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Kilmer S: An Introduction to Point-Set
Topology

An Introduction to Point-Set Topology

Developments in Mathematics

A large mathematical community throughout the world actively works in functional analysis and uses profound techniques from topology.&nbsp;Written by experts in the field, this book is a treasure trove for researchers and graduate students studying the interplay among the areas of point-set and descriptive topology, modern analysis, set theory, topological vector spaces, including Banach spaces, and continuous function spaces. This second edition continues in the same spirit of the acclaimed first edition, providing new insights into the connections between the topological properties of linear function spaces and their applications in functional analysis. It has been expanded by adding completely new Chapters 17-21, presenting results concerning, but not limited to, topological spaces and groups with G-bases, various concepts related to networks and their applications in topology and functional analysis, and those that develop topological and analytic methods related to Grothendieck Banach spaces and Boolean algebras with the Nikodym property.

The book will continue to serve as a reference for present and future work done in this area and could serve as a valuable supplement to advanced graduate courses in functional analysis, set-theoretic topology, or the theory of function spaces.

Updated and Expanded

Descriptive Topology in Selected Topics of Functional Analysis

Synthesis Lectures on Engineering, Science, and Technology

This book provides an introductory overview of generating functions (GFs) and their applications. The authors begin by providing background information on the origin of GFs. The book then introduces the most commonly encountered GFs in engineering and applied sciences, such as ordinary GFs, exponential GFs, and probability GFs. This third edition includes an expanded discussion of the applications of GFs in a variety of applied science and engineering fields. The authors have also added two new chapters that cover the applications in mathematics and computer science, including algebra, combinatorics, geometry, graph theory, number theory, trigonometry, algorithm analysis, signal processing, and machine learning.In addition, this book:<ul><li>Provides readers with an essential overview of generating functions and their applications</li><li>Introduces the concepts at an appropriate level for beginners in applied science and engineering fields</li><li>Demonstrates the various applications of generating functions using practical problems and examples</li></ul>About the AuthorsRajan Chattamvelli, Ph.D., is a Professor in the School of Computer Science and Engineering at Amrita University, Amaravati. &nbsp;He has published more than 20 research articles in international journals, and his research interests include computational statistics, design of algorithms, parallel computing, cryptography, data mining, machine learning, and big data analytics.
 Ramalingam Shanmugam, Ph.D., is an Honorary Professor in the School of Health Administration at Texas State University, San Marcos.&nbsp; He is the Editor-in-Chief of several journals including&nbsp;
 Advances in Life Sciences; Global Journal of Research and Review; Journal of Obesity and Metabolism; 
 and the&nbsp;
 International Journal of Research in Medical Sciences
 . He has published more than 200 research articles and 120 conference papers.&nbsp; His research interests include&nbsp;theoretical and computational statistics, number theory, operations research, biostatistics, decision making, infectious disease modeling, patient risk management, cost-effective analysis and epidemiology.

Generating Functions in Engineering and the Applied Sciences

Textbooks in Mathematics

This text focuses on the primary topics in a first course in Linear Algebra including additional advanced topics related to data analysis, singular value decomposition and connections to differential equations. This is a lab text that would lead a class through Linear Algebra using Mathematica demonstrations and Mathematica coding

Labs and Projects with Mathematica ®

Exploring Linear Algebra

Problem Solving in Mathematics and Beyond

"Geometry is often seen as one of the most beautiful aspects of mathematics. This beauty is probably a result of the fact that one can "see" this aspect of mathematics. Most people are exposed to the very basic elements of geometry throughout their schooling, concentrated in the secondary school curriculum. High schools in the United States offer one year of concentrated geometry teaching, allowing students to observe how a mathematician functions, since everything that is accepted beyond the basic axioms must be proved. However, as the course is only one year long, a great amount of geometry remains to be exposed to the general audience. That is the challenge of this book, wherein we will present a plethora of amazing geometric relationships. We begin with the special relationship of the Golden Ratio, before considering unexpected concurrencies and collinearities. Next, we present some surprising results that arise when squares and similar triangles are placed on triangle sides, followed by a discussion of concyclic points and the relationship between circles and various linear figures. Moving on to more advanced aspects of linear geometry, we consider the geometric wonders of polygons. Finally, we address geometric surprises and fallacies, before concluding with a chapter on the useful concept of homothety, which is not included in the American year-long course in geometry"--

