Real Analysis

This is a classical Real Analysis/Calculus problem book. This volume contains a huge number of engaging problems and solutions, as well as detailed explanations of how to achieve these solutions. This latter quality is something that many problem books lack, and it is hoped that this feature will be useful to students and instructors alike.

Gustavo da Silva Araújo is an Assistant professor at the State University of Paraíba, Brazil. His primary research interests encompass real and complex analysis, the geometry of Banach spaces, operator theory, series and summability, mathematical inequalities, and lineability. He has authored several papers in these areas, and also serves as reviewer for many mathematics journals. He earned his Ph.D. in mathematics from the Federal University of Paraíba in 2016.

Gustavo A. Muñoz Fernández graduated in Mathematics from Universidad Complutense in 1994 and in Physics from UNED in 2001. He earned his Ph.D. in Mathematics from Universidad Complutense in 1999. Dr. Muñoz is currently the Academic Secretary of the Interdisciplinary Mathematics Institute (IMI) and a Full Professor at the Department of Mathematical Analysis and Applied Mathematics at Universidad Complutense. Dr. Muñoz has co-authored more than 70 publications including a research book and several textbooks. The scientific interests of Dr. Muñoz are related, mainly, to geometry of Banach spaces, polynomials in normed spaces and algebraic genericity (lineability).

María E. Martínez Gómez is currently an Assistant Professor at the Department of Applied Mathematics, Materials Science and Engineering and Electronic Technology, Rey Juan Carlos University (Spain). In 2017, she graduated in Mathematics from the Complutense University of Madrid (UCM) and defended her PhD Thesis in 2021. Her areas of expertise include Real and Convex Analysis and Set Theory.

Luis Bernal González graduated in 1980 from the Universidad de Sevilla, Spain. He obtained his Ph.D. in Mathematics from the same university in 1984. Dr. Bernal has been a permanent faculty member at Sevilla since 1980 and was promoted to associate professor in 1987, and to full professor in 2010. He was an invited speaker at the International Congress on Hypercyclicity and Chaos for Linear Operators and Semigroups in Valencia (Spain) in 2009. His main interests are Complex Analysis, Operator Theory and, lately, the interdisciplinary subject of Lineability. Dr. Bernal has authored or co-authored more than 130 papers in these areas, many of them concerning the structure of the sets of the mathematical objects discovered. He has been plenary lecturer at many international conferences.

José L. Gámez Merino graduated from Universidad Complutense de Madrid (Spain) in 1989 and obtained his Ph.D. degree in Mathematics from the same university in 1997. He is an expert in Real Analysis. Dr. Gámez is, currently, an Associate Professor at the Department of Mathematical Analysis and Applied Mathematics at the Universidad Complutense de Madrid.

Juan B. Seoane Sepúlveda earned his first Ph.D. at the Universidad de Cádiz (Spain) jointly with Universität Karlsruhe (Germany) in 2005. He earned his second Ph.D. at Kent State University (Kent, Ohio, USA) in 2006. His main interests include Real and Complex Analysis, Operator Theory, Number Theory, Banach Space Geometry and Lineability. He has co-authored about 200 papers up to this day, together with several books. Dr. Seoane is currently a Full Professor at Universidad Complutense de Madrid (Spain), where he also holds the position of Director of the Master's Studies in Advanced Mathematics. He has delivered invited lectures at many international conferences and research institutes around the world.

Daniel L. Rodríguez Vidanes is currently a postdoctoral researcher within the Department of Mathematical Analysis and Applied Mathematics at Complutense University of Madrid (UCM). He defended his PhD Thesis on 2023 under the supervision of professors Juan B. Seoane Sepúlveda and Gustavo A. Muñoz Fernández from UCM (Spain), alongside Krzysztof C. Ciesielski from West Virginia University (WVU, USA). His academic journey includes over 20 scientific international publications. Additionally, he also co-authored a research book on the geometry of spaces of polynomials. Daniel's scholarly pursuits are deeply rooted in various domains within mathematics. His research interests span the analysis of real functions, functional analysis, geometry of Banach spaces, spaces of polynomials, and lineability.