**Author**: Martin D. Crossley

**Publisher:** Springer Science & Business Media

**ISBN:** 9781852337827

**Category : **Mathematics

**Languages : **en

**Pages : **244

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**Book Description**
This book brings the most important aspects of modern topology within reach of a second-year undergraduate student. It successfully unites the most exciting aspects of modern topology with those that are most useful for research, leaving readers prepared and motivated for further study. Written from a thoroughly modern perspective, every topic is introduced with an explanation of why it is being studied, and a huge number of examples provide further motivation. The book is ideal for self-study and assumes only a familiarity with the notion of continuity and basic algebra.

**Author**: Martin D. Crossley

**Publisher:** Springer Science & Business Media

**ISBN:** 9781852337827

**Category : **Mathematics

**Languages : **en

**Pages : **244

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**Book Description**
This book brings the most important aspects of modern topology within reach of a second-year undergraduate student. It successfully unites the most exciting aspects of modern topology with those that are most useful for research, leaving readers prepared and motivated for further study. Written from a thoroughly modern perspective, every topic is introduced with an explanation of why it is being studied, and a huge number of examples provide further motivation. The book is ideal for self-study and assumes only a familiarity with the notion of continuity and basic algebra.

**Author**: Avishek Adhikari

**Publisher:** Springer Nature

**ISBN:** 981166577X

**Category : **Mathematics

**Languages : **en

**Pages : **385

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**Book Description**
This second of the three-volume book is targeted as a basic course in topology for undergraduate and graduate students of mathematics. It focuses on many variants of topology and its applications in modern analysis, geometry, algebra, and the theory of numbers. Offering a proper background on topology, analysis, and algebra, this volume discusses the topological groups and topological vector spaces that provide many interesting geometrical objects which relate algebra with geometry and analysis. This volume follows a systematic and comprehensive elementary approach to the topology related to manifolds, emphasizing differential topology. It further communicates the history of the emergence of the concepts leading to the development of topological groups, manifolds, and also Lie groups as mathematical topics with their motivations. This book will promote the scope, power, and active learning of the subject while covering a wide range of theories and applications in a balanced unified way.

**Author**: Avishek Adhikari

**Publisher:** Springer Nature

**ISBN:** 9811665095

**Category : **
**Languages : **en

**Pages : **
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**Book Description**

**Author**: M.A. Armstrong

**Publisher:** Springer Science & Business Media

**ISBN:** 1475717938

**Category : **Mathematics

**Languages : **en

**Pages : **251

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**Book Description**
In this broad introduction to topology, the author searches for topological invariants of spaces, together with techniques for their calculating. Students with knowledge of real analysis, elementary group theory, and linear algebra will quickly become familiar with a wide variety of techniques and applications involving point-set, geometric, and algebraic topology. Over 139 illustrations and more than 350 problems of various difficulties help students gain a thorough understanding of the subject.

**Author**: Mohamed Abdelghani

**Publisher:** CRC Press

**ISBN:** 0429809247

**Category : **Business & Economics

**Languages : **en

**Pages : **400

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**Book Description**
It is well-known that modern stochastic calculus has been exhaustively developed under usual conditions. Despite such a well-developed theory, there is evidence to suggest that these very convenient technical conditions cannot necessarily be fulfilled in real-world applications. Optional Processes: Theory and Applications seeks to delve into the existing theory, new developments and applications of optional processes on "unusual" probability spaces. The development of stochastic calculus of optional processes marks the beginning of a new and more general form of stochastic analysis. This book aims to provide an accessible, comprehensive and up-to-date exposition of optional processes and their numerous properties. Furthermore, the book presents not only current theory of optional processes, but it also contains a spectrum of applications to stochastic differential equations, filtering theory and mathematical finance. Features Suitable for graduate students and researchers in mathematical finance, actuarial science, applied mathematics and related areas Compiles almost all essential results on the calculus of optional processes in unusual probability spaces Contains many advanced analytical results for stochastic differential equations and statistics pertaining to the calculus of optional processes Develops new methods in finance based on optional processes such as a new portfolio theory, defaultable claim pricing mechanism, etc. Authors Mohamed Abdelghani completed his PhD in mathematical finance from the University of Alberta, Edmonton, Canada. He is currently working as a vice president in quantitative finance and machine learning at Morgan Stanley, New York, USA. Alexander Melnikov is a professor in mathematical finance at the University of Alberta. His research interests belong to the area of contemporary stochastic analysis and its numerous applications in mathematical finance, statistics and actuarial science. He has written six books as well as over 100 research papers in leading academic journals.

**Author**: Mahima Ranjan Adhikari

**Publisher:** Springer

**ISBN:** 813222843X

**Category : **Mathematics

**Languages : **en

**Pages : **615

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**Book Description**
This book provides an accessible introduction to algebraic topology, a field at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Comprising eighteen chapters and two appendices, the book integrates various concepts of algebraic topology, supported by examples, exercises, applications and historical notes. Primarily intended as a textbook, the book offers a valuable resource for undergraduate, postgraduate and advanced mathematics students alike. Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups and cell complexes, etc. The book studies a variety of maps, which are continuous functions between spaces. It also reveals the importance of algebraic topology in contemporary mathematics, theoretical physics, computer science, chemistry, economics, and the biological and medical sciences, and encourages students to engage in further study.

**Author**: Dan Edwin Christie

**Publisher:** Macmillan Publishing Company

**ISBN:**
**Category : **Mathematics

**Languages : **en

**Pages : **256

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**Book Description**

**Author**:

**Publisher:**
**ISBN:**
**Category : **Electronic journals

**Languages : **en

**Pages : **
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**Book Description**
Fully refereed international journal dealing with all aspects of geometry and topology and their applications.

**Author**: David DeVidi

**Publisher:** Springer Science & Business Media

**ISBN:** 9400702140

**Category : **Philosophy

**Languages : **en

**Pages : **486

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**Book Description**
The volume includes twenty-five research papers presented as gifts to John L. Bell to celebrate his 60th birthday by colleagues, former students, friends and admirers. Like Bellâ€™s own work, the contributions cross boundaries into several inter-related fields. The contributions are new work by highly respected figures, several of whom are among the key figures in their fields. Some examples: in foundations of maths and logic (William Lawvere, Peter Aczel, Graham Priest, Giovanni Sambin); analytical philosophy (Michael Dummett, William Demopoulos), philosophy of science (Michael Redhead, Frank Arntzenius), philosophy of mathematics (Michael Hallett, John Mayberry, Daniel Isaacson) and decision theory and foundations of economics (Ken Bimore). Most articles are contributions to current philosophical debates, but contributions also include some new mathematical results, important historical surveys, and a translation by Wilfrid Hodges of a key work of arabic logic.

**Author**:

**Publisher:**
**ISBN:**
**Category : **Mathematical statistics

**Languages : **en

**Pages : **192

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**Book Description**