Published: 27 July 2017 (Estimated)
360 Pages
246x171mm
ISBN: 9780198777892
An ambitious new system of logic
Draws on expertise in mathematical, philosophical and computational logic
Makes original use of proof theory
A valuable resource for semantics, mathematics, philosophy of language, and formal epistemology
Neil Tennant presents an original logical system with unusual philosophical, proof-theoretic, metalogical, computational, and revision-theoretic virtues. Core Logic, which lies deep inside Classical Logic, best formalizes rigorous mathematical reasoning. It captures constructive relevant reasoning. And the classical extension of Core Logic handles non-constructive reasoning. These core systems fix all the mistakes that make standard systems harbor counterintuitive irrelevancies. Conclusions reached by means of core proof are relevant to the premises used. These are the first systems that ensure both relevance and adequacy for the formalization of all mathematical and scientific reasoning. They are also the first systems to ensure that one can make deductive progress with potential logical strengthening by chaining proofs together: one will prove, if not the conclusion sought, then (even better!) the inconsistency of one's accumulated premises. So Core Logic provides transitivity of deduction with potential epistemic gain. Because of its clarity about the true internal structure of proofs, Core Logic affords advantages also for the automation of deduction and our appreciation of the paradoxe
1: Introduction and Overview
2: The Road to Core Logic
3: The Logic of Evaluation
4: From the Logic of Evaluation to the Logic of Deduction
5: Motivating the Rules of Sequent Calculus
6: Transitivity of Deducibility
7: Epistemic Gain
8: Truthmakers and Consequence
9: Transmission of Truthmakers
10: The Relevance Properties of Core Logic
11: Core Logic and the Paradoxes
12: Replies to Critics of Core Logic
Published: 01 June 2017 (Estimated)
672 Pages
234x156mm
hard cover ISBN: 9780198788003
soft cover ISBN: 9780198788010
Presents a comprehensive introduction to the role that cryptography plays in the modern world
Introductory, self-contained and widely accessible
Focuses on the issues that are of concern to users and practitioners, rather than theorists
Can be used as the basis of an educational course through the provision of structured learning outcomes, further reading and activities for each chapter
Also considers wider societal issues that arise concerning the use of cryptography
Almost no prior knowledge of mathematics is required
New chapter on controlling use of cryptography following revelations by former NSA contractor Edward Snowden
New chapter on cryptographic protection of personal devices such as mobile phones, including cryptography behind WhatsApp and Apple's iOS operating system
New case studies concerning Tor and Bitcoin
Updated case studies to feature new developments including TLS 1.3, LTE and Apple Pay
Extended core material to include techniques gaining popularity such as SHA3, authenticated encryption modes, key derivation functions, and key wrapping
Setting the Scene
1: Basic Principles
2: Historical Cryptosystems
3: Theoretical versus Practical Security
The Cryptographic Toolkit
4: Symmetric Encryption
5: Public-Key Encryption
6: Data Integrity
7: Digital Signature Schemes
8: Entity Authentication
9: Cryptographic Protocols
Key Management
10: Key Management
11: Public-Key Management
Use of Cryptography
12: Cryptographic Applications
13: Cryptography for Personal Devices
14: Control of Cryptography
15: Closing Remarks
Lecture Notes of the Les Houches Summer School: Volume 104, July 2015
Published: 15 June 2017 (Estimated)
672 Pages | 64 figures/illustrations
246x171mm
ISBN: 9780198797319
Authoritative set of lecture notes on stochastic processes and Random Matrix Theory (RMT)
Suitable for graduate students, PhDs, post-docs in both Physics and Mathematics
Detailed presentation of recent advances
Includes topical subjects like the Kardar-Parisi-Zhang (KPZ) universality class, low dimensional heat transport, integrable probability
The field of stochastic processes and Random Matrix Theory (RMT) has been a rapidly evolving subject during the last fifteen years. The continuous development and discovery of new tools, connections and ideas have led to an avalanche of new results. These breakthroughs have been made possible thanks, to a large extent, to the recent development of various new techniques in RMT.
Matrix models have been playing an important role in theoretical physics for a long time and they are currently also a very active domain of research in mathematics. An emblematic example of these recent advances concerns the theory of growth phenomena in the Kardar-Parisi-Zhang (KPZ) universality class where the joint efforts of physicists and mathematicians during the last twenty years have unveiled the beautiful connections between this fundamental problem of statistical mechanics and the theory of random matrices, namely the fluctuations of the largest eigenvalue of certain ensembles of random matrices.
This text not only covers this topic in detail but also presents more recent developments that have emerged from these discoveries, for instance in the context of low dimensional heat transport (on the physics side) or integrable probability (on the mathematical side).
1: History, Oriol Bohigas, Hans Weidenmuller
2: Integrable Probability: Stochastic Vertex Models and Symmetric Functions, Alexei Borodin, Leonid Petrov
3: Free Probability, Alice Guionnet
4: The Kardar-Parisi-Zhang Equation: A Statistical Physics Perspective, Herbet Spohn
5: Random Matrix Theory and Quantum Chromodynamics, Gernot Akemann
6: Random Matrix Theory and (Big) Data Analysis, Jean-Philippe Bouchaud
7: Random Matrices and Loop Equations, Bertrand Eynard
8: Random Matrices and Number Theory: Some Recent Themes, Jon P. Keating
9: Modern Telecommunications: A Playground for Physicists?, Aris L. Moustakas
10: Random Matrix Approaches to Open Quantum Systems, Henning Schomerus
11: Impurity Models and Products of Random Matrices, Alain Comtet, Yves Tourigny
12: Gaussian Multiplicative Chaos and Lioville Quantum Gravity, Remi Rhodes, Vincent Vargas
13: Quantum Spin Chains and Classical Integrable Systems, Anton Zabrodin