Abstract Calculus A Categorical Approach

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

Biography

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.