Euclidean Geometry

A Guided Inquiry Approach

DOWNLOAD NOW »

Author: David M. Clark

Publisher: American Mathematical Soc.

ISBN: 0821889850

Category: Mathematics

Page: 127

View: 9666

Geometry has been an essential element in the study of mathematics since antiquity. Traditionally, we have also learned formal reasoning by studying Euclidean geometry. In this book, David Clark develops a modern axiomatic approach to this ancient subject, both in content and presentation. Mathematically, Clark has chosen a new set of axioms that draw on a modern understanding of set theory and logic, the real number continuum and measure theory, none of which were available in Euclid's time. The result is a development of the standard content of Euclidean geometry with the mathematical precision of Hilbert's foundations of geometry. In particular, the book covers all the topics listed in the Common Core State Standards for high school synthetic geometry. The presentation uses a guided inquiry, active learning pedagogy. Students benefit from the axiomatic development because they themselves solve the problems and prove the theorems with the instructor serving as a guide and mentor. Students are thereby empowered with the knowledge that they can solve problems on their own without reference to authority. This book, written for an undergraduate axiomatic geometry course, is particularly well suited for future secondary school teachers. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

The Learning and Teaching of Geometry in Secondary Schools

A Modeling Perspective

DOWNLOAD NOW »

Author: Pat Herbst,Taro Fujita,Stefan Halverscheid,Michael Weiss

Publisher: Routledge

ISBN: 1351973525

Category: Education

Page: 250

View: 9234

IMPACT (Interweaving Mathematics Pedagogy and Content for Teaching) is an exciting new series of texts for teacher education which aims to advance the learning and teaching of mathematics by integrating mathematics content with the broader research and theoretical base of mathematics education. The Learning and Teaching of Geometry in Secondary Schools reviews past and present research on the teaching and learning of geometry in secondary schools and proposes an approach for design research on secondary geometry instruction. Areas covered include: teaching and learning secondary geometry through history; the representations of geometric figures; students’ cognition in geometry; teacher knowledge, practice and, beliefs; teaching strategies, instructional improvement, and classroom interventions; research designs and problems for secondary geometry. Drawing on a team of international authors, this new text will be essential reading for experienced teachers of mathematics, graduate students, curriculum developers, researchers, and all those interested in exploring students’ study of geometry in secondary schools.

Distilling Ideas

An Introduction to Mathematical Thinking

DOWNLOAD NOW »

Author: Brian P. Katz,Michael Starbird,Michael P. Starbird

Publisher: MAA

ISBN: 1939512034

Category: Mathematics

Page: 171

View: 4984

Designed for undergraduate students and lecturers, this text guides its users to develop the skills, attitudes, and habits of mind of a mathematician. It presents a carefully designed sequence of exercises and theorems so that its readers will be directed to discover mathematical ideas, strategies of proof, and strategies of thinking. Through the exploration of interesting mathematical content including graphs, groups, and calculus, this book helps to foster habits of inquiry. This book can be used by instructors as a text for an inquiry-based introduction to proof course, or as an independent study guide for mathematics students. The three core mathematical topics are presented separately, and each helps students develop theorem-proving skills and strategies of thinking whilst also providing an organised set of challenges that lead students to understand the process of mathematical creativity and development.

Integers, Fractions, and Arithmetic

A Guide for Teachers

DOWNLOAD NOW »

Author: Judith D. Sally,Paul J. Sally (Jr.)

Publisher: American Mathematical Soc.

