This book is a compilation of approximately nine hundred problems, which have appeared on the preliminary exams in Berkeley over the last twenty years. It is an invaluable source of problems and solutions for every mathematics student who plans to enter a Ph.D. program. Students who work through this book will develop problem solving skills in areas such as real analysis, multivariable calculus, differential equations, metric spaces, complex analysis, algebra, and linear algebra. The problems are organized by subject and ordered in an increasing level of difficulty. This new edition contains approximately 120 new problems and 200 new solutions. It is an ideal means for students to strengthen their foundation in basic mathematics and to prepare for graduate studies.

Obesity Epidemic and the Environment: Latin America and the Caribbean Region provides a broad analysis of the macroeconomic impact of the obesity epidemic on environmental degradation in the LAC region. Case studies combine theory and practice to achieve critical conclusions (and subsequent policy implications), providing useful tools for those working on actual health, energy and environmental challenges. Written for researchers, policymakers, international organizations and practitioners in various fields, especially those in public health, health economics, energy and environmental economics and social sciences, this book thoroughly highlights the obesity epidemic in this region. In the LAC region, obesity has become a public health issue. The increase of this problem is related to the economic gains obtained from the process of liberalization and privatization, the increase of foreign investment, and infrastructure investments.

This book collects approximately nine hundred problems that have appeared on the preliminary exams in Berkeley over the last twenty years. It is an invaluable source of problems and solutions. Readers who work through this book will develop problem solving skills in such areas as real analysis, multivariable calculus, differential equations, metric spaces, complex analysis, algebra, and linear algebra.