Set theory is a rich and beautiful subject whose fundamental concepts permeate virtually every branch of mathematics. One could say that set theory is a unifying theory for mathematics, since nearly all mathematical concepts and results can be formalized within set theory. This textbook is meant for an upper undergraduate course in set theory. In this text, the fundamentals of abstract sets, including relations, functions, the natural numbers, order, cardinality, transfinite recursion, the...

Typically, undergraduates see real analysis as one of the most difficult courses that a mathematics major is required to take. The main reason for this perception is twofold: Students must comprehend new abstract concepts and learn to deal with these concepts on a level of rigor and proof not previously encountered. A key challenge for an instructor of real analysis is to find a way to bridge the gap between a student’s preparation and the mathematical skills that are required to be successfu...

This book presents the transformational progress in next-generation advanced converter circuit topologies based on the unique electrical properties of wide-bandgap semiconductors, including silicon carbide (SiC) and gallium nitride (GaN). It addresses the opportunities for significant advances in power electronics circuit performance opened by the availability of wide-bandgap power devices and the challenges associated with using these devices that must be overcome when applying them. The ...

The book is intended for students who want to learn how to prove theorems and be better prepared for the rigors required in more advance mathematics. One of the key components in this textbook is the development of a methodology to lay bare the structure underpinning the construction of a proof, much as diagramming a sentence lays bare its grammatical structure. Diagramming a proof is a way of presenting the relationships between the various parts of a proof. A proof diagram provides a too...

The lack of effective DC fault protection technology remains a major barrier for the DC paradigm shift. In addressing the key challenges, Direct Current Fault Protection: Basic Concepts and Technology Advances starts with an introduction to the advantages of DC power systems before moving on to an in-depth review of DC fault protection technologies, including mechanical circuit breaker (MCB), solid-state circuit breaker (SSCB), hybrid circuit breaker (HCB), converter based (breake...