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Art of Problem Solving Volume 2: and Beyond Text & Solutions
The Art of Problem Solving, Volume 2, is the classic problem solving textbook used by many successful high school math teams and enrichment programs and has been an important building block for students who, like the authors, performed well enough on the American Mathematics Contest series to qualify for the Math Olympiad Summer Program which trains students for the United States International Math Olympiad team.
Volume 2 is appropriate for students who have mastered the problem solving fundamentals presented in Volume 1 and are ready for a greater challenge. Although the Art of Problem Solving is widely used by students preparing for mathematics competitions, the book is not just a collection of tricks. The emphasis on learning and understanding methods rather than memorizing formulas enables students to solve large classes of problems beyond those presented in the book.
Speaking of problems, the Art of Problem Solving, Volume 2, contains over 500 examples and exercises culled from such contests as the Mandelbrot Competition, the AMC tests, and ARML. Full solutions (not just answers!) are available for all the problems in the solution manual. (Please note: The new 7th edition features a different look from previous editions, but has the same content.)
As with the Introductionbooks, the Art of Problem-Solving teaches approaches and methods for solving problems, usually in the context of example solutions, which are reinforced and expanded on by working through the exercises that follow. If you are familiar with the Introduction books, the general philosophy and presentation is basically the same. If you have not used them, PLEASE READ THE PRECEDING DESCRIPTION, as it also applies to this high-school level course. Because this course does not follow a traditional scope and sequence for algebra and geometry, you should consult the table of contents for each volume displayed at our website. Both volumes emphasize geometry, as the authors feel the subject is particularly neglected in most curricula. Think of these books as a banquet for the math-hungry. Students are urged to interact with the books, not just plod through them; to skip around and sample the various topics. If they have trouble digesting something, they should just skip over it and return later when they've had more practice solving problems. They are also encouraged to revisit "finished" topics in order to keep their understanding current.
Lesson text in the volumes is sparse and liberally punctuated with many, many examples. Example solutions are complete and provide the bulk of the instruction. Symbols appear in the margins to help students get the most out of the text. The eye symbol denotes especially important sections that should be read and re-read until understood. The threaded needle indicates difficult problems or concepts which may require additional help or explanation. A bomb highlights potential mistakes that the average math student makes, and helps your child to avoid them. Chapters are relatively short and are divided into smaller sections. This is not a lesson-by-lesson book. Students should work as far as they can in each chapter, depending on their own ease of understanding. Each chapter is followed by problems to solve, often culminated by a "Big Picture" interesting math vignette. Completely worked and explained solutions to the problems are in the meaty Solutions Manualwhich is requisite to the course.
< Did you know that logarithms were actually invented as a trick to do multiplication? They literally turn multiplication and division problems into addition and subtraction ones. Did you know that a formula like the quadratic formula exists for solving cubic equations? It's true and ingeniously simple. If any of this excites you (or more relevantly, your student), this is the course for you. Albert Einstein would have eaten this up as a youth.
Texts are self-study and strictly for the highly-motivated math student. When she finishes these, she will be ready for any college-level math course, to ace the SAT, and to compete in the Mandelbrot Competition. Not only that, but instead of just learning how to work specific math problems, your child will know math in a way that sets him apart from his peers, preparing him for excellence in science, engineering, math, or any other field that requires exceptional problem-solving ability.
Product Format: | Other |
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Brand: | Art of Problem Solving |
Grades: | 9-12 |