Abstract Calculus

Abstract Calculus: A Categorical Approach provides an abstract approach to calculus. It is intended for graduate students pursuing a Ph.D. in Pure Mathematics, but may also find an interested audience among junior and senior researchers in basically anyfield of Mathematics and Theoretical Physics. Any calculus text for undergraduate students majoring in Engineering, Mathematics or Physics deals with the classical concepts of limits, continuity, differentiability, optimization, integrability, summability, and approximation. This book covers the exact same topics but from a categorical perspective, taking the Category of Topological Modules as the main category involved. Features: Suitable for PhD candidates and researchers. Requires prerequisites in settheory, general topology and abstract algebra, but is otherwise self-contained--