Chapman Mathematical Notes – serie

This text presents a collection of mathematical exercises with the aim of guiding readers to study topics in statistical physics, equilibrium thermodynamics, information theory, and their various connections.  It explores essential tools from linear algebra, elementary functional analysis, and probability theory in detail and demonstrates their applications in topics such as entropy, machine learning, error-correcting codes, and quantum channels.  The theory of communication and signal theory are also in the background, and many exercises have been chosen from the theory of wavelets and machine learning.  Exercises are selected from a number of different domains, both theoretical and more applied.  Notes and other remarks provide motivation for the exercises, and hints and full solutions are given for many.  For senior undergraduate and beginning graduate students majoring in mathematics, physics, or engineering, this text will serve as a valuable guide as theymove on to more advanced work.

This text presents a collection of mathematical exercises with the aim of guiding readers to study topics in statistical physics, equilibrium thermodynamics, information theory, and their various connections.  It explores essential tools from linear algebra, elementary functional analysis, and probability theory in detail and demonstrates their applications in topics such as entropy, machine learning, error-correcting codes, and quantum channels.  The theory of communication and signal theory are also in the background, and many exercises have been chosen from the theory of wavelets and machine learning.  Exercises are selected from a number of different domains, both theoretical and more applied.  Notes and other remarks provide motivation for the exercises, and hints and full solutions are given for many.  For senior undergraduate and beginning graduate students majoring in mathematics, physics, or engineering, this text will serve as a valuable guide as theymove on to more advanced work.

Alexander Grothendieck is often considered one of the greatest mathematicians of the twentieth century (if not all time), and his unique vision continues to impact and inspire many fields and researchers today. Utilizing a multidisciplinary approach, this edited volume explores the profound influence his work and ideas have had not only on mathematics, but also on logic and philosophy. Chapters are written by international scholars, and many were inspired by talks given at the conference “Grothendieck, A Multifarious Giant” at Chapman University (May 24-28, 2022). Some chapters are written from a historical perspective and discuss the development of the main themes that characterized Grothendieck's work. Others are more mathematical in nature, analyzing and extending some of his more relevant and obscure results that are still not well understood. Philosophical implications and applications in logic are the subjects of other chapters. This volume will be of interest not only to mathematicians working in algebraic geometry, category theory, and other areas to which Grothendieck contributed, but also to philosophers, logicians, and historians of science.