ISBN: 082188798X

Category: Mathematics

Page: 208

View: 7502

This book, which consists of twelve interactive seminars, is a comprehensive and careful study of the fundamental topics of K-8 arithmetic. The guide aims to help teachers understand the mathematical foundations of number theory in order to strengthen and enrich their mathematics classes. Five seminars are dedicated to fractions and decimals because of their importance in the classroom curriculum. The standard topics are covered in detail, but are arranged in an order that is slightly different from the usual one. Multiplication is treated first, and with that in hand, common denominators and equivalent fractions are more readily understood and are available for use when discussing addition. The book is intended for the professional development of teachers. It is appropriate for teacher education programs as well as for enrichment programs such as Mathematical Circles for Teachers. There are numerous activities in each seminar that teachers can bring into their classrooms. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

The Shape of Inner Space

String Theory and the Geometry of the Universe's Hidden Dimensions

DOWNLOAD NOW »

Author: Shing-Tung Yau,Steve Nadis

Publisher: Basic Books

ISBN: 0465022669

Category: Science

Page: 400

View: 9105

String theory says we live in a ten-dimensional universe, but that only four are accessible to our everyday senses. According to theorists, the missing six are curled up in bizarre structures known as Calabi-Yau manifolds. In The Shape of Inner Space, Shing-Tung Yau, the man who mathematically proved that these manifolds exist, argues that not only is geometry fundamental to string theory, it is also fundamental to the very nature of our universe. Time and again, where Yau has gone, physics has followed. Now for the first time, readers will follow Yau’s penetrating thinking on where we’ve been, and where mathematics will take us next. A fascinating exploration of a world we are only just beginning to grasp, The Shape of Inner Space will change the way we consider the universe on both its grandest and smallest scales.

A Decade of the Berkeley Math Circle

The American Experience, Volume II

DOWNLOAD NOW »

Author: Zvezdelina Stankova, Tom Rike

Publisher: American Mathematical Soc.

ISBN: 0821849123

Category: Mathematics

Page: 376

View: 9795

Many mathematicians have been drawn to mathematics through their experience with math circles. The Berkeley Math Circle (BMC) started in 1998 as one of the very first math circles in the U.S. Over the last decade and a half, 100 instructors--university professors, business tycoons, high school teachers, and more--have shared their passion for mathematics by delivering over 800 BMC sessions on the UC Berkeley campus every week during the school year. This second volume of the book series is based on a dozen of these sessions, encompassing a variety of enticing and stimulating mathematical topics, some new and some continuing from Volume I: from dismantling Rubik's Cube and randomly putting it back together to solving it with the power of group theory;from raising knot-eating machines and letting Alexander the Great cut the Gordian Knot to breaking through knot theory via the Jones polynomial;from entering a seemingly hopeless infinite raffle to becoming friendly with multiplicative functions in the land of Dirichlet, Möbius, and Euler;from leading an army of jumping fleas in an old problem from the International Mathematical Olympiads to improving our own essay-writing strategies;from searching for optimal paths on a hot summer day to questioning whether Archimedes was on his way to discovering trigonometry 2000 years ago Do some of these scenarios sound bizarre, having never before been associated with mathematics? Mathematicians love having fun while doing serious mathematics and that love is what this book intends to share with the reader. Whether at a beginner, an intermediate, or an advanced level, anyone can find a place here to be provoked to think deeply and to be inspired to create. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession. Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).

Mathematical Circle Diaries, Year 1

Complete Curriculum for Grades 5 to 7

DOWNLOAD NOW »

Author: Anna Burago

Publisher: American Mathematical Soc.

ISBN: 0821887459

Category: Education

Page: 335

View: 9169

Early middle school is a great time for children to start their mathematical circle education. This time is a period of curiosity and openness to learning. The thinking habits and study skills acquired by children at this age stay with them for a lifetime. Mathematical circles, with their question-driven approach and emphasis on creative problem-solving, have been rapidly gaining popularity in the United States. The circles expose children to the type of mathematics that stimulates development of logical thinking, creativity, analytical abilities and mathematical reasoning. These skills, while scarcely touched upon at school, are in high demand in the modern world. This book contains everything that is needed to run a successful mathematical circle for a full year. The materials, distributed among 29 weekly lessons, include detailed lectures and discussions, sets of problems with solutions, and contests and games. In addition, the book shares some of the know-how of running a mathematical circle. The curriculum, which is based on the rich and long-standing Russian math circle tradition, has been modified and adapted for teaching in the United States. For the past decade, the author has been actively involved in teaching a number of mathematical circles in the Seattle area. This book is based on her experience and on the compilation of materials from these circles. The material is intended for students in grades 5 to 7. It can be used by teachers and parents with various levels of expertise who are interested in teaching mathematics with the emphasis on critical thinking. Also, this book will be of interest to mathematically motivated children. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

Circle in a Box

DOWNLOAD NOW »

Author: Sam Vandervelde

Publisher: American Mathematical Soc.

