Details an original approach to the history of logic and mathematics
Contributes to debates on proof-theoretic semantics, databank management,
and stochastics
Features papers from a meeting at the University of Konstanz
Open Access
This volume examines the many contributions of Paul Lorenzen, an outstanding philosopher
from the latter half of the 20th century. It features papers focused on integrating Lorenzen's
original approach into the history of logic and mathematics. The papers also explore how
practitioners can implement Lorenzen’s systematical ideas in today’s debates on proof-theoretic
semantics, databank management, and stochastics. Coverage details key contributions of
Lorenzen to constructive mathematics, Lorenzen’s work on lattice-groups and divisibility theory,
and modern set theory and Lorenzen’s critique of actual infinity. The contributors also look at
the main problem of Grundlagenforschung and Lorenzen’s consistency proof and Hilbert’s
larger program. In addition, the papers offer a constructive examination of a Russell-style
Ramified Type Theory and a way out of the circularity puzzle within the operative justification
of logic and mathematics. Paul Lorenzen's name is associated with the Erlangen School of
Methodical Constructivism, of which the approach in linguistic philosophy and philosophy of
science determined philosophical discussions especially in Germany in the 1960s and 1970s.
This volume features 10 papers from a meeting that took place at the University of Konstanz
Due 2021-07-17
1st ed. 2021, IX, 264 p.
Hardcover
ISBN 978-3-030-65823-6
Product category : Contributed volume
Series : Logic, Epistemology, and the Unity of Scienc
Philosophy : Philosophy of Mathematics
Presents original research papers on the topic of complex slant submanifolds
and geometry
Includes contributions from experts from around the world
Discusses significant research problems, gives rigorous proofs, and motivates
for further research
This book contains an up-to-date survey and self-contained chapters on complex slant
submanifolds and geometry, authored by internationally renowned researchers. The book
discusses a wide range of topics, including slant surfaces, slant submersions, nearly Kaehler,
locally conformal Kaehler, and quaternion Kaehler manifolds. It provides several classification
results of minimal slant surfaces, quasi-minimal slant surfaces, slant surfaces with parallel
mean curvature vector, pseudo-umbilical slant surfaces, and biharmonic and quasi biharmonic
slant surfaces in Lorentzian complex space forms. Furthermore, this book includes new results
on slant submanifolds of para-Hermitian manifolds. This book also includes recent results on
slant lightlike submanifolds of indefinite Hermitian manifolds, which are of extensive use in
general theory of relativity and potential applications in radiation and electromagnetic fields.
Various open problems and conjectures on slant surfaces in complex space forms are also
included in the book. It presents detailed information on the most recent advances in the area,
making it valuable for scientists, educators and graduate students.
Due 2021-09-11
1st ed. 2021, XII, 338 p.
Hardcover
ISBN 978-981-16-0020-3
Product category : Contributed volume
Mathematics : Differential Geometry
Provides an extended collection of warm-up and fun activities to start a
lecture on logic or computer science
Illustrates the complete process of modelling and solving puzzles with
theorem provers
Maximizes students insights into modelling with logic, interpretation models,
or theorem proving
Shares many tips and examples on formalising natural language into logic
Keeping students involved and actively learning is challenging. Instructors in computer science
are aware of the cognitive value of modelling puzzles and often use logical puzzles as an
efficient pedagogical instrument to engage students and develop problem-solving skills. This
unique book is a comprehensive resource that offers teachers and students fun activities to
teach and learn logic. It provides new, complete, and running formalisation in Propositional
and First Order Logic for over 130 logical puzzles, including Sudoku-like puzzles, zebra-like
puzzles, island of truth, lady and tigers, grid puzzles, strange numbers, or self-reference
puzzles. Solving puzzles with theorem provers can be an effective cognitive incentive to
motivate students to learn logic. They will find a ready-to-use format which illustrates how to
model each puzzle, provides running implementations, and explains each solution. This concise
and easy-to-follow textbook is a much-needed support tool for students willing to explore
beyond the introductory level of learning logic and lecturers looking for examples to heighten
student engagement in their computer science courses.
Due 2021-10-11
1st ed. 2021, XIV, 360 p. 70 illus. in color.
Softcover
ISBN 978-3-030-62546-7
Product category : Undergraduate textbook
Computer Science : Mathematical Logic and Formal Languages
May 2021
Pages: 316
ISBN: 978-1-80061-008-8 (hardcover)
Boolean Structures: Combinatorics, Codification, Representation offers the first analytical and architectural approach to Boolean algebras based
combinatorial calculus and codification with applications in IT, quantum information and classification of data.
Introduction
Preliminary Notions
B3
B4
B5
Codification
Logical Spaces and Quantum Information
Application of Representation Theory
A Few Concluding Words
Glossary
Bibliography
Graduates and researchers in mathematical logic and physicists working on quantum information. May also be of interest to IT researchers and philosophers working on logic and information theory.
July 2021
Pages: 220
ISBN: 978-981-122-862-9 (hardcover)
The book is designed for undergraduate or beginning level graduate students, and students from interdisciplinary areas including engineers, and others who need to use partial differential equations, Fourier series, Fourier and Laplace transforms. The prerequisite is a basic knowledge of calculus, linear algebra, and ordinary differential equations.
The textbook aims to be practical, elementary, and reasonably rigorous; the book is concise in that it describes fundamental solution techniques for first order, second order, linear partial differential equations for general solutions, fundamental solutions, solution to Cauchy (initial value) problems, and boundary value problems for different PDEs in one and two dimensions, and different coordinates systems. Analytic solutions to boundary value problems are based on Sturm?Liouville eigenvalue problems and series solutions.
The book is accompanied with enough well tested Maple files and some Matlab codes that are available online. The use of Maple makes the complicated series solution simple, interactive, and visible. These features distinguish the book from other textbooks available in the related area.
Introduction
First Order Partial Differential Equations
Solution to One Dimensional Wave Equations
Orthogonal Functions & Expansions, and Sturm-Liouville Theory
Method of Separation Variables for Solving PDE BVPs in Cartesian Coordinates
Various Fourier Series, Properties and Convergence
Series Solutions of PDEs
Fourier and Laplace Transforms
Numerical Solution Techniques
Appendices:
ODE Review and Other Useful Information
Introduction to Maple
Undergraduate, beginning level mathematics/physics graduate students, students from interdisciplinary areas and engineering.
October 2021
Pages: 130
ISBN: 978-981-123-487-3 (hardcover)
The book is based on lecture notes of a course "from elementary number theory to an introduction to matrix theory" given at the Technion to gifted high school students. It is problem based, and covers topics in undergraduate mathematics that can be introduced in high school through solving challenging problems. These topics include Number theory, Set Theory, Group Theory, Matrix Theory, and applications to cryptography and search engines.
Introduction
Algebraic Structures
The Natural Numbers
The Integers
The Real Numbers
Introduction to Set Theory
The Pigeon Hole Principle and the Base 2 Number System
Introduction to Group Theory
Introduction to Matrix Theory
Fibonacci Numbers
Determinants and Eigenvalues
Page Rank and a Game of Numbers
High school students who love mathematics and mathematics teachers. Also good for professors of mathematics and maths education, students in the mathematical sciences and pre-service math teachers.