Mathematics of Networks

Modulus Theory and Convex Optimization

Nathan Albin, Pietro Poggi-Corradini

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Hardback

Forthcoming
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English

Chapman & Hall/CRC
29 August 2025

Complex analysis, complex variables; Geometry; Optimisation; Algorithms & data structures; Mathematical theory of computation

Mathematics of Networks: Modulus Theory and Convex Optimization explores the question: “What can be learned by adapting the theory of p-modulus (and related continuum analysis concepts) to discrete graphs?” This book navigates the rich landscape of p-modulus on graphs, demonstrating how this theory elegantly connects concepts from graph theory, probability, and convex optimization.

This book is ideal for anyone seeking a deeper understanding of the theoretical foundations of network analysis and applied graph theory. It serves as an excellent primary text or reference for graduate and advanced undergraduate courses across multiple disciplines, including mathematics, data science, and engineering, particularly those focusing on network analysis, applied graph theory, optimization, and related areas.

Features:

Accessible to students with a solid foundation in multivariable calculus and linear algebra. Broad interdisciplinary appeal, relevant to mathematics, data science, and engineering curricula. Numerous engaging exercises.

By: Nathan Albin, Pietro Poggi-Corradini
Imprint: Chapman & Hall/CRC
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 156mm,
ISBN: 9780367457075
ISBN 10: 0367457075
Pages: 388
Publication Date: 29 August 2025
Audience: College/higher education , Primary
Format: Hardback
Publisher's Status: Forthcoming

Nathan Albin received a BA in Mathematics from the University of Hawaii and Hilo in 2001. Following a short stint as a software engineer, he attended graduate school at the University of Utah and received a PhD in Mathematics in 2006. He was then awarded an NSF Mathematical Sciences Postdoctoral Research Fellowship, hence spent one year researching at the University of Duisburg-Essen, before moving to Pasadena, CA to complete his postdoctoral research at Caltech. He was hired as an Assistant Professor of Mathematics in 2011 and was promoted to Associate Professor in 2016. His primary research interests include Applied Mathematics, Network Theory, Optimization Theory, and Numerical Analysis. Pietro Poggi-Corradini grew up in Milan, Italy, and in 1992 received a Bachelor in Mathematics from the University of Milan. He then pursued his studies at the University of Washington in Seattle (USA) and graduated in 1996 with a PhD Thesis in Complex Dynamics and Operator Theory under Professor Don Marshall. Thereafter he became Whyburn Instructor at the University of Virginia and in 1998 joined the faculty at Kansas State University. He has been Full Professor at Kansas State University since 2005. His interests currently span Network Theory, Complex Analysis, Probability, and Applied Mathematics.