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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.
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