Mathematics Exercises

SINCE the first edition was published, numerical work with machines has come to play a regular part in education whether in mathematics or as a step to computer studies. This fact has been recognised in some syllabuses, notably that of the project for Mathematics in Education and Industry (M.E.I.). Since this text has been used in preparation for such examinations, it has been expanded to include suitable revision questions. The author wishes to thank the Oxford and Cambridge Board for leave to reprint questions from the M.E.I. A Level and Special Papers, and also to the Examinations Council of London University for questions from that University's Teachers' Certificate.

The author, the founder of the Greek Statistical Institute, has based this book on the two volumes of his Greek edition which has been used by over ten thousand students during the past fifteen years. It can serve as a companion text for an introductory or intermediate level probability course.

The author, the founder of the Greek Statistical Institute, has based this book on the two volumes of his Greek edition which has been used by over ten thousand students during the past fifteen years. It can serve as a companion text for an introductory or intermediate level probability course.

Authors: Gasiński, Leszek, Papageorgiou, Nikolaos S.
​Contains exercises ranging from easy to difficult, with level of difficulty designated
Features an encyclopedic volume of exercises in five core topics of mathematical analysis
Prepares students well for qualifying exams and tests their depth of understanding of the material

This book supplements the textbook of the authors" Lectures on Graph The­ ory" [6] by more than thousand exercises of varying complexity. The books match each other in their contents, notations, and terminology. The authors hope that both students and lecturers will find this book helpful for mastering and verifying the understanding of the peculiarities of graphs. The exercises are grouped into eleven chapters and numerous sections accord­ ing to the topics of graph theory: paths, cycles, components, subgraphs, re­ constructibility, operations on graphs, graphs and matrices, trees, independence, matchings, coverings, connectivity, matroids, planarity, Eulerian and Hamiltonian graphs, degree sequences, colorings, digraphs, hypergraphs. Each section starts with main definitions and brief theoretical discussions. They constitute a minimal background, just a reminder, for solving the exercises. the presented facts and a more extended exposition may be found in Proofs of the mentioned textbook of the authors, as well as in many other books in graph theory. Most exercises are supplied with answers and hints. In many cases complete solutions are given. At the end of the book you may find the index of terms and the glossary of notations. The "Bibliography" list refers only to the books used by the authors during the preparation of the exercisebook. Clearly, it mentions only a fraction of available books in graph theory. The invention of the authors was also driven by numerous journal articles, which are impossible to list here.