EMS Tracts in Mathematics Vol. 32
ISBN print 978-3-03719-208-5,
DOI 10.4171/208
March 2020, 250 pages, hardcover, 17 x 24 cm.
K3 surfaces are a key piece in the classification of complex analytic or
algebraic surfaces. The term was coined by A. Weil in 1958 a result of
the initials Kummer, Kahler, Kodaira, and the mountain K2 found in Karakoram.
The most famous example is the Kummer surface discovered in the 19th century.
K3 surfaces can be considered as a 2-dimensional analogue of an elliptic curve, and the theory of periods ? called the Torelli-type theorem for K3 surfaces ? was established around 1970. Since then, several pieces of research on K3 surfaces have been undertaken and more recently K3 surfaces have even become of interest in theoretical physics.
The main purpose of this book is an introduction to the Torelli-type theorem for complex analytic K3 surfaces, and its applications. The theory of lattices and their reflection groups is necessary to study K3 surfaces, and this book introduces these notions. The book contains, as well as lattices and reflection groups, the classification of complex analytic surfaces, the Torelli-type theorem, the subjectivity of the period map, Enriques surfaces, an application to the moduli space of plane quartics, finite automorphisms of K3 surfaces, Niemeier lattices and the Mathieu group, the automorphism group of Kummer surfaces and the Leech lattice.
The author seeks to demonstrate the interplay between several sorts of mathematics and hopes the book will prove helpful to researchers in algebraic geometry and related areas, and to graduate students with a basic grounding in algebraic geometry.
Keywords: K3 surface, Enriques surface, Kummer surface, Torelli-type theorem, period, lattice, reflection group, automorphism group
ISBN: 978-1-119-62680-0 April 2020
This new edition provides an updated approach for students, engineers, and researchers to apply numerical methods for solving problems using MATLABR
This accessible book makes use of MATLABR software to teach the fundamental concepts for applying numerical methods to solve practical engineering and/or science problems. It presents programs in a complete form so that readers can run them instantly with no programming skill, allowing them to focus on understanding the mathematical manipulation process and making interpretations of the results.
Applied Numerical Methods Using MATLABR, Second Edition begins with an introduction to MATLAB usage and computational errors, covering everything from input/output of data, to various kinds of computing errors, and on to parameter sharing and passing, and more. The system of linear equations is covered next, followed by a chapter on the interpolation by Lagrange polynomial. The next sections look at interpolation and curve fitting, nonlinear equations, numerical differentiation/integration, ordinary differential equations, and optimization. Numerous methods such as the Simpson, Euler, Heun, Runge-kutta, Golden Search, Nelder-Mead, and more are all covered in those chapters. The eighth chapter provides readers with matrices and Eigenvalues and Eigenvectors. The book finishes with a complete overview of differential equations.
Provides examples and problems of solving electronic circuits and neural networks
Includes new sections on adaptive filters, recursive least-squares estimation, Bairstow's method for a polynomial equation, and more
Explains Mixed Integer Linear Programing (MILP) and DOA (Direction of Arrival) estimation with eigenvectors
Aimed at students who do not like and/or do not have time to derive and prove mathematical results
Applied Numerical Methods Using MATLABR, Second Edition is an excellent text for students who wish to develop their problem-solving capability without being involved in details about the MATLAB codes. It will also be useful to those who want to delve deeper into understanding underlying algorithms and equations.
ISBN: 978-1-119-52024-5
July 2020
384 Pages
This book, which is the update of a 1992 survey by the same authors, summarizes some known constructions of Hadamard Matrices that are based on algebraic and number theoretic methods. Hadamard matrices are of practical use in signal processing and design experiments among other applications. This book begins with basic definitions, and is followed by a chapter on Gauss sums, Jacobi sums and relative Gauss sums. Next, the authors discuss plug-in matrices, arrays, and sequences. M-structure is covered next, along with Menon Hadamard differences sets and regular Handmard matrices. The authors then discuss Paley difference sets, skew-Handmard matrices, and skew Handmard differences sets. Finally, the book concludes with a discussion of asymptotic existence of Handmard matrices and more on maximal determinant matrices.
ISBN : 9780198852247
Hardback
Published: 03 February 2020
192 Pages
234x156mm
ISBN: 9780198852247
As the famous Pythagorean statement reads, 'Number rules the universe', and its veracity is proven in the many mathematical discoveries that have accelerated the development of science, engineering, and even philosophy. A so called ", mathematics has guided and stimulated many aspects of human innovation down through the centuries.
