By Parallel Reasoning is the first comprehensive philosophical examination of analogical reasoning in more than forty years designed to formulate and justify standards for the critical evaluation of analogical arguments. It proposes a normative theory with special focus on the use of analogies in mathematics and science.

In recent decades, research on analogy has been dominated by computational theories whose objective has been to model analogical reasoning as a psychological process. These theories have devoted little attention to normative questions. In this book Bartha...

A rigorous introduction to calculus in vector spaces

The concepts and theorems of advanced calculus combined with related computational methods are essential to understanding nearly all areas of quantitative science. Analysis in Vector Spaces presents the central results of this classic subject through rigorous arguments, discussions, and examples. The book aims to cultivate not only knowledge of the major theoretical results, but also the geometric intuition needed for both mathematical problem-solving and modeling in the formal sciences.

The authors begin with an...

A thorough treatment of the portion of analysis that addresses functions of several variables and multiple integrals, this book is self-contained, and the background material in the first few chapters is sufficient to enable well-motivated students to follow the book without undue difficulties.