DATE PUBLISHED: August 2022
available from December 2023
FORMAT: Paperback
ISBN: 9781108940573
Is mathematics 'entangled' with its various formalisations? Or are the central concepts of mathematics largely insensitive to formalisation, or 'formalism free'? What is the semantic point of view and how is it implemented in foundational practice? Does a given semantic framework always have an implicit syntax? Inspired by what she calls the 'natural language moves' of Godel and Tarski, Juliette Kennedy considers what roles the concepts of 'entanglement' and 'formalism freeness' play in a range of logical settings, from computability and set theory to model theory and second order logic, to logicality, developing an entirely original philosophy of mathematics along the way. The treatment is historically, logically and set-theoretically rich, and topics such as naturalism and foundations receive their due, but now with a new twist.
'Kennedy creatively embeds Godel's ideal of 'formalism freeness' into myriad results in contemporary logic and foundations of mathematics, offering novel historical reconstructions of Tarski and Turing. A cutting-edge work of philosophy that synthesizes, while going beyond, our current ideas about foundations.' Juliet Floyd, Boston University
ISBN 9780367624118
Published August 1, 2022
350 Pages 94 B/W Illustrations
Lorentz Geometry is a very important intersection between Mathematics and Physics, being the mathematical language of General Relativity.
Learning this type of geometry is the first step in properly understanding questions regarding the structure of the universe, such as: What is the shape of the universe? What is a spacetime? What is the relation between gravity and curvature? Why exactly is time treated in a different manner than other spatial dimensions?
Introduction to Lorentz Geometry: Curves and Surfaces intends to provide the reader with the minimum mathematical background needed to pursue these very interesting questions, by presenting the classical theory of curves and surfaces in both Euclidean and Lorentzian ambient spaces simultaneously.
Over 300 exercises
Suitable for senior undergraduates and graduates studying Mathematics and Physics
Written in an accessible style without loss of precision or mathematical rigor
Solution manual available on www.routledge.com/9780367468644
1. Welcome to Lorentz-Minkowski Space. 1.1. Pseudo?Euclidean Spaces. 1.2. Subspaces of R??. 1.3. Contextualization in Special Relativity. 1.4. Isometries in R??. 1.5. Investigating O1(2, R) And O1(3, R). 1.6 Cross Product in R??. 2. Local Theory of Curves. 2.1. Parametrized Curves in R??. 2.2. Curves in the Plane. 2.3. Curves in Space. 3. Surfaces in Space. 3.1. Basic Topology of Surfaces. 3.2. Casual type of Surfaces, First Fundamental Form. 3.3. Second Fundamental Form and Curvatures. 3.4. The Diagonalization Problem. 3.5. Curves in Surface. 3.6. Geodesics, Variational Methods and Energy. 3.7. The Fundamental Theorem of Surfaces. 4. Abstract Surfaces and Further Topics. 4.1. Pseudo-Riemannian Metrics. 4.2. Riemannfs Classification Theorem. 4.3. Split-Complex Numbers and Critical Surfaces. 4.4 Digression: Completeness and Causality
ISBN 9781032384115
November 14, 2022 Forthcoming
198 Pages
This book introduces the vast subject of supersymmetry along with many specific examples of engineering applications, for example:
The design of quantum unitary gates using supersymmetric actions
Bosonic and Fermionic noise in quantum systems using the Hudson-Parthasarathy quantum stochastic calculus
Superstring theory applied to the quantum mechanics of neurons and supersymmetric quantum filtering theory which can, for example, be used to filter out the noise in a cavity resonator electromagnetic field produced by the presence electrons and positrons in a bath surrounding it
Simplified versions of super-Yang-Mills theory with gauge and gaugino fields, both transforming under the adjoint representation of the gauge group and elementary super-gravity models have also been introduced
All through the book, emphasis is laid upon exploiting the supersymmetry existing in the nature of Boson-Fermion exchange in designing engineering systems like quantum computers and analyzing the performance of systems in the presence of supersymmetric quantum noise.
1. Supersymmetry
2. Some Aspects of Superstring Theory
3. Interaction Between Light and Matter in a Cavity of Arbitrary Shape
4. Supersymmetric Yang-Mills Theory for non-Abelian Gauge Fields
5. Supersymmetric Quantum Stochastic Filtering Theory
6. Problems and Study Projects in non-Abelian Gauge and String Theory
7. The Atiyah-Singer Index Theorem and Its Application to Anomalies in Quantum Field Theory
ISBN 9780367634315
December 9, 2022 Forthcoming
248 Pages 1 Color & 46 B/W Illustrations
This book introduces best practices in longitudinal data analysis at intermediate level, with a minimum number of formulas without sacrificing depths. It meets the need to understand statistical concepts of longitudinal data analysis by visualizing important techniques instead of using abstract mathematical formulas. Different solutions such as multiple imputation are explained conceptually and consequences of missing observations are clarified using visualization techniques. Key features include the following:
? Provides datasets and examples online
? Gives state-of-the-art methods of dealing with missing observations in a non-technical way with a special focus on sensitivity analysis
? Conceptualises the analysis of comparative (experimental and observational) studies
It is the ideal companion for researcher and students in epidemiological, health, and social and behavioral sciences working with longitudinal studies without a mathematical background.
1. Scientific Framework of Data Analysis
2. Revisiting and Shortcomings of Standard Linear Regression Models
3. An Introduction to the Analysis of Longitudinal Data
4. Model Building for Longitudinal Data Analysis
5. Analysis of a Pre/Post Measurement Design
6. Analysis of Longitudinal Life-Event Studies
7. Analysis of Longitudinal Experimental Studies
Volume 7 in the series Advances in Analysis and Geometry
https://doi.org/10.1515/9783110642995
The book constructs explicitly the fundamental solution of the sub-Laplacian operator for a family of model domains in Cn+1. This type of domain is a good point-wise model for a Cauchy-Rieman (CR) manifold with diagonalizable Levi form. Qualitative results for such operators have been studied extensively, but exact formulas are difficult to derive. Exact formulas are closely related to the underlying geometry and lead to equations of classical types such as hypergeometric equations and Whittakerfs equations.
A mathematically rigorous study of sub-Laplacian operators on some model domains in C^{n+1}.
Presents the advanced theories in an easy-to-understand way.
Of interest to researchers and graduate students working in analysis and geometry.
Author information
Der-Chen Chang, Georgetown University, Washington, D.C., USA; Jingzhi Tie, University of Georgia, Georgia, USA.
Analysis
Mathematics
In the series De Gruyter Textbook
https://doi.org/10.1515/9783110780925
This exploration of a selection of fundamental topics and general purpose tools provides a roadmap to undergraduate students who yearn for a deeper dive into many of the concepts and ideas they have been encountering in their classes whether their motivation is pure curiosity or preparation for graduate studies. The topics intersect a wide range of areas encompassing both pure and applied mathematics. The emphasis and style of the book are motivated by the goal of developing self-reliance and independent mathematical thought. Mathematics requires both intuition and common sense as well as rigorous, formal argumentation.
This book attempts to showcase both, simultaneously encouraging readers to develop their own insights and understanding and the adoption of proof writing skills. The most satisfying proofs/arguments are fully rigorous and completely intuitive at the same time.
This reference provides a roadmap for students transitioning from an undergraduate mathematics curriculum and degree into a graduate mathematics curriculum and program.
Patrick Guidotti
graduated from the Universitat Zurich, did postdoctoral research at the Martin-Luther Universitat Halle-Wittenberg and at the California Institute of Technology, where he later held the position of Von Karman Instructor. He is currently a professor at UC Irvine.
General Mathematics
Mathematic