This volume is an excellent resource for professionals in various areas of applications of mathematics, modeling, and computational science. It focuses on recent progress and modern challenges in these areas. The volume provides a balance between fundamental theoretical and applied developments, emphasizing the interdisciplinary nature of modern trends and detailing state-of-the-art achievements in Applied Mathematics, Modeling, and Computational Science. The chapters have been authored by international experts in their respective fields, making this book ideal for researchers in academia, practitioners, and graduate students. It can also serve as a reference in the diverse selected areas of applied mathematics, modelling, and computational sciences, and is ideal for interdisciplinary collaborations.

A standards-based, comprehensive math intervention curriculum for the state of California. Designed for students identified with math deficiencies who have not responded to reteaching efforts or who have a sustained lack of adquate progress in mathematics. This program provides intensive focus on developing foundational understanding and skills. It provides explicit, scientifically based instruction emphasizing the five critical elements of mathematics proficiency: understanding, computing, applying reasoning/problem solving , and engagement.

Focusing on the formal development of mathematics, this book shows readers how to read, understand, write, and construct mathematical proofs.Uses elementary number theory and congruence arithmetic throughout. Focuses on writing in mathematics. Reviews prior mathematical work with “Preview Activities” at the start of each section. Includes “Activities” throughout that relate to the material contained in each section. Focuses on Congruence Notation and Elementary Number Theorythroughout.For professionals in the sciences or engineering who need to brush up on their advanced mathematics skills. Mathematical Reasoning: Writing and Proof, 2/E Theodore Sundstrom

This book focuses on a selection of special topics, with emphasis on past and present research of the authors on “canonical” Riemannian metrics on smooth manifolds. On the backdrop of the fundamental contributions given by many experts in the field, the volume offers a self-contained view of the wide class of “Curvature Conditions” and “Critical Metrics” of suitable Riemannian functionals. The authors describe the classical examples and the relevant generalizations. This monograph is the winner of the 2020 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics.

The purpose of this handbook is to help launch institutional transformations in mathematics departments to improve student success. We report findings from the Student Engagement in Mathematics through an Institutional Network for Active Learning (SEMINAL) study. SEMINAL's purpose is to help change agents, those looking to (or currently attempting to) enact change within mathematics departments and beyond--trying to reform the instruction of their lower division mathematics courses in order to promote high achievement for all students. SEMINAL specifically studies the change mechanisms that al.

This book consists of five chapters presenting problems of current research in mathematics, with its history and development, current state, and possible future direction. Four of the chapters are expository in nature while one is based more directly on research. All deal with important areas of mathematics, however, such as algebraic geometry, topology, partial differential equations, Riemannian geometry, and harmonic analysis. This book is addressed to researchers who are interested in those subject areas. Young-Hoon Kiem discusses classical enumerative geometry before string theory and improvements after string theory as well as some recent advances in quantum singularity theory, Donaldson–Thomas theory for Calabi–Yau 4-folds, and Vafa–Witten invariants. Dongho Chae discusses the finite-time singularity problem for three-dimensional incompressible Euler equations. He presents Kato's classical local well-posedness results, Beale–Kato–Majda's blow-up criterion, and recent studies on the singularity problem for the 2D Boussinesq equations. Simon Brendle discusses recent developments that have led to a complete classification of all the singularity models in a three-dimensional Riemannian manifold. He gives an alternative proof of the classification of noncollapsed steady gradient Ricci solitons in dimension 3. Hyeonbae Kang reviews some of the developments in the Neumann–Poincare operator (NPO). His topics include visibility and invisibility via polarization tensors, the decay rate of eigenvalues and surface localization of plasmon, singular geometry and the essential spectrum, analysis of stress, and the structure of the elastic NPO. Danny Calegari provides an explicit description of the shift locus as a complex of spaces over a contractible building. He describes the pieces in terms of dynamically extended laminations and of certain explicit “discriminant-like” affine algebraic varieties.