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Excursions in Calculus: An Interplay of the Continuous and the Discrete (Dolciani Mathematical Expositions) First Print Edition

5.0 out of 5 stars 3 customer reviews
ISBN-13: 978-0883853177
ISBN-10: 0883853175
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Editorial Reviews

Review

'If I were stranded on a desert island with my junior and senior math majors and could give them only one book to read, this is the one I would choose. In fact, this year we will be doing precisely that (requiring the book, that is) for all of our junior math majors.' SIAM-DM Newsletter

Book Description

This book explores the rich and elegant interplay between the two main currents of mathematics, the continuous and the discrete. Such fundamental notions in discrete mathematics as induction, recursion, combinatorics, number theory, discrete probability, and the algorithmic point of view as a unifying principle are continually explored as they interact with traditional calculus.
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Product Details

  • Series: Dolciani Mathematical Expositions (Book 13)
  • Paperback: 432 pages
  • Publisher: The Mathematical Association of America; First Print edition (October 1, 1992)
  • Language: English
  • ISBN-10: 0883853175
  • ISBN-13: 978-0883853177
  • Product Dimensions: 6 x 0.8 x 9 inches
  • Shipping Weight: 1.6 pounds (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (3 customer reviews)
  • Amazon Best Sellers Rank: #1,399,210 in Books (See Top 100 in Books)

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Format: Paperback
I know of very few people who can make mathematics come alive the way Prof. Robert Young (Oberlin College) does. I have been a student of his for the past year-and-a-half. With him my mathematical maturity, integrity, and knowledge have soared. The acquisition of Excursions In Calculus has added tremendously to my growth.
Prof. Young's book is a collection of some of his favourite topics in teaching elementary calculus and analysis. Intended for both teachers and motivated students of the calculus, he takes the reader through several beautiful realms of mathematical inquiry and discovery. His topics are diverse: infinite sums and products (including a brilliant presentation of some of the work of Euler, one of his favourite mathematicians), exponential spirals, Wallis's formula for pi, chaos and fractals, Cantor functions, the Weierstrass approximation theorem, and many more with an ambitious appendix on modular arithmetic and related topics such as the celebrated Chinese Remainder Theorem.
Prof. Young treats each of his subjects with not only the highest responsibility and technical acuity of a trained professional mathematician, but also with the greatest reverence and passion for the glorious field to which he has devoted his life. The book reads not like a sterile mathematical text but as an intricately woven epic of centuries of mathematical inquiry and the rich personalities responsible. Complete with hundreds of very challenging and non-trivial exercises, this book has something for everyone, whether a motivated student of freshman calculus or a sophisticated mathematician. None will be bored, all will be mystified.
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Format: Paperback
This unique book is a precious addition to anyone's bookshelf, whether student or teacher. The material within is fun and fascinating. Much of it is accessible to those with minimal knowledge of calculus, yet the book also contains some deep topics and outlines a number of unsolved problems in mathematics. Many recurring themes appear in the book, including the interplay between the finite and infinite, the discrete and continuous, and the connections between fields such as analysis and number theory.

This is one of those rare books that actually teaches people how to think "outside the box"--how to come up with different ways of looking at things, creative ways of solving problems. The author places an emphasis on simplicity and elegance.

If you want a book that will be a fun, easy read, yet that you will keep coming back to over and over again--or if you want a book to help you create some new and fun problems--or if you feel like you need a little infusion of that mathematical creativity that is so critically needed in advanced mathematical work, this book will be able to help you a great deal.
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Format: Paperback
This publication was exciting when I first perused it in the late 1990's. It still makes great bedtime reading after all these years.
I urged its adoption by the Calculus instructor at that time, and sang its praises at that time, but to no avail.
(In fairness to the fine Mathematics Department, at the time computer technology was being fully integrated into classrooms,
leaving little time for new instructional books.)
Now, I do the same---that is, I urge its perusal--- utilizing this platform.
This book bristles with excitement and charm. The exposition is lucid, the mathematics ever fresh and approached with vigor.
Most of this material should be easily accessible to students, certainly by their junior year of college (or, sooner)--however,
more often than not this material is neglected , if not downplayed, in traditional Calculus courses.
Much (if not all) of the material certainly was absent from my academic curricula. A random miscellany of its contents include:
a fine selection of fascinating problems accompanying each new section, Mathematical Induction, Binomial Theorem, Fermat, Euler, Fibonacci,Generating Functions, Averages, Approximations, Dirac Delta, Number Theory ,Infinite Sums. The scope is panoramic: Numbers, Algebra, Geometry, Calculus--espousing the interplay of the discrete and the continuous. The author presents each in masterful prose and clear mathematical detail. The problems/exercises are exploratory and fun(!) to solve. The Bibliography provides entree into much more. Herewith is presented a beautiful exploration of relevant mathematical gems.
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