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Conceptual Mathematics: A First Introduction to Categories

Conceptual Mathematics: A First Introduction to Categories

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F. William Lawvere
Cambridge University Press
Edition: 2, 10/26/2011
EAN 9780521719162, ISBN10: 052171916X

Paperback, 408 pages, 24.4 x 17 x 2.3 cm
Language: English

In the last 60 years, the use of the notion of category has led to a remarkable unification and simplification of mathematics. Conceptual Mathematics introduces this tool for the learning, development, and use of mathematics, to beginning students and also to practising mathematical scientists. This book provides a skeleton key that makes explicit some concepts and procedures that are common to all branches of pure and applied mathematics. The treatment does not presuppose knowledge of specific fields, but rather develops, from basic definitions, such elementary categories as discrete dynamical systems and directed graphs; the fundamental ideas are then illuminated by examples in these categories. This second edition provides links with more advanced topics of possible study. In the new appendices and annotated bibliography the reader will find concise introductions to adjoint functors and geometrical structures, as well as sketches of relevant historical developments.

Foreword
Note to the reader
Preview
Part I. The Category of Sets
1. Sets, maps, composition
Part II. The Algebra of Composition
2. Isomorphisms
Part III. Categories of Structured Sets
3. Examples of categories
Part IV. Elementary Universal Mapping Properties
4. Universal mapping properties
Part V. Higher Universal Mapping Properties
5. Map objects
6. The contravariant parts functor
7. The components functor
Appendix 1. Geometry of figures and algebra of functions
Appendix 2. Adjoint functors
Appendix 3. The emergence of category theory within mathematics
Appendix 4. Annotated bibliography.

Review of the first edition: 'This book is a remarkable achievement. It covers all the pressing international economic issues of our day in an accessible yet thorough manner. The authors adroitly combine illustrative data and essential theory to explain the hows and whys of trade and trade liberalisation, the delocation of firms and multinational activity, capital flows, currency and financial crises, and the role of international organisations such as the IMF and WTO. It is appropriate for students without an economics specialisation both at the undergraduate and non-specialists graduate level, e.g. MBA and Masters of Public Administration. The facts and real-world feel of the book make it interesting as a supplement for specialist students as well.' Richard Baldwin, Graduate Institute of International Studies, Geneva

Review of the first edition: 'International trade and international business have hitherto existed in two separate worlds - a world of nations and a world of firms - in academic teaching and even in research. This book gives us a welcome integration of the two at the level of teaching. Students who use it will develop a unified vision that will benefit them in their future careers, whether in business, government, international institutions, or academic research.' Avinash K. Dixit, Princeton University

Advance praise: 'Very few textbooks exist that examine the working of the global economy through the three lenses of international trade, international finance, and international investment. This book provides an excellent introduction to all three lenses and to the linkages among them. The authors show how macro-level forces of trade, investment and finance reflect the micro-level actions of firms and households. For students and instructors looking for a textbook that blends international economics (trade and finance) with international business (international investment and multinational enterprises), look no further. This book has it all and does it well.' Lorraine Eden, Mays Business School, Texas A and M University

Review of the first edition: 'This book offers a valuable integration of the economics and business aspects of globalization. The integrated approach makes the book a unique and valuable resource for students of international economics and business studies.' Joseph Francois, J. Kepler University

'The world economy has changed more rapidly in the last twenty years than in the previous two millennia, driven by three fundamental forces: the rise of intangibles in value creation, the disaggregation of the value chain and the increasing extent of international intra-firm trade. These changes have made even the most basic measures of the international economy like GDP, imports and exports, and even balance of payments, far less meaningful. In their place we need new models that take a more holistic view of place, space and organization. This new second edition of International Economics and Business by Beugelsdijk, Brakman, Garretsen and van Marrewijk does precisely that. It will serve as a valuable resource to educate the new generation of managers and policymakers that must function in the new environment of rising complexity.' Ram Mudambi, Fox School of Business, Temple University

Review of the first edition: 'Understanding the enormous changes taking place in the world economy requires the perspectives of many different disciplines, of which international economics and international business are two of the most relevant. Yet until now these two fields have interacted very little. This new text does a superb job of combining the insights of these two complementary academic fields. The authors present a lucid overview of theories of international economics, with an emphasis on recent contributions such as imperfect competition, multinational corporations, agglomeration and financial crises. In addition they present a wealth of relevant and insightful case studies from the international business literature which helps bridge the gap between theory and reality. Students in a range of courses will benefit from this integration of different approaches, and researchers who want an overview of recent work in fields outside their own will learn a lot too.' J. Peter Neary, University of Oxford

Review of the first edition: 'This is a fascinating book with a practical approach to international economics that enhances our understanding of the globalisation process.' Hans-Werner Sinn, President, Ifo Institute for Economic Research, Munich

'A monumental achievement. The only international economics textbook on the market that appropriately describes the role of the firm in the global economy.' Alain Verbeke, Haskayne School of Business, University of Calgary and Solvay Business School, University of Brussels