Using the dichotomy of structure and pseudorandomness as a central theme, this accessible text provides a modern introduction to extremal graph theory and additive combinatorics. Readers will explore central results in additive combinatorics-notably the cornerstone theorems of Roth, Szemerédi, Freiman, and Green-Tao-and will gain additional insights into these ideas through graph theoretic perspectives. Topics discussed include the Turán problem, Szemerédi's graph regularity method, pseudorandom graphs, graph limits, graph homomorphism inequalities, Fourier analysis in additive combinatorics, the structure of set addition, and the sum-product problem. Important combinatorial, graph theoretic, analytic, Fourier, algebraic, and geometric methods are highlighted. Students will appreciate the chapter summaries, many figures and exercises, and freely available lecture videos on MIT OpenCourseWare. Meant as an introduction for students and researchers studying combinatorics, theoretical computer science, analysis, probability, and number theory, the text assumes only basic familiarity with abstract algebra, analysis, and linear algebra.

Two-dimensional (2D) materials for photocatalytic applications have attracted attention in recent years due to their unique thickness-dependent physiochemical properties. 2D materials offer enhanced functionality over traditional three-dimensional (3D) photocatalysts due to modified chemical composition and electronic structures, as well as abundant surface active sites. This book reviews the applications of 2D-related nano-materials in solar-driven catalysis, providing an up-to-date introduction to the design and use of 2D-related photo(electro)catalysts. This includes not only application areas such as fine chemicals synthesis, water splitting, CO2 reduction, and N2 fixation, but also catalyst design and preparation. Some typical 2D and 2D-related materials (such as layered double hydroxides (LDHs), layered metal oxides, transition metal dichalcogenide (TMDs), metal-organic frameworks (MOFs), graphene, g-C3N4, etc.) are classified, and relationships between structure and property are demonstrated, with emphasis on how to improve 2D-related materials performance for practical applications. While the focus of this book will primarily be on experimental studies, computational results will serve as a necessary reference. With chapters written by expert researchers in their fields, Photocatalysis Using 2D Nanomaterials will provide advanced undergraduates, postgraduates and other researchers convenient introductions to these topics.