Roozbeh Hazrat - Böcker

This study of graded rings includes the first systematic account of the graded Grothendieck group, a powerful and crucial invariant in algebra which has recently been adopted to classify the Leavitt path algebras. The book begins with a concise introduction to the theory of graded rings and then focuses in more detail on Grothendieck groups, Morita theory, Picard groups and K-theory. The author extends known results in the ungraded case to the graded setting and gathers together important results which are currently scattered throughout the literature. The book is suitable for advanced undergraduate and graduate students, as well as researchers in ring theory.

This textbook introduces Python and its programming through a multitude of clearly presented examples and worked-out exercises.Based on a course taught to undergraduate students of mathematics, science, engineering and finance, the book includes chapters on handling data, calculus, solving equations, and graphics, thus covering all of the basic topics in Python. Each section starts with a description of a new topic and some basic examples. The author then demonstrates the new concepts through worked out exercises. The intention is to enable the reader to learn from the codes, thus avoiding lengthy, exhausting explanations. With its strong focus on programming and problem solving, and an emphasis on numerical problems that do not require advanced mathematics, this textbook is also ideal for self-study, for instance for researchers who wish to use Python as a computational tool.

An introduction to the vast array of features and powerful mathematical functions of Mathematica that uses a multitude of clearly presented examples and worked-out problems that enable the reader to learn from the codes and avoids lengthy explanations.

The book offers a comprehensive introduction to Leavitt path algebras (LPAs) and graph C*-algebras. Highlighting their significant connection with classical K-theory—which plays an important role in mathematics and its related emerging fields—this book allows readers from diverse mathematical backgrounds to understand and appreciate these structures. The articles on LPAs are mostly of an expository nature and the ones dealing with K-theory provide new proofs and are accessible to interested students and beginners of the field.  It is a useful resource for graduate students and researchers working in this field and related areas, such as C*-algebras and symbolic dynamics.