This book is a rare resource consisting of problems and solutions similar to those seen in mathematics contests from around the world. It is an excellent training resource for high school students who plan to participate in mathematics contests, and a wonderful collection of problems that can be used by teachers who wish to offer their advanced students some challenging nontraditional problems to work on to build their problem solving skills. It is also an excellent source of problems for the mathematical hobbyist who enjoys solving problems on various levels.Problems are organized by topic and level of difficulty and are cross-referenced by type, making finding many problems of a similar genre easy. An appendix with the mathematical formulas needed to solve the problems has been included for the reader's convenience. We expect that this book will expand the mathematical knowledge and help sharpen the skills of students in high schools, universities and beyond.

Linear programming is an extremely useful area of applied mathematics and is used on a daily basis by many industries. Most books on linear programming require an in depth knowledge of linear algebra in their exposition, making the subject matter inaccessible to the average reader. This second edition continues the presentation of the subject from a very elementary point of view, using as a foundation just a basic knowledge of high school algebra. The author manages to go into great depth with these minimal prerequisites, and helps the reader understand even some of the most subtle aspects of the subject. This is accomplished by weaving some of the more difficult ideas into informal proofs, with the result that the reader often doesn't even know he or she is reading very difficult material. Some formal proofs are included, and even these are often broken down into small steps to give them clarity. The reader who gets through the whole book will have a strong knowledge of linear programming and also a good basic knowledge of the related areas of game theory, integer programming, goal programming, network analysis, and dynamic programming. This book can be (and has been) used as a primary text for a course in linear programming and related topics. It can also be used for self study by the person who wants to know more about this fascinating and very useful subject. Exercises have been carefully chosen to illustrate a broad range of applications that occur in practice leaving the reader with an appreciation of the wide applicability of this subject to real life problems. Also, solutions to many of the exercises are given, making this an ideal book for the person who is studying this subject independently. A limited number of examination copies are available for instructors who wish to consider this book for adoption. Please contact the author at [email protected] to receive one.

Designed to help pre-service and in-service teachers gain the knowledge they need to facilitate students' understanding, competency, and interest in mathematics, the revised and updated Second Edition of this popular text and resource bridges the gap between the mathematics learned in college and the mathematics taught in secondary schools. Highlighting multiple types of mathematical understanding to deepen insight into the secondary school mathematics curriculum, it addresses typical areas of difficulty and common student misconceptions so teachers can involve their students in learning mathematics in a way that is interesting, interconnected, understandable, and often surprising and entertaining. Six content strands are discussed-Numbers and Operations; Algebra; Geometry; Measurement; Data Analysis and Probability; and Proof, Functions, and Mathematical Modeling. The informal, clear style supports an interactive learner-centered approach through engaging pedagogical features: Launch Questions at the beginning of each section capture interest and involve readers in learning the mathematical concepts. Practice Problems provide opportunities to apply what has been learned and complete proofs. Questions from the Classroom bring the content to life by addressing the deep "why" conceptual questions that middle or secondary school students are curious about, and questions that require analysis and correction of typical student errors and misconceptions; focus on counter intuitive results; and contain activities and/or tasks suitable for use with students. Changes in the Second Edition New sections on Robotics, Calculators, Matrix Operations, Cryptography, and the Coefficient of Determination New problems, simpler proofs, and more illustrative examples Answers and hints for selected problems provided

Designed to help pre-service and in-service teachers gain the knowledge they need to facilitate students' understanding, competency, and interest in mathematics, the revised and updated Second Edition of this popular text and resource bridges the gap between the mathematics learned in college and the mathematics taught in secondary schools. Highlighting multiple types of mathematical understanding to deepen insight into the secondary school mathematics curriculum, it addresses typical areas of difficulty and common student misconceptions so teachers can involve their students in learning mathematics in a way that is interesting, interconnected, understandable, and often surprising and entertaining. Six content strands are discussed-Numbers and Operations; Algebra; Geometry; Measurement; Data Analysis and Probability; and Proof, Functions, and Mathematical Modeling. The informal, clear style supports an interactive learner-centered approach through engaging pedagogical features: Launch Questions at the beginning of each section capture interest and involve readers in learning the mathematical concepts. Practice Problems provide opportunities to apply what has been learned and complete proofs. Questions from the Classroom bring the content to life by addressing the deep "why" conceptual questions that middle or secondary school students are curious about, and questions that require analysis and correction of typical student errors and misconceptions; focus on counter intuitive results; and contain activities and/or tasks suitable for use with students. Changes in the Second Edition New sections on Robotics, Calculators, Matrix Operations, Cryptography, and the Coefficient of Determination New problems, simpler proofs, and more illustrative examples Answers and hints for selected problems provided

Mathematics educators have long worked to help students to develop problem-solving skills. More recently, they have sought to provide students with the knowledge in the Common Core State Standards (CCSS). This volume is the second in a series from NCTM that equips classroom teachers with targeted, highly effective problems for achieving both goals at once. For every mathematics educator, the books in this series will illuminate a crucial link between problem solving and the Common Core State Standards. The 37 problems and tasks for students in this book are organised into the major areas of the Common Core for grades 6-8: ratios and proportional relationships; the number system; geometry; statistics and probability; and expressions, equations, and functions. For each task, teachers will find a rich, engaging problem or set of problems to use as a lesson starting point, with accompanying discussions that tie the tasks to specific Common Core domains and clusters. This book provides middle school mathematics teachers with dozens of problems they can use as is, adapt for their classrooms, or be inspired by while creating related problems on other topics. For every mathematics educator, the books in this series will help to illuminate a crucial link between problem solving and the Common Core State Standards.

Mathematics educators have long recognised the importance of helping students to develop problem-solving skills. More recently, they have searched for the best ways to provide their students with the knowledge encompassed in the Common Core State Standards (CCSS). This volume is one in a series from NCTM that equips classroom teachers with targeted, highly effective problems for achieving both goals at once. The 44 problems and tasks for students in this book are organised into the major areas of the high school Common Core: algebra, functions, geometry, statistics and probability, and number and quantity. Examples of modelling, the other main CCSS area, are incorporated throughout. Every domain that is required of all mathematics students is represented. For each task, teachers will find a rich, engaging problem or set of problems to use as a lesson starting point. An accompanying discussion ties these tasks to the specific Common Core domains and clusters they help to explore. Follow-up sections highlight the relevant CCSS Standards for Mathematical Practice that students will engage in as they work on these problems. This book provides high school mathematics teachers with dozens of problems they can use as is, adapt for their classrooms, or be inspired by while creating related problems on other topics. For every mathematics educator, the books in this series will help to illuminate a crucial link between problem solving and the Common Core State Standards.