ISBN: 082184752X

Category: Mathematics

Page: 217

View: 9095

Math circles provide a setting in which mathematicians work with secondary school students who are interested in mathematics. This form of outreach, which has existed for decades in Russia, Bulgaria, and other countries, is now rapidly spreading across the United States as well. The first part of this book offers helpful advice on all aspects of math circle operations, culled from conversations with over a dozen directors of successful math circles. Topics include creative means for getting the word out to students, sound principles for selecting effective speakers, guidelines for securing financial support, and tips for designing an exciting math circle session. The purpose of this discussion is to enable math circle coordinators to establish a thriving group in which students can experience the delight of mathematical investigation. The second part of the book outlines ten independent math circle sessions, covering a variety of topics and difficulty levels. Each chapter contains detailed presentation notes along with a useful collection of problems and solutions. This book will be an indispensable resource for any individual involved with a math circle or anyone who would like to see one begin in his or her community. Sam Vandervelde teaches at St. Lawrence University. He launched the Stanford Math Circle and also writes and coordinates the Mandelbrot Competition, a math contest for high schools. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession. Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).

A Moscow Math Circle

Week-by-week Problem Sets

DOWNLOAD NOW »

Author: Sergey Dorichenko

Publisher: American Mathematical Soc.

ISBN: 0821868748

Category: Mathematics

Page: 240

View: 2358

Moscow has a rich tradition of successful math circles, to the extent that many other circles are modeled on them. This book presents materials used during the course of one year in a math circle organized by mathematics faculty at Moscow State University, and also used at the mathematics magnet school known as Moscow School Number 57. Each problem set has a similar structure: it combines review material with a new topic, offering problems in a range of difficulty levels. This time-tested pattern has proved its effectiveness in engaging all students and helping them master new material while building on earlier knowledge. The introduction describes in detail how the math circles at Moscow State University are run. Dorichenko describes how the early sessions differ from later sessions, how to choose problems, and what sorts of difficulties may arise when running a circle. The book also includes a selection of problems used in the competition known as the Mathematical Maze, a mathematical story based on actual lessons with students, and an addendum on the San Jose Mathematical Circle, which is run in the Russian style. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

The Legacy of Alladi Ramakrishnan in the Mathematical Sciences

DOWNLOAD NOW »

Author: Krishnaswami Alladi,John R. Klauder,Calyampudi R. Rao

Publisher: Springer Science & Business Media

ISBN: 9781441962638

Category: Mathematics

Page: 575

View: 6376

In the spirit of Alladi Ramakrishnan’s profound interest and contributions to three fields of science — Mathematics, Statistics, and Physics — this volume contains invited surveys and research articles from prominent members of these communities who also knew Ramakrishnan personally and greatly respected his influence in these areas of science. Historical photos, telegrams, and biographical narratives of Alladi Ramakrishnan’s illustrious career of special interest are included as well.

Geometry in Problems

DOWNLOAD NOW »

Author: Alexander Shen

Publisher: American Mathematical Soc.

