Concepts of Modern Mathematics (Dover Books on Mathematics) 1st Edition by Ian Stewart (PDF)

Description

Some years ago, “new math” took the country’s classrooms by storm. Based on the abstract, general style of mathematical exposition favored by research mathematicians, its goal was to teach students not just to manipulate numbers and formulas, but to grasp the underlying mathematical concepts. The result, at least at first, was a great deal of confusion among teachers, students, and parents. Since then, the negative aspects of “new math” have been eliminated and its positive elements assimilated into classroom instruction.In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts underlying “new math”: groups, sets, subsets, topology, Boolean algebra, and more. According to Professor Stewart, an understanding of these concepts offers the best route to grasping the true nature of mathematics, in particular the power, beauty, and utility of pure mathematics. No advanced mathematical background is needed (a smattering of algebra, geometry, and trigonometry is helpful) to follow the author’s lucid and thought-provoking discussions of such topics as functions, symmetry, axiomatics, counting, topology, hyperspace, linear algebra, real analysis, probability, computers, applications of modern mathematics, and much more.By the time readers have finished this book, they’ll have a much clearer grasp of how modern mathematicians look at figures, functions, and formulas and how a firm grasp of the ideas underlying “new math” leads toward a genuine comprehension of the nature of mathematics itself.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐We are in 1975, Ian is teasing us with bits of modern mathematics. He warms up remembering us that mathematicians are juggling concepts (instead of numbers) mostly for intellectual satisfaction. Impressive jugglers playing with axioms, functions, sets and so on. Everything connected together by powerful and enjoyable concepts from the “queen of the sciences”. Here, we must put emphasis on enjoyable because our math majesty is introduced to layperson by a very good teacher. The whole thing is well illustrated with examples and plots in an engaging parade of abstractions; majestic indeed.

⭐I plan on rereading this book to ensure I understand all of the concepts. I enjoyed the writing style and it helped with a few of the concepts that I had not been exposed to yet.

⭐This is the third Stewart book I’ve read, and I’m looking forward to reading more of his work. This book would be a great follower to his work on the 25 mathematicians.

⭐I wish I had discovered Ian Stewart when I was still in school. His texts are accessible but deep enough to give the reader an educated interest in various fields of mathematics. This book kindled a love for math in me. I think everyone should read at least one book by Ian Stewart.

⭐I am very greating with Mr Stewart because he is consequential in his dialogue.

⭐Great book. I bought the Kindle version, which (like most Kindle books with illustrations) has problems with the figures. Illustrations run off the page, etc. Annoying.

⭐Very well written. Easy to understand for those with only high school or 1st year college Math level like me.

⭐Aus meiner Sicht ein schönes Buch, dem es inhaltlich an nichts mangelt. Sehr schön die div. graphischen Darstellungen, die mir zum Verständnis sehr geholfen haben. Auch wenn der “reine” Mathematiker Anschaulichkeit nicht wichtig findet – für mich sind praktische Beispiele der Ausgangspunkt von dem Abstraktion erst entspringen kann.

⭐

⭐Clearly written so it is easy to read. You should have some familiarity with Maths if you want to read this and get the most out of it.

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