algebra and topology. It consists of comprehensive texts of some hours courses on the preliminaries for several advanced theories in (categorical) algebra and topology. Often, this kind of presentations is not so easy to find in the literature, where one begins articles by assuming a lot of knowledge in the field. This volume can both help young researchers to quickly get into the subject by offering a kind of « roadmap » and also help master students to be aware of the basics of other research directions in these fields before deciding to specialize in one of them. Furthermore, it can be used by established researchers who need a ...
An Introduction to the Language of Mathematics
This is a textbook for an undergraduate mathematics major transition course from technique-based mathematics (such as Algebra and Calculus) to proof-based mathematics. It motivates the introduction of the formal language of logic and set theory and develops the basics with examples, exercises with solutions and exercises without. It then moves to a discussion of proof structure and basic proof techniques, including proofs by induction with extensive examples. An in-depth treatment of relations, particularly equivalence and order relations completes the exposition of the basic language of mathematics. The last chapter treats infinite cardinalities. An appendix gives some complement on induction and order, and another provides full solutions of the in-text exercises. The primary audience is undergraduate mathematics major, but independent readers interested in mathematics can also use the book for self-study.
Spectral Spaces
Offers a comprehensive presentation of spectral spaces focussing on their topology and close connections with algebra, ordered structures, and logic.
Frames and Locales
Until the mid-twentieth century, topological studies were focused on the theory of suitable structures on sets of points. The concept of open set exploited since the twenties offered an expression of the geometric intuition of a "realistic" place (spot, grain) of non-trivial extent. Imitating the behaviour of open sets and their relations led to a new approach to topology flourishing since the end of the fifties.It has proved to be beneficial in many respects. Neglecting points, only little information was lost, while deeper insights have been gained; moreover, many results previously dependent on choice principles became constructive. The result is often a smoother, rather than a more entangled, theory. No monograph of this nature has appeared since Johnstone's celebrated Stone Spaces in 1983. The present book is intended as a bridge from that time to the present. Most of the material appears here in book form for the first time or is presented from new points of view. Two appendices provide an introduction to some requisite concepts from order and category theories.
Papers in Honour of Bernhard Banaschewski
Proceedings of the BB Fest 96, a conference held at the University of Cape Town, 15-20 July 1996, on Category Theory and its Applications to Topology, Order and Algebra
Separation in Point-Free Topology
This book is the first systematic treatment of this area so far scattered in a vast number of articles. As in classical topology, concrete problems require restricting the (generalized point-free) spaces by various conditions playing the roles of classical separation axioms. These are typically formulated in the language of points; but in the point-free context one has either suitable translations, parallels, or satisfactory replacements. The interrelations of separation type conditions, their merits, advantages and disadvantages, and consequences are discussed. Highlights of the book include a treatment of the merits and consequences of subfitness, various approaches to the Hausdorff's axio...
