Elementary introduction to stable maps and quantum cohomology presents the problem of counting rational plane curves Viewpoint is mostly that of enumerative geometry Emphasis is on examples, heuristic discussions, and simple applications to best convey the intuition behind the subject Ideal for self-study, for a mini-course in quantum cohomology, or as a special topics text in a standard course in intersection theory

This book explores the theory’s history, recent developments, and some promising future directions through invited surveys written by prominent researchers in the field. The first three surveys provide historical background on the subject; the last three address Euclidean Ramsey theory and related coloring problems. In addition, open problems posed throughout the volume and in the concluding open problem chapter will appeal to graduate students and mathematicians alike.

Presents many major differential geometric acheivements in the theory of CR manifolds for the first time in book form Explains how certain results from analysis are employed in CR geometry Many examples and explicitly worked-out proofs of main geometric results in the first section of the book making it suitable as a graduate main course or seminar textbook Provides unproved statements and comments inspiring further study

Collection of the most interesting recent writings on the philosophy of mathematics written by highly respected researchers from philosophy, mathematics, physics, and chemistry Interdisciplinary book that will be useful in several fields—with a cross-disciplinary subject area, and contributions from researchers of various disciplines

A highly practical resource for special educators and classroom teachers, this book provides specific instructional guidance illustrated with vignettes, examples, and sample lesson plans. Every chapter is grounded in research and addresses the nuts and bolts of teaching math to students who are not adequately prepared for the challenging middle school curriculum. Presented are a range of methods for helping struggling learners build their understanding of foundational concepts, master basic skills, and develop self-directed problem-solving strategies. While focusing on classroom instruction, the book also includes guidelines for developing high-quality middle school mathematics programs and evaluating their effectiveness.

* Stanley represents a broad perspective with respect to two significant topics from Combinatorial Commutative Algebra: 1) The theory of invariants of a torus acting linearly on a polynomial ring, and 2) The face ring of a simplicial complex * In this new edition, the author further develops some interesting properties of face rings with application to combinatorics

"Demonstrates problem solving strategies with solutions and teaching notes and allows the teacher to create a collection of problems to fit a particular grade level."-Janice L. Richardson, Associate Professor and Education Coordinator, Department of MathematicsElon UniversityHelp students succeed as problem solvers in and out of the classroom! Problem solving skills are critical to students' success in mathematics, but the techniques can't be caught; they must be taught. Based on the premise that educators must take a deliberate approach to the teaching of problem solving skills, this book helps teachers engage students in the process. Problem Solving in Mathematics, Grades 3-6 stresses the importance of problem solving in mathematics and presents nine strategies that students can use to solve problems, such as working backwards, finding a pattern, making a drawing, or solving a simpler equivalent problem. Each chapter demonstrates how teachers can:Apply the strategies to problems at different grade levels Incorporate these strategies into a mathematics program Understand how each strategy can be applied to real-life situations Make each strategy an integral part of students' thinking processesWith helpful teaching notes, sample problems for students that fit into any mathematics curriculum, and step-by-step solutions to sample problems, this book is perfect for teachers who want their students to succeed in mathematics!

Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.

The art or skill of problem solving in mathematics is mostly relegated to the strategies one can use to solve problems in the field. Although this book addresses that issue, it delves deeply into the psychological aspects that affect successful problem-solving. Such topics as decision-making, judgment, and reasoning as well as using memory effectively and a discussion of the thought processes that could help address certain problem-solving situations.Most books that address problem-solving and mathematics focus on the various skills. This book goes beyond that and investigates the psychological aspects to solving problems in mathematics.