In this book, Marcel Danesi presents a historical overview of the ten greatest achievements in mathematics, and dynamically explores their importance and effects on our daily lives. Considered as a chain of events rather than isolated incidents, Danesi takes us from the beginnings of modern day mathematics with Pythagoras, through the concept of zero, right the way up to modern computational algorithms.
Loaded with thought-provoking practical exercises and puzzles, Pythagoras' Legacy allows the reader to apply their knowledge and discover the significance of mathematics in their everyday lives.
1 The Pythagorean Theorem: The Birth of Mathematics
2 Prime Numbers: The DNA of Mathematics
3 Zero: Place-Holder and Peculiar Number
4 Pi: A Ubiquitous and Strange Number
5 Exponents: Notation and Discovery
6 e: A Very Special Number
7 i: Imaginary Numbers
8 Infinity: A Counterintuitive and Paradoxical Idea
9 Decidability: The Foundations of Mathematics
10 The Algorithm: Mathematics and Computers
ISBN : 9780190641221
Hardback
Published: 30 April 2020 (Estimated)
472 Pages
235x156mm
Logic and Computation in Philosophy Series
Recently, debates about mathematical structuralism have picked up steam again within the philosophy of mathematics, probing ontological and epistemological issues in novel ways. These debates build on discussions of structuralism which began in the 1960s in the work of philosophers such as Paul Benacerraf and Hilary Putnam; going further than these previous thinkers, however, these new debates also recognize that the motivation for structuralist views should be tied to methodological developments within mathematics. In fact, practically all relevant ideas and methods have roots in the structuralist transformation that modern mathematics underwent in the 19th and early 20th centuries.
This edited volume of new essays by top scholars in the philosophy of mathematics explores this previously overlooked 'pre-history' of mathematical structuralism. The contributors explore this historical background along two distinct but interconnected dimensions. First, they reconsider the methodological contributions of major figures in the history of mathematics, such as Dedekind, Hilbert, and Bourbaki, who are responsible for the introduction of new number systems, algebras, and geometries that transformed the landscape of mathematics. Second, they reexamine a range of philosophical reflections by mathematically inclined philosophers, like Russell, Cassirer, and Quine, whose work led to profound conclusions about logical, epistemological, and metaphysical aspects of structuralism.
Overall, the essays in this volume show not only that the pre-history of mathematical structuralism is much richer than commonly appreciated, but also that it is crucial to take into account this broader intellectual history for enriching current debates in the philosophy of mathematics. The insights included in this volume will interest scholars and students in the philosophy of mathematics, the philosophy of science, and the history of philosophy.
1. Erich Reck & Georg Schiemer: The Prehistory of Mathematical Structuralism: Introduction and Overview
Part I: Mathematical Developments
2. Paola Cantu: Grassmann's Concept Structuralism
3. Jose Ferreiros & Erich Reck: Dedekind's Mathematical Structuralism: From Galois Theory to Numbers, Sets, and Functions
4. Dirk Schlimm: Pasch's Empiricism as Methodological Structuralism
5. Georg Schiemer: Transfer Principles, Klein's Erlangen Program, and Methodological Structuralism
6. Wilfried Sieg: The Ways of Hilbert's Axiomatics: Structural and Formal
7. Audrey Yap: Noether as Mathematical Structuralist
8. Gerhard Heinzmann & Jean Petitot: The Functional Role of Structures in Bourbaki
9. Colin McLarty: Saunders Mac Lane: From Principia Mathematica through Gottingen to the Working Theory of Structures
Part II: Logical and Philosophical Reflections
10. Jessica Carter: Logic of Relations and Diagrammatic Reasoning: Structuralist Elements in the Work of Charles Sanders Peirce
11. Janet Folina: Poincare and the Pre-History of Mathematical Structuralism
12. Jeremy Heis: 'If Numbers Are To Be Anything At All, They Must Be Intrinsically Something': Bertrand Russell and Mathematical Structuralism
13. Erich Reck: Cassirer's Reception of Dedekind and the Structuralist Transformation of Mathematics
14. Wilfried Sieg: Methodological Frames: Paul Bernays, Mathematical Structuralism, and Proof Theory
15. Georg Schiemer: Carnap's Structuralist Thesis
16. Sean Morris: Explication as Elimination: W.V. Quine and Mathematical Structuralism