This textbook, aimed at advanced undergraduate or beginning graduate students in mathematics, introduces both the theory of Riemann surfaces, and of analytic functions between Riemann surfaces. The fi
This textbook, aimed at advanced undergraduate or beginning graduate students in mathematics, introduces both the theory of Riemann surfaces, and of analytic functions between Riemann surfaces. The f
Mathematical Explorations follows on from the author's previous book, Creative Mathematics, in the same series, and gives the reader experience in working on problems requiring a little more mathematical maturity. The author's main aim is to show that problems are often solved by using mathematics that is not obviously connected to the problem, and readers are encouraged to consider as wide a variety of mathematical ideas as possible. In each case, the emphasis is placed on the important underlying ideas rather than on the solutions for their own sake. To enhance understanding of how mathematical research is conducted, each problem has been chosen not for its mathematical importance, but because it provides a good illustration of how arguments can be developed. While the reader does not require a deep mathematical background to tackle these problems, they will find their mathematical understanding is enriched by attempting to solve them.
This text is about the geometric theory of discrete groups and the associated tesselations of the underlying space. The theory of Mobius transformations in n-dimensional Euclidean space is developed.
Intended as an undergraduate text on real analysis, this book includes all the standard material such as sequences, infinite series, continuity, differentiation, and integration, together with worked
Describing two cornerstones of mathematics, this basic textbook presents a unified approach to algebra and geometry. It covers the ideas of complex numbers, scalar and vector products, determinants, linear algebra, group theory, permutation groups, symmetry groups and aspects of geometry including groups of isometries, rotations, and spherical geometry. The book emphasises the interactions between topics, and each topic is constantly illustrated by using it to describe and discuss the others. Many ideas are developed gradually, with each aspect presented at a time when its importance becomes clearer. To aid in this, the text is divided into short chapters, each with exercises at the end. The related website features an HTML version of the book, extra text at higher and lower levels, and more exercises and examples. It also links to an electronic maths thesaurus, giving definitions, examples and links both to the book and to external sources.
With its emphasis on the argument principle in analysis and topology, this book represents a different approach to the teaching of complex analysis. The three-part treatment provides geometrical insig
Describing two cornerstones of mathematics, this basic textbook presents a unified approach to algebra and geometry. It covers the ideas of complex numbers, scalar and vector products, determinants, linear algebra, group theory, permutation groups, symmetry groups and aspects of geometry including groups of isometries, rotations, and spherical geometry. The book emphasises the interactions between topics, and each topic is constantly illustrated by using it to describe and discuss the others. Many ideas are developed gradually, with each aspect presented at a time when its importance becomes clearer. To aid in this, the text is divided into short chapters, each with exercises at the end. The related website features an HTML version of the book, extra text at higher and lower levels, and more exercises and examples. It also links to an electronic maths thesaurus, giving definitions, examples and links both to the book and to external sources.
This text is about the geometric theory of discrete groups and the associated tesselations of the underlying space. The theory of M bius transformations in n-dimensional Euclidean space is developed.
How do mathematicians approach a problem, explore the possibilities, and develop an understanding of a whole area around it? The issue is not simply about obtaining 'the answer'; rather, Beardon explains that a mathematical problem is just one of many related ones that should be simultaneously investigated and discussed at various levels, and that understanding this is a crucial step in becoming a creative mathematician. The book begins with some good advice about procedure, presentation, and organisation that will benefit every mathematician, budding, teaching or practised. In the rest of the book, Beardon presents a series of simple problems, then, through discussion, consideration of special cases, computer experiments, and so on, the reader is taken through these same problems, but at an increasing level of sophistication and generality. Mathematics is rarely a closed book, and seemingly innocent problems, when examined and explored, can lead to results of significance.
This book focuses on complex analytic dynamics, which dates from 1916 and is currently attracting considerable interest. The text provides a comprehensive, well-organized treatment of the foundations
