Abstract Calculus : A Categorical Approach

Any calculus text for undergraduates majoring in engineering, maths or physics deals with the concepts of limits, continuity, differentiability, optimization, integrability, summability, and approximation. This book covers the same topics but from a categorical perspective, making the classification of topological modules the main category.

Abstract Calculus: A Categorical Approach provides an abstract approach to calculus. 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, making the classification of topological modules the main category. This book is primarily intended for graduate students pursuing PhDs in pure mathematics, but junior and senior researchers in basically any field of mathematics and theoretical physics will also find the material of interest. New to the Second Edition:The first section of Chapter One (Set Theory section) has been moved to the Appendix and has been endowed with more content related to the Zermelo-Fraenkel Axiomatic SystemThe first chapter of the Appendix (Category Theory chapter) has been restructured to reinforce universal objects, universal properties, and representationsThe order topology in partially ordered sets has been reviewed in depth and applied to the study of ordered universal algebras, such as ordered groups/rings/modulesConvergence topologies, as well as convergence uniformities, are fully developed and have been relocated in the second chapter (Limits)Unit segments in rings have been completely covered and related to ring orderings, highlighting applications to convexity in both nodules and abstract cones.