Advanced Lectures in Mathematics, Volume 35
Published: 22 April 2016
Paperback
768 pages
Bernhard Riemann (1826?1866) possessed an original and broad vision of mathematics together with powerful skill. His work continues to influence almost all major branches of mathematics. The twenty-three papers in this two-volume set examine Riemann, his work, and his significance in the context of modern mathematical developments.
Contributing authors: Michael F. Atiyah, M. V. Berry, Ching-Li Chai, Brian Conrey, Jean-Pierre Demailly, F. T. Farrell, James Glimm, David Harbater, Lizhen Ji, Jurgen Jost, Wolfgang Luck, Dan Marchesin, William H. Meeks III, Peter W. Michor, James S. Milne, Frans Oort, Joaquin Perez, Bradley Plohr, Herman J. J. te Riele, Michael Rubinstein, Norbert Schappacher, Chi-Wang Shu, Dennis Sullivan, Claire Voisin, Shing-Tung Yau.
This is a set comprising the following volumes, which may be purchased independently:
The Legacy of Bernhard Riemann After One Hundred and Fifty Years, Volume I (vol. 35.1 of the ALM series)
The Legacy of Bernhard Riemann After One Hundred and Fifty Years, Volume II (vol. 35.2 of the ALM series)
This volume is part of the Advanced Lectures in Mathematics book series.
262 pages, hardcover, smythe-sewn binding, 108 color illustrations. $63.
April 2016, ISBN 978-1-943863-00-6
Table of Contents
Chapter 8 The classification of homeomorphisms of surfaces
8.1 The classification theorem
8.2 Periodic and reducible homeomorphisms
8.3 Pseudo-Anosov homeomorphisms
8.4 Proof of the classification theorem
8.5 The structure in the reducible case
Chapter 9 Dynamics of polynomials
9.1 Julia sets
9.2 Fixed points
9.3 Green's functions, Bottcher coordinates
9.4 Extending f_0 to S^1
9.5 External rays at rational angles land
Chapter 10 Rational functions
10.1 Introduction
10.1 Thurston mappings
10.2 Thurston mapps associated to spiders
10.3 Thurston obstructions for spider maps and Levy cycles
10.4 Julia sets of quadratic polynomials with superattracting cycles
10.5 Parameter spaces for quadratic polynomials
10.6 The Thurston pullback mapping s_f
10.7 The derivative and coderivative of s_f
10.8 The necessity of the eigenvalue criterion
10.9 Convergence in moduli spaces implies convergence in Teichmuller space
10.10 Asymptotic geometry of Riemann surfaces
10.11 Sufficiency of the eigenvalue criterion
Appendix C1 The Perron-Frobenius theorem
Appendix C2 The Alexander trick
Appendix C3 Homotopy implies isotopy
Appendix C4 The mapping class group and outer automorphisms
Appendix C5 Totally real stretch factors
Appendix C6 Irrationally indifferent fixed points
Appendix C7 Examples of Thurston pullback maps
Appendix C8 Branched maps with nonhyperbolic orbifolds
Appendix C9 The Sullivan dictionary
Groundbreaking work by two leading figures
Will encourage vigorous debate and stimulate further work
Clear and accessible, with technicalities kept to a minimum
Will appeal to mathematicians and linguists as well as logicians and philosophers
This second edition includes a greatly expanded treatment of the paradigm empty term zilch,
a much strengthened treatment of Cantorian set theory, and a new chapter on higher-level plural logic
Alex Oliver and Timothy Smiley provide a natural point of entry to what for most readers will be a new subject. Plural logic deals with plural terms ('Whitehead and Russell', 'Henry VIII's wives', 'the real numbers', 'the square root of -1', 'they'), plural predicates ('surrounded the fort', 'are prime', 'are consistent', 'imply'), and plural quantification ('some things', 'any things'). Current logic is singularist: its terms stand for at most one thing. By contrast, the foundational thesis of this book is that a particular term may legitimately stand for several things at once; in other words, there is such a thing as genuinely plural denotation. The authors argue that plural phenomena need to be taken seriously and that the only viable response is to adopt a plural logic, a logic based on plural denotation. They expound a framework of ideas that includes the distinction between distributive and collective predicates, the theory of plural descriptions, multivalued functions, and lists. A formal system of plural logic is presented in three stages, before being applied to Cantorian set theory as an illustration.
Technicalities have been kept to a minimum, and anyone who is familiar with the classical predicate calculus should be able to follow it. The authors' approach is an attractive blend of no-nonsense argumentative directness and open-minded liberalism, and they convey the exciting and unexpected richness of their subject. Mathematicians and linguists, as well as logicians and philosophers, will find surprises in this book.
Hardback
Published: 09 June 2016 (Estimated)
400 Pages
234x153mm
ISBN: 9780198768685
An ambitious new philosophical worldview
A ground-breaking integrated theory of knowledge, truth, and logic
New answers to timeless philosophical questions
Gila Sher approaches knowledge from the perspective of the basic human epistemic situation?the situation of limited yet resourceful beings, living in a complex world and aspiring to know it in its full complexity. What principles should guide them? Two fundamental principles of knowledge are epistemic friction and freedom. Knowledge must be substantially constrained by the world (friction), but without active participation of the knower in accessing the world (freedom) theoretical knowledge is impossible. This requires a grounding of all knowledge, empirical and abstract, in both mind and world, but the fall of traditional foundationalism has led many to doubt the viability of this 'classical' project. The book challenges this skepticism, charting a new foundational methodology, foundational holism, that differs from others in being holistic, world-oriented, and universal (i.e., applicable to all fields of knowledge). Using this methodology, Epistemic Friction develops an integrated theory of knowledge, truth, and logic. This includes (i) a dynamic model of knowledge, incorporating some of Quine's revolutionary ideas while rejecting his narrow empiricism, (ii) a substantivist, non-traditional correspondence theory of truth, and (iii) an outline of a joint grounding of logic in mind and world. The model of knowledge subjects all disciplines to robust norms of both veridicality and conceptualization. The correspondence theory is at once robust, universal, and flexible, allowing multiple patterns of correspondence, including complex and indirect patterns. Logic's systematic grounding brings it in line with other disciplines without neglecting its strong necessity, generality, and normativity, which are explained by its semantic formality.