Number Theory and Its Applications
Title | Number Theory and Its Applications PDF eBook |
Author | Cem Y. Yildrim |
Publisher | CRC Press |
Pages | 368 |
Release | 2020-03-06 |
Genre | Mathematics |
ISBN | 1000673138 |
This valuable reference addresses the methods leading to contemporary developments in number theory and coding theory, originally presented as lectures at a summer school held at Bilkent University, Ankara, Turkey.
Logic and Algebra
Title | Logic and Algebra PDF eBook |
Author | Aldo Ursini |
Publisher | Routledge |
Pages | 728 |
Release | 2017-10-05 |
Genre | Mathematics |
ISBN | 1351434721 |
""Attempts to unite the fields of mathematical logic and general algebra. Presents a collection of refereed papers inspired by the International Conference on Logic and Algebra held in Siena, Italy, in honor of the late Italian mathematician Roberto Magari, a leading force in the blossoming of research in mathematical logic in Italy since the 1960s.
Lectures on Symplectic Geometry
Title | Lectures on Symplectic Geometry PDF eBook |
Author | Ana Cannas da Silva |
Publisher | Springer |
Pages | 240 |
Release | 2004-10-27 |
Genre | Mathematics |
ISBN | 354045330X |
The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and clarifications have been made, and the layout has been improved.
Lecture Notes On Calculus Of Variations
Title | Lecture Notes On Calculus Of Variations PDF eBook |
Author | Kung-ching Chang |
Publisher | World Scientific |
Pages | 325 |
Release | 2016-09-16 |
Genre | Mathematics |
ISBN | 981314470X |
This is based on the course 'Calculus of Variations' taught at Peking University from 2006 to 2010 for advanced undergraduate to graduate students majoring in mathematics. The book contains 20 lectures covering both the theoretical background material as well as an abundant collection of applications. Lectures 1-8 focus on the classical theory of calculus of variations. Lectures 9-14 introduce direct methods along with their theoretical foundations. Lectures 15-20 showcase a broad collection of applications. The book offers a panoramic view of the very important topic on calculus of variations. This is a valuable resource not only to mathematicians, but also to those students in engineering, economics, and management, etc.
Lecture Notes in Algebraic Topology
Title | Lecture Notes in Algebraic Topology PDF eBook |
Author | James F. Davis |
Publisher | American Mathematical Society |
Pages | 385 |
Release | 2023-05-22 |
Genre | Mathematics |
ISBN | 1470473682 |
The amount of algebraic topology a graduate student specializing in topology must learn can be intimidating. Moreover, by their second year of graduate studies, students must make the transition from understanding simple proofs line-by-line to understanding the overall structure of proofs of difficult theorems. To help students make this transition, the material in this book is presented in an increasingly sophisticated manner. It is intended to bridge the gap between algebraic and geometric topology, both by providing the algebraic tools that a geometric topologist needs and by concentrating on those areas of algebraic topology that are geometrically motivated. Prerequisites for using this book include basic set-theoretic topology, the definition of CW-complexes, some knowledge of the fundamental group/covering space theory, and the construction of singular homology. Most of this material is briefly reviewed at the beginning of the book. The topics discussed by the authors include typical material for first- and second-year graduate courses. The core of the exposition consists of chapters on homotopy groups and on spectral sequences. There is also material that would interest students of geometric topology (homology with local coefficients and obstruction theory) and algebraic topology (spectra and generalized homology), as well as preparation for more advanced topics such as algebraic $K$-theory and the s-cobordism theorem. A unique feature of the book is the inclusion, at the end of each chapter, of several projects that require students to present proofs of substantial theorems and to write notes accompanying their explanations. Working on these projects allows students to grapple with the “big picture”, teaches them how to give mathematical lectures, and prepares them for participating in research seminars. The book is designed as a textbook for graduate students studying algebraic and geometric topology and homotopy theory. It will also be useful for students from other fields such as differential geometry, algebraic geometry, and homological algebra. The exposition in the text is clear; special cases are presented over complex general statements.
Harmonic Analysis on Free Groups
Title | Harmonic Analysis on Free Groups PDF eBook |
Author | Figa-Talamanca |
Publisher | CRC Press |
Pages | 164 |
Release | 1983-08-17 |
Genre | Mathematics |
ISBN | 9780824770426 |
This book presents an account of recent results on the theory of representations and the harmonic analysis of free groups. It emphasizes the analogy with the theory of representations of noncompact semisimple Lie groups and restricts the focus to a class of irreducible unitary representations.
Arbeitstagung Bonn, 1984
Title | Arbeitstagung Bonn, 1984 PDF eBook |
Author | Friedrich Hirzebruch |
Publisher | Springer |
Pages | 514 |
Release | 1985 |
Genre | Electronic books |
ISBN |