Abstract Calculus

A Categorical Approach
2 ed
ISBN: 978-1-041-14339-0
Verlag: Taylor & Francis Ltd

Buch, Englisch, 450 Seiten, Format (B × H): 178 mm x 254 mm, Gewicht: 675 g

Reihe: Chapman & Hall/CRC Monographs and Research Notes in Mathematics

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 System

- The first chapter of the Appendix (Category Theory chapter) has been restructured to reinforce universal objects, universal properties, and representations

- The 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/modules

- Convergence 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.

Zielgruppe

Academic and Postgraduate

Autoren/Hrsg.

Garcia-Pacheco, Francisco Javier

Fachgebiete

• Mathematik | Informatik Mathematik Algebra
• Mathematik | Informatik Mathematik Mathematische Analysis

Inhaltsverzeichnis

Part 1: Functional Calculus 1. Functions 2. Limits 3. Continuity Part 2: Differential Calculus 4. Differentiability 5. Optimization Part 3: Integral Calculus 6. Summability 7. Integrability Part 4: Appendix A. Category Theory B. Set Theory

Über Autor(innen)

Francisco Javier Garcia-Pacheco graduated in Mathematics from the University of Cadiz (Spain, EU) in 2000. Later, he became an Adjunct Professor at the University of Cadiz and did a doctorate in Pure Mathematics, under the tutelage of Prof. Dr. Antonio Aizpuru, defending his dissertation on May 27, 2005. One year before defending his dissertation, in August 2004, he was awarded a Graduate Teaching Assistantship at Kent State University (Ohio, USA) to pursue a second doctorate in Nonlinear Analysis, under the tutelage of Prof. Dr. Richard Aron. He defended this second dissertation on January 19, 2007, obtaining the Kent State Outstanding Dissertation Award. During the first two years at Kent State University, he was hired as a Graduate Teaching Assistant. He was then awarded a Teaching Fellowship during his last year at Kent State. In August 2007, he was hired by Texas A&M University (Texas, USA) as a Visiting Assistant Professor until August 2010, under the tutelage of Prof. Dr. Bill Johnson. Since September 2010, he has been at the University of Cadiz, first as an Assistant Professor (September 2010 through May 2012), then as an Associate Professor (June 2012 through February 2019), and finally as a Full Professor (March 2019 to present). During the Summer semester of 2011, he did a research and teaching stay at Texas A&M University-Central Texas as Visiting Associate Professor. He also has experience in Academic Management. From December 2017 through July 2019, he held the academic position of Director of Secretariat for International Projects at the Vice-rectorate for Transference and Technological Innovation of the University of Cadiz. From March 2020 through October 2021, he was Director of the Departmental Section of Mathematics at the College of Engineering of the University of Cadiz. From October 2021 through February 2024, he has been the Head of Mathematics Department at the University of Cadiz. Finally, from February 2024 he is currently Director of Secretariat for Academic Affairs.