ISBN: 1470419211

Category: Geometry

Page: 214

View: 8437

Classical Euclidean geometry, with all its triangles, circles, and inscribed angles, remains an excellent playground for high-school mathematics students, even if it looks outdated from the professional mathematician's viewpoint. It provides an excellent choice of elegant and natural problems that can be used in a course based on problem solving. The book contains more than 750 (mostly) easy but nontrivial problems in all areas of plane geometry and solutions for most of them, as well as additional problems for self-study (some with hints). Each chapter also provides concise reminders of basic notions used in the chapter, so the book is almost self-contained (although a good textbook and competent teacher are always recommended). More than 450 figures illustrate the problems and their solutions. The book can be used by motivated high-school students, as well as their teachers and parents. After solving the problems in the book the student will have mastered the main notions and methods of plane geometry and, hopefully, will have had fun in the process. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession. What a joy! Shen's ``Geometry in Problems'' is a gift to the school teaching world. Beautifully organized by content topic, Shen has collated a vast collection of fresh, innovative, and highly classroom-relevant questions, problems, and challenges sure to enliven the minds and clever thinking of all those studying Euclidean geometry for the first time. This book is a spectacular resource for educators and students alike. Users will not only sharpen their mathematical understanding of specific topics but will also sharpen their problem-solving wits and come to truly own the mathematics explored. Also, Math Circle leaders can draw much inspiration for session ideas from the material presented in this book. --James Tanton, Mathematician-at-Large, Mathematical Association of America We learn mathematics best by doing mathematics. The author of this book recognizes this principle. He invites the reader to participate in learning plane geometry through carefully chosen problems, with brief explanations leading to much activity. The problems in the book are sometimes deep and subtle: almost everyone can do some of them, and almost no one can do all. The reader comes away with a view of geometry refreshed by experience. --Mark Saul, Director of Competitions, Mathematical Association of America

Aesthetics of Interdisciplinarity: Art and Mathematics

DOWNLOAD NOW »

Author: Kristóf Fenyvesi,Tuuli Lähdesmäki

Publisher: Birkhäuser

ISBN: 3319572598

Category: Mathematics

Page: 290

View: 5091

This anthology fosters an interdisciplinary dialogue between the mathematical and artistic approaches in the field where mathematical and artistic thinking and practice merge. The articles included highlight the most significant current ideas and phenomena, providing a multifaceted and extensive snapshot of the field and indicating how interdisciplinary approaches are applied in the research of various cultural and artistic phenomena. The discussions are related, for example, to the fields of aesthetics, anthropology, art history, art theory, artistic practice, cultural studies, ethno-mathematics, geometry, mathematics, new physics, philosophy, physics, study of visual illusions, and symmetry studies. Further, the book introduces a new concept: the interdisciplinary aesthetics of mathematical art, which the editors use to explain the manifold nature of the aesthetic principles intertwined in these discussions.

Math from Three to Seven

The Story of a Mathematical Circle for Preschoolers

DOWNLOAD NOW »

Author: Aleksandr Kalmanovich Zvonkin

Publisher: American Mathematical Soc.

ISBN: 082186873X

Category: Mathematics

Page: 300

View: 5964

This book is a captivating account of a professional mathematician's experiences conducting a math circle for preschoolers in his apartment in Moscow in the 1980s. As anyone who has taught or raised young children knows, mathematical education for little kids is a real mystery. What are they capable of? What should they learn first? How hard should they work? Should they even "work" at all? Should we push them, or just let them be? There are no correct answers to these questions, and the author deals with them in classic math-circle style: he doesn't ask and then answer a question, but shows us a problem--be it mathematical or pedagogical--and describes to us what happened. His book is a narrative about what he did, what he tried, what worked, what failed, but most important, what the kids experienced. This book does not purport to show you how to create precocious high achievers. It is just one person's story about things he tried with a half-dozen young children. Mathematicians, psychologists, educators, parents, and everybody interested in the intellectual development in young children will find this book to be an invaluable, inspiring resource. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession. Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).

Lectures and Problems: A Gift to Young Mathematicians

DOWNLOAD NOW »

Author: V. I. Arnold

Publisher: American Mathematical Soc.

