Topology for Beginners
Topology for Beginners is written for undergraduate students enrolled in a 4-year Bachelor of Science programme. The mathematical content covers a full introductory course on topology. The authors explain why the subject is worth understanding and convince the reader that it is fun and useful. It builds up gradually, explaining why one needs to go to more abstraction, rather than using the ‘Definition-Theorem-Proof’ method. It does not avoid geometrical descriptions that help the reader to see what is meant, rather than relying on symbol manipulation to obtain results that will be true but in a manner that doesn’t develop the intuition of the reader.
This book belongs to the genre of modern books that first motivate pictorially and then gently move up the path of mathematical rigour. Where concepts are introduced, or results are proved, the authors also indicate how and where they are used further in Topology, that lead to direct mathematical, natural science, and social science applications. By the end of the book, advanced topics are introduced in a way that makes them intelligible. It also provides many exercises to hone the reader’s skills at problem solving in Topology.
Noor Muhammad (1951–2004) was a notable mathematician who made original contributions to the fields of C*-algebras and the use of Topology in Functional Analysis. As a student of the distinguished Russian topologist, Grigory Barenblatt, he did significant work in topological algebras. Dr Noor Muhammad was Associate Professor in the Department of Mathematics at Quaid-i-Azam University, Islamabad.
Asghar Qadir is a mathematician, physicist and economist who did his PhD in Twistor Theory under Roger Penrose (NL) in 1971. He works in Relativity, Astrophysics, Cosmology, Lie Analysis and Special Functions and was Professor of Mathematics at Quaid-i-Azam University and then Physics at the National University of Sciences and Technology, Islamabad. He is a Fellow of the Pakistan Academy of Sciences and was a Senior Fellow of the Pakistan Institute of Development Economics and Associate Member of the International Centre for Theoretical Physics. He is also a Distinguished National Professor of the Higher Education Commission of Pakistan.
Imran Parvez Khan is presently Visiting Faculty at Bahria University, Islamabad. Apart from having a diverse teaching experience, he has supervised undergraduate research projects on Teaching of Topology and Recreational Mathematics. His research area is Topological String Theory.