Journey Through The Wonders Of Plane Geometry, A

This surprisingly accessible book uses key math concepts and more than 500 short exercises to teach functional programming to experienced coders. Functional programming is a coding paradigm that emphasizes functions, repeatable computations that take input data and produce corresponding outputs. Functions are also important concepts in math, and a lot of deep mathematical insights shed light on functional computer programming. In this book, the author uses functional programming to introduce mathematical concepts – most notably set theory, abstract algebra, and category theory – and in turn uses that math to describe functional programming design patterns. The more than 500 short programming exercises included in the book will help you master functional programming and math skills alike, with code examples presented in the F# language.

Explore Set Theory, Abstract Algebra, and Category Theory with Functional Programming

The Book of Functions

The Mending of Broken Bones reveals that far from a set of mundane exercises, algebra is the delicate craft of untangling numerical puzzles to uncover the hidden patterns and surprising behaviors of the numbers themselves. As Paul Lockhart shows, you don't have to be a mathematician to experience the joy and creativity of mathematical discovery.

A Modern Guide to Classical Algebra

The Mending of Broken Bones

Number Systems: A Path into Rigorous Mathematics aims to introduce number systems to an undergraduate audience in a way that emphasises the importance of rigour, and with a focus on providing detailed but accessible explanations of theorems and their proofs.

A Path into Rigorous Mathematics

Number Systems

Calculus for the Curious

Numerical Linear Algebra with Applications: Using MATLAB and Octave, Second Edition provides practical knowledge on modern computational techniques for the numerical solution of linear algebra problems. The book offers a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions. Useful to readers regardless of background, the text begins with six introductory courses to provide background for those who haven’t taken applied or theoretical linear algebra. This approach offers a thorough explanation of the issues and methods for practical computing using MATLAB as the vehicle for computation. Appropriate for advanced undergraduate and early graduate courses on numerical linear algebra, this useful textbook explores numerous applications to engineering and science.

Using MATLAB and Octave

Numerical Linear Algebra with Applications

Oxford Logic Guides

This book contains the first systematic exposition of a new discipline called positive topology, which brings many conceptual and mathematical innovations and many benefits for mathematical practice and applications, for the first time extending Darwin's evolutionary vision to the practice of mathematics.

A New Practice in Constructive Mathematics

Positive Topology

Weight representations are representations that include many important examples studied by both mathematicians and physicists. Using a combination of algebraic, geometric, and combinatorial methods, description of various classes (simple and indecomposable) of representations is provided in the book. The book serves advanced graduate students and junior researchers who work in the field of representation theory of Lie algebras.

Weight Representations

Princeton Mathematical Series

Princeton Legacy Library

An authoritative introduction to the essential features of étale cohomology A. Grothendieck’s work on algebraic geometry is one of the most important mathematical achievements of the twentieth century. In the early 1960s, he and M. Artin introduced étale cohomology to extend the methods of sheaf-theoretic cohomology from complex varieties to more general schemes. This work found many applications, not only in algebraic geometry but also in several different branches of number theory and in the representation theory of finite and p-adic groups. In this classic book, James Milne provides an invaluable introduction to étale cohomology, covering the essential features of the theory. Milne begins with a review of the basic properties of flat and étale morphisms and the algebraic fundamental group. He then turns to the basic theory of étale sheaves and elementary étale cohomology, followed by an application of the cohomology to the study of the Brauer group. After a detailed analysis of the cohomology of curves and surfaces, Milne proves the fundamental theorems in étale cohomology—those of base change, purity, Poincaré duality, and the Lefschetz trace formula—and applies these theorems to show the rationality of some very general L-series.

Étale Cohomology

An Introduction to Point-Set Topology

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