How many groups of order n are there? This is a natural question for anyone studying group theory, and this Tract provides an exhaustive and up-to-date account of research into this question spanning almost fifty years. The authors presuppose an undergraduate knowledge of group theory, up to and including Sylow's Theorems, a little knowledge of how a group may be presented by generators and relations, a very little representation theory from the perspective of module theory, and a very little cohomology theory - but most of the basics are expounded here and the book is more or less self-contained. Although it is principally devoted to a connected exposition of an agreeable theory, the book does also contain some material that has not hitherto been published. It is designed to be used as a graduate text but also as a handbook for established research workers in group theory.
How many groups of order n are there? This is a natural question for anyone studying group theory, and this Tract provides an exhaustive and up-to-date account of research into this question spanning almost fifty years. The authors presuppose an undergraduate knowledge of group theory, up to and including Sylow's Theorems, a little knowledge of how a group may be presented by generators and relations, a very little representation theory from the perspective of module theory, and a very little cohomology theory - but most of the basics are expounded here and the book is more or less self-contained. Although it is principally devoted to a connected exposition of an agreeable theory, the book does also contain some material that has not hitherto been published. It is designed to be used as a graduate text but also as a handbook for established research workers in group theory.
This book helps readers bridge the gap between school-level mathematical skills and the quantitative and analytical skills required at the professional level. It presents basic mathematical concepts in an everyday context, enabling readers to pick up skills with ease. Mathematics for Social Scientists: • Focuses on building foundational skills in reasoning, data analysis and quantitative methods that are a requisite for progressing to higher levels; • Helps readers express mathematical ideas in the form of sets, analyse arguments and their validity mathematically, interpret and handle data, and understand the concept and use of probability; • Includes a dedicated chapter on symmetry, perspective and art to encourage readers to reason, model and objectively evaluate everyday situations. The volume will be useful to students of various disciplines in Social Sciences and Liberal Arts. It will also be an invaluable companion to practitioners of social sciences, humanities and life sciences, as well as schoolteachers at the middle and higher secondary level.
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