ISBN: 147042259X

Category: Mathematics

Page: 176

View: 9799

Vladimir Arnold (1937-2010) was one of the great mathematical minds of the late 20th century. He did significant work in many areas of the field. On another level, he was keeping with a strong tradition in Russian mathematics to write for and to directly teach younger students interested in mathematics. This book contains some examples of Arnold's contributions to the genre. "Continued Fractions" takes a common enrichment topic in high school math and pulls it in directions that only a master of mathematics could envision. "Euler Groups" treats a similar enrichment topic, but it is rarely treated with the depth and imagination lavished on it in Arnold's text. He sets it in a mathematical context, bringing to bear numerous tools of the trade and expanding the topic way beyond its usual treatment. In "Complex Numbers" the context is physics, yet Arnold artfully extracts the mathematical aspects of the discussion in a way that students can understand long before they master the field of quantum mechanics. "Problems for Children 5 to 15 Years Old" must be read as a collection of the author's favorite intellectual morsels. Many are not original, but all are worth thinking about, and each requires the solver to think out of his or her box. Dmitry Fuchs, a long-term friend and collaborator of Arnold, provided solutions to some of the problems. Readers are of course invited to select their own favorites and construct their own favorite solutions. In reading these essays, one has the sensation of walking along a path that is found to ascend a mountain peak and then being shown a vista whose existence one could never suspect from the ground. Arnold's style of exposition is unforgiving. The reader--even a professional mathematician--will find paragraphs that require hours of thought to unscramble, and he or she must have patience with the ellipses of thought and the leaps of reason. These are all part of Arnold's intent. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

Advanced Computational and Communication Paradigms

Proceedings of International Conference on ICACCP 2017

DOWNLOAD NOW »

Author: Siddhartha Bhattacharyya,Tapan Gandhi,Kalpana Sharma,Paramartha Dutta

Publisher: Springer

ISBN: 9811082405

Category: Technology & Engineering

Page: 592

View: 9078

The book titled Advanced Computational and Communication Paradigms: Proceedings of International Conference on ICACCP 2017, Volume 1 presents refereed high-quality papers of the First International Conference on Advanced Computational and Communication Paradigms (ICACCP 2017) organized by the Department of Computer Science and Engineering, Sikkim Manipal Institute of Technology, held from 8– 10 September 2017. ICACCP 2017 covers an advanced computational paradigms and communications technique which provides failsafe and robust solutions to the emerging problems faced by mankind. Technologists, scientists, industry professionals and research scholars from regional, national and international levels are invited to present their original unpublished work in this conference. There were about 550 technical paper submitted. Finally after peer review, 142 high-quality papers have been accepted and registered for oral presentation which held across 09 general sessions and 05 special sessions along with 04 keynote address and 06 invited talks. This volume comprises 65 accepted papers of ICACCP 2017.

Introduction to Functional Equations

Theory and Problem-solving Strategies for Mathematical Competitions and Beyond

DOWNLOAD NOW »

Author: Costas Efthimiou

Publisher: American Mathematical Soc.

ISBN: 0821853147

Category: Mathematics

Page: 363

View: 3772

Functions and their properties have been part of the rigorous precollege curriculum for decades. And functional equations have been a favorite topic of the leading national and international mathematical competitions. Yet the subject has not received equal attention by authors at an introductory level. The majority of the books on the topic remain unreachable to the curious and intelligent precollege student. The present book is an attempt to eliminate this disparity. The book opens with a review chapter on functions, which collects the relevant foundational information on functions, plus some material potentially new to the reader. The next chapter presents a working definition of functional equations and explains the difficulties in trying to systematize the theory. With each new chapter, the author presents methods for the solution of a particular group of equations. Each chapter is complemented with many solved examples, the majority of which are taken from mathematical competitions and professional journals. The book ends with a chapter of unsolved problems and some other auxiliary material. The book is an invaluable resource for precollege and college students who want to deepen their knowledge of functions and their properties, for teachers and instructors who wish to enrich their curricula, and for any lover of mathematical problem-solving techniques. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

Essentials of Mathematics

Introduction to Theory, Proof, and the Professional Culture

DOWNLOAD NOW »

Author: Margie Hale

Publisher: MAA

ISBN: 0883857294

Category: Mathematics

Page: 180

View: 6513

Textbook and self-study guide for students beginning to study mathematics requiring proof.

