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This is a pedagogical introduction to the coordinate-free approach in basic finite-dimensional linear algebra. The reader should be already exposed to the array-based formalism of vector and matrix calculations. This book makes extensive use of the exterior (anti-commutative, "wedge") product of vectors. The coordinate-free formalism and the exterior product, while somewhat more abstract, provide a deeper understanding of the classical results...

In this book, I discuss the long-standing technical and conceptual problems arising within the statistical framework describing models of cosmological inflation, known collectively as the "measure problem" in multiverse cosmology. After reviewing various existing approaches and mathematical techniques developed in the past two decades for studying these issues, I describe a new proposal for a measure in the multiverse, called the reheating-vol...

This volume is the only monograph covering the exciting and dazzling recent developments in quantum cosmology, including the theory of the ¿multiverse¿ and eternal inflation pioneered by A Vilenkin, A Linde, S W Hawking, and others. Written by a leading expert in the field known for his depth and clarity of presentation, the volume presents an overview of 20 years of development of the theory of eternal inflation as well as a comprehensive, re...