Abstract Algebra

Mathematics

Abstract Algebra by Justin R Smith
Algebraic Modeling of Topological and Computational Structures and Applications: THALES, Athens, Greece, July 1-3, 2015 By Sofia Lambropoulou
Plain Plane Geometry 1st Edition by Amol Sasane
Real Analysis: Series, Functions of Several Variables, and Applications By Miklós Laczkovich
Introduction to Cryptography (Undergraduate Texts in Mathematics) by Johannes Buchmann

Abstract Algebra by Justin R Smith

English | 2016 | ISBN: 1541014006 | 462 Pages | PDF | 4.3 MB

This book arose out of courses the author taught in Abstract Algebra, combinatorial group theory, Galois Theory, Algebraic Geometry, and Manifold Theory. It can be used for self-study or as a course textbook. It covers classic areas such as group theory, ring theory, linear algebra, and Galois theory. Its treatment of divison algebras over the real numbers includes quaternions and octonions. It also covers 20th century material on Gröbner bases, category theory and cohomology. The section on category theory also covers some multilinear and exterior algebra.

Algebraic Modeling of Topological and Computational Structures and
Applications: THALES, Athens, Greece, July 1-3, 2015 By Sofia Lambropoulou

English | PDF,EPUB | 2017 | 481 Pages | ISBN : 3319681028 | 19.85 MB

This interdisciplinary book covers a wide range of subjects, from pure mathematics (knots, braids, homotopy theory, number theory) to more applied mathematics (cryptography, algebraic specification of algorithms, dynamical systems) and concrete applications (modeling of polymers and ionic liquids, video, music and medical imaging). The main mathematical focus throughout the book is on algebraic modeling with particular emphasis on braid groups.
The research methods include algebraic modeling using topological structures, such as knots, 3-manifolds, classical homotopy groups, and braid groups. The applications address the simulation of polymer chains and ionic liquids, as well as the modeling of natural phenomena via topological surgery. The treatment of computational structures, including finite fields and cryptography, focuses on the development of novel techniques. These techniques can be applied to the design of algebraic specifications for systems modeling and verification.
This book is the outcome of a workshop in connection with the research project Thales on Algebraic Modeling of Topological and Computational Structures and Applications, held at the National Technical University of Athens, Greece in July 2015. The reader will benefit from the innovative approaches to tackling difficult questions in topology, applications and interrelated research areas, which largely employ algebraic tools.

Plain Plane Geometry 1st Edition by Amol Sasane

English | 7 Dec. 2015 | ISBN: 9814740438 | ASIN: B01B29FSYA | 287 Pages | AZW3 | 11.41 MB

The book constitutes an elementary course on Plane Euclidean Geometry, pitched at pre-university or at advanced high school level. It is a concise book treating the subject axiomatically, but since it is meant to be a first introduction to the subject, excessive rigour is avoided, making it appealing to a younger audience as well. The aim is to cover the basics of the subject, while keeping the subject lively by means of challenging and interesting exercises. This makes it relevant also for students participating in mathematics circles and in mathematics olympiads.
Each section contains several problems, which are not purely drill exercises, but are intended to introduce a sense of “play” in mathematics, and inculcate appreciation of the elegance and beauty of geometric results. There is an abundance of colour pictures illustrating results and their proofs. A section on hints and a further section on detailed solutions to all the exercises appear at the end of the book, making the book ideal also for self-study.

Real Analysis: Series, Functions of Several Variables, and Applications By Miklós Laczkovich

English | PDF,EPUB | 2017 | 396 Pages | ISBN : 1493973673 | 15.79 MB

This book develops the theory of multivariable analysis, building on the single variable foundations established in the companion volume, Real Analysis: Foundations and Functions of One Variable. Together, these volumes form the first English edition of the popular Hungarian original, Valós Analízis I & II, based on courses taught by the authors at Eötvös Loránd University, Hungary, for more than 30 years. Numerous exercises are included throughout, offering ample opportunities to master topics by progressing from routine to difficult problems. Hints or solutions to many of the more challenging exercises make this book ideal for independent study, or further reading.
Intended as a sequel to a course in single variable analysis, this book builds upon and expands these ideas into higher dimensions. The modular organization makes this text adaptable for either a semester or year-long introductory course. Topics include: differentiation and integration of functions of several variables; infinite numerical series; sequences and series of functions; and applications to other areas of mathematics. Many historical notes are given and there is an emphasis on conceptual understanding and context, be it within mathematics itself or more broadly in applications, such as physics. By developing the student’s intuition throughout, many definitions and results become motivated by insights from their context.

Introduction to Cryptography (Undergraduate Texts in Mathematics) by Johannes Buchmann

English | 1 Jan. 2001 | ISBN: 0387950346 | 292 Pages | PDF | 17 MB

Cryptography is a key technology in electronic key systems. It is used to keep data secret, digitally sign documents, access control and other such areas.