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A Gentle Introduction to the American Invitational Mathematics Exam

A Gentle Introduction to the American Invitational Mathematics Exam
Author: Scott A. Annin
Publisher: The Mathematical Association of America
Total Pages: 399
Release: 2015-11-16
Genre: Mathematics
ISBN: 0883858355

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This book is a celebration of mathematical problem solving at the level of the high school American Invitational Mathematics Examination. There is no other book on the market focused on the AIME. It is intended, in part, as a resource for comprehensive study and practice for the AIME competition for students, teachers, and mentors. After all, serious AIME contenders and competitors should seek a lot of practice in order to succeed. However, this book is also intended for anyone who enjoys solving problems as a recreational pursuit. The AIME contains many problems that have the power to foster enthusiasm for mathematics – the problems are fun, engaging, and addictive. The problems found within these pages can be used by teachers who wish to challenge their students, and they can be used to foster a community of lovers of mathematical problem solving! There are more than 250 fully-solved problems in the book, containing examples from AIME competitions of the 1980’s, 1990’s, 2000’s, and 2010’s. In some cases, multiple solutions are presented to highlight variable approaches. To help problem-solvers with the exercises, the author provides two levels of hints to each exercise in the book, one to help stuck starters get an idea how to begin, and another to provide more guidance in navigating an approach to the solution.


Euclidean Geometry in Mathematical Olympiads

Euclidean Geometry in Mathematical Olympiads
Author: Evan Chen
Publisher: American Mathematical Soc.
Total Pages: 311
Release: 2021-08-23
Genre: Education
ISBN: 1470466201

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This is a challenging problem-solving book in Euclidean geometry, assuming nothing of the reader other than a good deal of courage. Topics covered included cyclic quadrilaterals, power of a point, homothety, triangle centers; along the way the reader will meet such classical gems as the nine-point circle, the Simson line, the symmedian and the mixtilinear incircle, as well as the theorems of Euler, Ceva, Menelaus, and Pascal. Another part is dedicated to the use of complex numbers and barycentric coordinates, granting the reader both a traditional and computational viewpoint of the material. The final part consists of some more advanced topics, such as inversion in the plane, the cross ratio and projective transformations, and the theory of the complete quadrilateral. The exposition is friendly and relaxed, and accompanied by over 300 beautifully drawn figures. The emphasis of this book is placed squarely on the problems. Each chapter contains carefully chosen worked examples, which explain not only the solutions to the problems but also describe in close detail how one would invent the solution to begin with. The text contains a selection of 300 practice problems of varying difficulty from contests around the world, with extensive hints and selected solutions. This book is especially suitable for students preparing for national or international mathematical olympiads or for teachers looking for a text for an honor class.


Concepts and Problems for Mathematical Competitors

Concepts and Problems for Mathematical Competitors
Author: Alexander Sarana
Publisher: Courier Dover Publications
Total Pages: 430
Release: 2020-08-12
Genre: Mathematics
ISBN: 0486842533

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This original work discusses mathematical methods needed by undergraduates in the United States and Canada preparing for competitions at the level of the International Mathematical Olympiad (IMO) and the Putnam Competition. The six-part treatment covers counting methods, number theory, inequalities and the theory of equations, metrical geometry, analysis, and number representations and logic. Includes problems with solutions plus 1,000 problems for students to finish themselves.


First Steps for Math Olympians

First Steps for Math Olympians
Author: J. Douglas Faires
Publisher: MAA
Total Pages: 344
Release: 2006-12-21
Genre: Mathematics
ISBN: 9780883858240

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A major aspect of mathematical training and its benefit to society is the ability to use logic to solve problems. The American Mathematics Competitions have been given for more than fifty years to millions of students. This book considers the basic ideas behind the solutions to the majority of these problems, and presents examples and exercises from past exams to illustrate the concepts. Anyone preparing for the Mathematical Olympiads will find many useful ideas here, but people generally interested in logical problem solving should also find the problems and their solutions stimulating. The book can be used either for self-study or as topic-oriented material and samples of problems for practice exams. Useful reading for anyone who enjoys solving mathematical problems, and equally valuable for educators or parents who have children with mathematical interest and ability.


Counterrevolution

Counterrevolution
Author: Walden Bello
Publisher:
Total Pages: 0
Release: 2019
Genre: Conservatism
ISBN: 9781773632216

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"The far right is on the rise globally, with the rhetoric of anger and resentment emanating from personalities like Donald Trump, Marine Le Pen, Rodrigo Duterte, and Viktor Orban captivating and mobilizing large numbers of people. Indeed, in a number of countries, the extreme right has already captured the government or is on the threshold of power. While the swift turn of events has shocked or surprised many in the North, the extreme right's seizure of power is not an uncommon event in the South. Deploying what he calls the "dialectic of revolution and counterrevolution" and harnessing the methods of comparative history and comparative sociology, Walden Bello's Counterrevolution is a bold, sweeping enterprise that seeks to deconstruct the challenge from the far right. Using as case studies Italy in the 1920's, Indonesia in the 1960s', Chile in the 1970's, and contemporary Thailand, India, and the Philippines, Bello lays bare the origins, dynamics, and consequences of counterrevolutionary movements. Reflections on the rise of the right in the United States, Europe, and Brazil round out this remarkable, timely study by one of the premier intellectuals of the South. Bello weds his well-known analytical scalpel to vigorous and clear writing to produce what reviewers have already dubbed one of the most profound, exciting, and controversial contributions to the study of social movements in years, one that bears comparison to the classic works of Barrington Moore, Jr., and Theda Skocpol. While he is well known for his progressive views, Bello, who was a recipient of the Right Livelihood Award (aka the Alternative Nobel Prize) and named the International Studies Association's Outstanding Public Scholar, is one of those rare analysts who does not let politics get in the way of clear-sighted analysis."--