Intelligent Information and Database Systems

Second International Conference, ACIIDS 2010, Hue City, Vietnam, March 24-26, 2010, Proceedings

DOWNLOAD NOW »

Author: Manh Thanh Le,Jerzy Swiatek,Ngoc Thanh Nguyen

Publisher: Springer Science & Business Media

ISBN: 3642121004

Category: Computers

Page: 483

View: 8612

The 2010 Asian Conference on Intelligent Information and Database Systems (ACIIDS) was the second event of the series of international scientific conferences for research and applications in the field of intelligent information and database systems. The aim of ACIIDS 2010 was to provide an international forum for scientific research in the technologies and applications of intelligent information, database systems and their applications. ACIIDS 2010 was co-organized by Hue University (Vietnam) and Wroclaw University of Technology (Poland) and took place in Hue city (Vietnam) during March 24–26, 2010. We received almost 330 papers from 35 countries. Each paper was peer reviewed by at least two members of the International Program Committee and International Reviewer Board. Only 96 best papers were selected for oral presentation and publi- tion in the two volumes of the ACIIDS 2010 proceedings. The papers included in the proceedings cover the following topics: artificial social systems, case studies and reports on deployments, collaborative learning, collaborative systems and applications, data warehousing and data mining, database management technologies, database models and query languages, database security and integrity,- business, e-commerce, e-finance, e-learning systems, information modeling and - quirements engineering, information retrieval systems, intelligent agents and mul- agent systems, intelligent information systems, intelligent internet systems, intelligent optimization techniques, object-relational DBMS, ontologies and information sharing, semi-structured and XML database systems, unified modeling language and unified processes, Web services and Semantic Web, computer networks and communication systems.

Plant Metabolic Networks

DOWNLOAD NOW »

Author: Jörg Schwender

Publisher: Springer Science & Business Media

ISBN: 9780387787459

Category: Science

Page: 339

View: 9025

Plants are the basis for human nutrition and of increasing interest for the chemical industry as a source of chemical feed stocks. Fuels derived from plant biomass will increasingly replace fossil fuels in the future. In order to increase crop productivity, design new plant products, and create new energy crops, there is need for methods of qualitative and quantitative analysis of metabolism which are able to guide the rational re-design of metabolic networks. In this book, recent advances in qualitative and quantitative analysis of metabolism are summarized to give an overview of the current state of knowledge. Principles of the analysis of network structure, flux analysis, and kinetic modeling are described. Analytical methods necessary to produce the data needed for metabolic flux analysis and for kinetic modeling are described. The analysis of larger metabolic networks is only possible by using computer assistance. Therefore each chapter of the book shall also describe software available for this purpose.

The Cauchy-Schwarz Master Class

An Introduction to the Art of Mathematical Inequalities

DOWNLOAD NOW »

Author: J. Michael Steele

Publisher: Cambridge University Press

ISBN: 9780521546775

Category: Mathematics

Page: 306

View: 1437

This lively, problem-oriented text, first published in 2004, is designed to coach readers toward mastery of the most fundamental mathematical inequalities. With the Cauchy-Schwarz inequality as the initial guide, the reader is led through a sequence of fascinating problems whose solutions are presented as they might have been discovered - either by one of history's famous mathematicians or by the reader. The problems emphasize beauty and surprise, but along the way readers will find systematic coverage of the geometry of squares, convexity, the ladder of power means, majorization, Schur convexity, exponential sums, and the inequalities of Hölder, Hilbert, and Hardy. The text is accessible to anyone who knows calculus and who cares about solving problems. It is well suited to self-study, directed study, or as a supplement to courses in analysis, probability, and combinatorics.