Cultivating Mathematical Hearts: Culturally Responsive Mathematics Teaching in Elementary Classrooms
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Help students see their whole selves in the math they're learning with culturally responsive teaching. Cultivating Mathematical Hearts: Culturally Responsive Mathematics Teaching in Elementary Classrooms, aims to re-center mathematics as a humanizing endeavor because putting children and their humanity at the heart of mathematics education can result in more engaged, meaningful, and joyful learning. This book introduces a model and a tool for Culturally Responsive Mathematics Teaching, constructed to create a safe, inclusive space where all learners can come together in their own educational journey and develop a love for math that centers their experiences and comes from the heart. Implementing the Culturally Responsive Mathematics Teaching Tool (CRMT2) will help you cultivate and sustain meaningful, rich, and rigorous mathematical learning spaces for all your students-experiences that foster mathematical curiosity and joy. The book walks you through each aspect of the framework and tool, guiding you to consider how your classroom structures, lessons, tasks, and assessments: Honor the existing cultural strengths, experiences, and lived realities of all your students Elicit diverse mathematical thinking and ideas Support equitable access to rigorous mathematical learning and discourse for all students Invite a sense of agency in each student's learning experience Promote high engagement and excitement while learning mathematics Nurture an understanding that mathematics is a powerful tool for making sense of the world By weaving these strategies into classroom lessons, teachers can humanize mathematics instruction to successfully build a love for math while providing equitable learning opportunities that empower student voice and promote success in mathematics.
Elliptic Partial Differential Equations from an Elementary Viewpoint: A Fresh Glance at the Classical Theory
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This is a textbook that covers several selected topics in the theory of elliptic partial differential equations which can be used in an advanced undergraduate or graduate course.The book considers many important issues such as existence, regularity, qualitative properties, and all the classical topics useful in the wide world of partial differential equations. It also includes applications with interesting examples.The structure of the book is flexible enough to allow different chapters to be taught independently.The book is friendly, welcoming, and written for a newcomer to the subject.It is essentially self-contained, making it easy to read, and all the concepts are fully explained from scratch, combining intuition and rigor, and therefore it can also be read independently by students, with limited or no supervision.
Real Algebraic Geometry and Optimization
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This book provides a comprehensive and user-friendly exploration of the tremendous recent developments that reveal the connections between real algebraic geometry and optimization, two subjects that were usually taught separately until the beginning of the 21st century. Real algebraic geometry studies the solutions of polynomial equations and polynomial inequalities over the real numbers. Real algebraic problems arise in many applications, including science and engineering, computer vision, robotics, and game theory. Optimization is concerned with minimizing or maximizing a given objective function over a feasible set. Presenting key ideas from classical and modern concepts in real algebraic geometry, this book develops related convex optimization techniques for polynomial optimization. The connection to optimization invites a computational view on real algebraic geometry and opens doors to applications. Intended as an introduction for students of mathematics or related fields at an advanced undergraduate or graduate level, this book serves as a valuable resource for researchers and practitioners. Each chapter is complemented by a collection of beneficial exercises, notes on references, and further reading. As a prerequisite, only some undergraduate algebra is required.
A Royal Road to Topology: Convergence of Filters
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Topological spaces are a special case of convergence spaces. This textbook introduces topology within a broader context of convergence theory. The title alludes to advantages of the present approach, which is more gratifying than many traditional ones: you travel more comfortably through mathematical landscapes and you see more.The book is addressed both to those who wish to learn topology and to those who, being already knowledgeable about topology, are curious to review it from a different perspective, which goes well beyond the traditional knowledge.Usual topics of classic courses of set-theoretic topology are treated at an early stage of the book -- from a viewpoint of convergence of filters, but in a rather elementary way. Later on, most of these facts reappear as simple consequences of more advanced aspects of convergence theory.The mentioned virtues of the approach stem from the fact that the class of convergences is closed under several natural, essential operations, under which the class of topologies is not! Accordingly, convergence theory complements topology like the field of complex numbers algebraically completes the field of real numbers.Convergence theory is intuitive and operational because of appropriate level of its abstraction, general enough to grasp the underlying laws, but not too much in order not to lose intuitive appeal.