The Art and Craft of Problem Solving

The Art and Craft of Problem Solving
Author: Paul Zeitz
Publisher: John Wiley & Sons
Total Pages: 389
Release: 2017
Genre: Problem solving
ISBN: 1119239907

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This text on mathematical problem solving provides a comprehensive outline of "problemsolving-ology," concentrating on strategy and tactics. It discusses a number of standard mathematical subjects such as combinatorics and calculus from a problem solver's perspective.


Mathematics for Computer Science

Mathematics for Computer Science
Author: Eric Lehman
Publisher:
Total Pages: 988
Release: 2017-03-08
Genre: Business & Economics
ISBN: 9789888407064

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This book covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.


Hungarian Problem Book IV

Hungarian Problem Book IV
Author: Robert Barrington Leigh
Publisher: MAA
Total Pages: 132
Release: 2011
Genre: Education
ISBN: 0883858312

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Forty-eight challenging problems from the oldest high school mathematics competition in the world. This book is a continuation of Hungarian Problem Book III and takes the contest from 1944 through to 1963. This book is intended for beginners, although the experienced student will find much here.


Developing Assessments for the Next Generation Science Standards

Developing Assessments for the Next Generation Science Standards
Author: National Research Council
Publisher: National Academies Press
Total Pages: 296
Release: 2014-05-29
Genre: Education
ISBN: 0309289548

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Assessments, understood as tools for tracking what and how well students have learned, play a critical role in the classroom. Developing Assessments for the Next Generation Science Standards develops an approach to science assessment to meet the vision of science education for the future as it has been elaborated in A Framework for K-12 Science Education (Framework) and Next Generation Science Standards (NGSS). These documents are brand new and the changes they call for are barely under way, but the new assessments will be needed as soon as states and districts begin the process of implementing the NGSS and changing their approach to science education. The new Framework and the NGSS are designed to guide educators in significantly altering the way K-12 science is taught. The Framework is aimed at making science education more closely resemble the way scientists actually work and think, and making instruction reflect research on learning that demonstrates the importance of building coherent understandings over time. It structures science education around three dimensions - the practices through which scientists and engineers do their work, the key crosscutting concepts that cut across disciplines, and the core ideas of the disciplines - and argues that they should be interwoven in every aspect of science education, building in sophistication as students progress through grades K-12. Developing Assessments for the Next Generation Science Standards recommends strategies for developing assessments that yield valid measures of student proficiency in science as described in the new Framework. This report reviews recent and current work in science assessment to determine which aspects of the Framework's vision can be assessed with available techniques and what additional research and development will be needed to support an assessment system that fully meets that vision. The report offers a systems approach to science assessment, in which a range of assessment strategies are designed to answer different kinds of questions with appropriate degrees of specificity and provide results that complement one another. Developing Assessments for the Next Generation Science Standards makes the case that a science assessment system that meets the Framework's vision should consist of assessments designed to support classroom instruction, assessments designed to monitor science learning on a broader scale, and indicators designed to track opportunity to learn. New standards for science education make clear that new modes of assessment designed to measure the integrated learning they promote are essential. The recommendations of this report will be key to making sure that the dramatic changes in curriculum and instruction signaled by Framework and the NGSS reduce inequities in science education and raise the level of science education for all students.


Mathematics via Problems

Mathematics via Problems
Author: Arkadiy Skopenkov
Publisher: American Mathematical Society, Mathematical Sciences Research Institute
Total Pages: 196
Release: 2021-02-11
Genre: Mathematics
ISBN: 1470448785

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This book is a translation from Russian of Part I of the book Mathematics Through Problems: From Olympiads and Math Circles to Profession. The other two parts, Geometry and Combinatorics, will be published soon. The main goal of this book is to develop important parts of mathematics through problems. The author tries to put together sequences of problems that allow high school students (and some undergraduates) with strong interest in mathematics to discover and recreate much of elementary mathematics and start edging into the sophisticated world of topics such as group theory, Galois theory, and so on, thus building a bridge (by showing that there is no gap) between standard high school exercises and more intricate and abstract concepts in mathematics. Definitions and/or references for material that is not standard in the school curriculum are included. However, many topics in the book are difficult when you start learning them from scratch. To help with this, problems are carefully arranged to provide gradual introduction into each subject. Problems are often accompanied by hints and/or complete solutions The book is based on classes taught by the author at different times at the Independent University of Moscow, at a number of Moscow schools and math circles, and at various summer schools. It can be used by high school students and undergraduates, their teachers, and organizers of summer camps and math circles. 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.