Paperback (ISBN-13: 9780521714013)
Page extent: 400 pages
Size: 228 x 152 mm
Alfred Tarski, one of the greatest logicians of all time, is widely thought of as ‘the man who defined truth’. His work on the concepts of truth and logical consequence are cornerstones of modern logic, influencing developments in mathematics, philosophy, linguistics, and computer science. Tarski was a charismatic teacher and zealous promoter of his view of logic as the foundation of all rational thought, a bon vivant and a womanizer, who played the ‘great man’ to the hilt. Born in Warsaw in 1901 to Jewish parents, he changed his name and converted to Catholicism but was never able to obtain a professorship in his home country. A fortuitous trip to the United States at the outbreak of World War II saved his life and turned his career around, even while it separated him from his family for years. By the war’s end he was established as a professor of mathematics at the University of California, Berkeley. There Tarski built an empire in logic and methodology that attracted students and distinguished researchers from all over the world. From the cafes of Warsaw and Vienna to the mountains and deserts of California, this first full-length biography places Tarski in the social, intellectual, and historical context of his times and presents a frank, vivid picture of a personally and professionally passionate man - interlaced with an account of his major scientific achievements.
The first book-length biography of the great logician Alfred Tarski based
on first-hand knowledge and original sources It places Tarski within his
historical, social and intellectual context, contrasting the first half
of his life in Poland with the second half in the U.S. Includes Tarski’s
main achievements in logic, set theory and algeraic logic and how and why
they have become important in many fields. Many photographs
Contents
1. The two Tarskis; 2. Independence and university; Interlude I. The Banach-Tarski paradox, set theory and the axiom of choice; 3. Polot! The Polish attribute; Interlude II. The completeness and decidability of algebra and geometry; 4. A wider sphere of influence; Interlude III. Truth and definability; 5. How the ‘Unity of Science’ saved Tarski’s life; 6. Berkeley is so far from Princeton; 7. Building a school; Interlude IV. The publication campaigns; 8 ‘Papa Tarski’ and his students; 9. Three meetings and two departures; 10. Logic and methodology, center stage; 11. Heydays; Interlude V. Model theory and the 1963 symposium; 12. Around the world; 13. Los Angeles and Berkeley; Interlude VI. Algebras of logic; 14. A decade of honors; 15. The last times.
Hardback (ISBN-13: 9780521894852)
Paperback (ISBN-13: 9780521719162)
575 line diagrams 12 tables 213 exercises
Page extent: 394 pages
Size: 253 x 177 mm
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.
Authors are world class authorities on the subject Only text at this
elementary level - requires only high-school algebra Applications in pure
and applied mathematics, computer science, physics, linguistics, logic
and philosophy
Contents
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.
Series: Cambridge Series in Statistical and Probabilistic Mathematics (No. 27)
Hardback (ISBN-13: 9780521852258)
45 line diagrams 1 half-tone 35 tables 65 exercises 45 figures 75 worked examples
Page extent: 250 pages
Size: 253 x 177 mm
Given a data set, you can fit thousands of models at the push of a button,
but how do you choose the best With so many candidate models, overfitting
is a real danger. Is the monkey who typed Hamlet actually a good writer
Choosing a model is central to all statistical work with data. We have
seen rapid advances in model fitting and in the theoretical understanding
of model selection, yet this book is the first to synthesize research and
practice from this active field. Model choice criteria are explained, discussed
and compared, including the AIC, BIC, DIC and FIC. The uncertainties involved
with model selection are tackled, with discussions of frequentist and Bayesian
methods; model averaging schemes are presented. Real-data examples are
complemented by derivations providing deeper insight into the methodology,
and instructive exercises build familiarity with the methods. The companion
website features Data sets and R code.
Not just oriented towards one single model choice criterion, but to many,
including the AIC, BIC, DIC and FIC Exercises and literature reviews at
the end of each chapter make this ideal for students All data analyses
compatible with open-source R software; data sets and R code available
from companion Website
Contents
Preface; A guide to notation; 1. Model selection: data examples and introduction; 2. Akaike’s information criterion; 3. The Bayesian information criterion; 4. A comparison of some selection methods; 5. Bigger is not always better; 6. The focussed information criterion; 7. Frequentist and Bayesian model averaging; 8. Lack-of-fit and goodness-of-fit tests; 9. Model selection and averaging schemes in action; 10. Further topics; Overview of data examples; Bibliography; Author index; Subject index.