This volume is dedicated to Paul Erdos, who profoundly influenced mathematics in the twentieth century, with over 1200 papers in number theory, complex analysis, probability theory, geometry, interpretation theory, algebra set theory and combinatorics. One of Erdos' hallmarks was the host of stimulating problems and conjectures, to many of which he attached monetary prices, in accordance with their notoriety. A feature of this volume is a collection of some 50 outstanding unsolved problems, together with their 'value'! Eminent mathematicians from around the world have contributed articles to this volume that reflect the diversity of Erdos' interests, and it will be a fund of insight for number theorists, combinatorialists, set theorists and analysts.

Number theory, the branch of mathematics which studies the properties of the integers, is a repository of interesting and quite varied problems, sometimes impossibly difficult ones. The authors have gathered together a collection of problems from various topics in number theory that they find beautiful, intriguing, and from a certain point of view instructive. In addition to revealing the beauty of the problems themselves, they have tried to give glimpses into deeper, related mathematics. The book presents problems whose solutions can be obtained using elementary methods. No prior knowledge of number theory is assumed.

The authors'' aim is to present a review of experimental and theoretical research that has been done to establish and to explain the physical properties of actinide compounds. The book is aimed at physicists and chemists. It was thought useful to collect a large selection of diagrams of experimental data scattered in the literature. Experiment and theory are presented separately, with cross­ references. Not all work has been included: rather, typical examples are discussed. We apologize to all researchers whose work has not been quoted. Since we report on an active field of research, clearly the data and their interpretation are subject to change. We benefitted greatly from discussions with many of our colleagues, particularly with Drs. G. H. Lander and W. Suski. The help of Mrs. C. Bovey and Ch. Lewis in the preparation of the manuscript, and the artwork and photo­ graphic work of Ms. Y. Magnenat and E. Spielmann of the Institute of Experi­ mental Physics of the University of Lausanne, are gratefully acknowledged. Our particular thanks are due to Ms. J. Ubby for her skillful and patient editorial work.

This volume is dedicated to Paul Erdos, who profoundly influenced mathematics in the twentieth century, with over 1200 papers in number theory, complex analysis, probability theory, geometry, interpretation theory, algebra set theory and combinatorics. One of Erdos' hallmarks was the host of stimulating problems and conjectures, to many of which he attached monetary prices, in accordance with their notoriety. A feature of this volume is a collection of some 50 outstanding unsolved problems, together with their 'value'! Eminent mathematicians from around the world have contributed articles to this volume that reflect the diversity of Erdos' interests, and it will be a fund of insight for number theorists, combinatorialists, set theorists and analysts.

Number theory, the branch of mathematics which studies the properties of the integers, is a repository of interesting and quite varied problems, sometimes impossibly difficult ones. The authors have gathered together a collection of problems from various topics in number theory that they find beautiful, intriguing, and from a certain point of view instructive. In addition to revealing the beauty of the problems themselves, they have tried to give glimpses into deeper, related mathematics. The book presents problems whose solutions can be obtained using elementary methods. No prior knowledge of number theory is assumed.

The authors'' aim is to present a review of experimental and theoretical research that has been done to establish and to explain the physical properties of actinide compounds. The book is aimed at physicists and chemists. It was thought useful to collect a large selection of diagrams of experimental data scattered in the literature. Experiment and theory are presented separately, with cross­ references. Not all work has been included: rather, typical examples are discussed. We apologize to all researchers whose work has not been quoted. Since we report on an active field of research, clearly the data and their interpretation are subject to change. We benefitted greatly from discussions with many of our colleagues, particularly with Drs. G. H. Lander and W. Suski. The help of Mrs. C. Bovey and Ch. Lewis in the preparation of the manuscript, and the artwork and photo­ graphic work of Ms. Y. Magnenat and E. Spielmann of the Institute of Experi­ mental Physics of the University of Lausanne, are gratefully acknowledged. Our particular thanks are due to Ms. J. Ubby for her skillful and patient editorial work.