Numbers and geometry
by John C. Stillwell · first published 1998
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…to set for yourself to build deeper understanding, and the FAQ article "Learning Mathematics" http://www.epsiloncamp.org/faq/faq_3.php points to writings by various mathematicians, including the book Numbers and Geometry by John Stillwell, about how to appreciate mathematics as a deep, connected subject. The submitted article mentioned "Numerous studies over the past thirty years have shown that when people of any age…
on “In Math You Have to Remember, In Other Subjects You Can Think About It” ↗…summer course. Books that I found helpful for understanding mathematics when my oldest son, a mathematics-lover, was growing up include Concepts of Modern Mathematics by Ian Stewart (Dover reprint) Numbers and Geometry by John Stillwell (Springer) Vision in Elementary Mathematics by W. W. Sawyer (Dover reprint) The Art of Problem Solving by Sandor Lehoczky and Richard Rusczyk (Art of Problem Solving) A frequently…
on “Ask HN: Books for Parents of Mathematics-Loving Children?” ↗…that it combines reasoning about discrete, countable things, that is numbers, with reasoning about shapes, that is geometry. An especially good book about both aspects of mathematics is John Stillwell's Numbers and Geometry. http://www.amazon.com/Numbers-Geometry-John-Stillwell/dp/038... I'll quote a bit of Stillwell's preface to give the flavor of the book: "What should every aspiring mathematician know? The answer for…
on “Human beings are born with numbers in the brain ” ↗A suggestion for an addition (or replacement) for the list: http://www.amazon.com/Numbers-Geometry-John-Stillwell/dp/038... Numbers and Geometry by John Stillwell is very readable and full of very interesting math problems, covering a lot of topics that are accessible to anyone with a good high school education but often aren't covered even by…
on “My mid-2009 math reading list” ↗…maintaining ties between these disciplines, it is possible to present a more unified view of mathematics, yet at the same time to include more spice and variety." That's from the preface to his book Numbers and Geometry (New York: Springer-Verlag, 1998), which is a delight to read and full of thought-provoking problems. http://www.amazon.com/gp/product/0387982892/
on “Computer Science students: Learn to write” ↗…mathematics education in the years indicated, and the author of the submitted article is on to something. One of my favorite authors on mathematics, Professor John Stillwell, writes, in the preface to his book Numbers and Geometry (New York: Springer-Verlag, 1998): "What should every aspiring mathematician know? The answer for most of the 20th century has been: calculus. . . . Mathematics today is . . . much more than calculus;…
on “Economist's View: "The Mathematics Generation Gap"” ↗Some favorites about mathematics: Concepts of Modern Mathematics by Ian Stewart http://www.amazon.com/Concepts-Modern-Mathematics-Ian-Stewar... Numbers and Geometry by John Stillwell. http://www.amazon.com/Numbers-Geometry-John-Stillwell/dp/038... The Pleasures of Counting by T. W. Körner http://www.amazon.com/Pleasures-Counting-T-W-K%C3%B6rner/dp/... Mathematics:…
on “Ask HN: Books That Gratify One's Intellectual Curiosity?” ↗…good (I've read other books by Sawyer). http://www.amazon.co.uk/gp/product/0486462404/ Read those for background as you get my favorite overviews of mathematics: Basic Mathematics by Serge Lang and Numbers and Geometry by Joseph Stillwell. http://www.amazon.com/Basic-Mathematics-Serge-Lang/dp/038796... (Basic Mathematics is mostly high school level math, with a minimum of fuss and bother, and good exercises.) http://www.amazon.com/Numbers-Geometry-John-Stillwell/dp/038...…
on “Ask HN: Best Mathematics book for complete noobie?” ↗If you managed to survive high school algebra, you might be able to 'redo' your basic math education with a geometric bent from Stillwell's book 'Numbers and Geometry', which teaches the classical link between the two subjects that has been eliminated from elementary education to some extent. However, the kind of intuition he presents is still semi-abstract - it's…
on “A most unexpected answer to a counting puzzle [video]” ↗I'd consider something by John Stillwell. For example, Numbers and Geometry, which investigates the connections between number theory and plane geometry -- two subjects which your child has probably seen, but not seen related. Stillwell is a magnificent writer -- he loves to…
on “Ask HN: Recommend a maths book for a teenager?” ↗…AFTER EDIT: Here's what one math professor says about the delightful aspects of mathematics to learn besides calculus as it is now taught. Professor John Stillwell writes, in the preface to his book Numbers and Geometry (New York: Springer Verlag, 1998): "What should every aspiring mathematician know? The answer for most of the 20th century has been: calculus. . . . Mathematics today is . . . much more than calculus;…
on “The Calculus Trap” ↗…that mathematics once known can be forgotten or neglected, and mathematics written up for mathematics journals can be difficult to understand. Professor John Stillwell writes, in the preface to his book Numbers and Geometry (New York: Springer-Verlag, 1998): "What should every aspiring mathematician know? The answer for most of the 20th century has been: calculus. . . . Mathematics today is . . . much more than calculus;…
on “Will Our Understanding of Math Deteriorate Over Time?” ↗…deeper and connects topics together better than the standard curriculum in United States schools. Other authors have written on the same topic. Professor John Stillwell writes, in the preface to his book Numbers and Geometry (New York: Springer-Verlag, 1998): "What should every aspiring mathematician know? The answer for most of the 20th century has been: calculus. . . . Mathematics today is . . . much more than calculus;…
on “The Calculus Trap (2005)” ↗Professor John Stillwell writes, in the preface to his book Numbers and Geometry (New York: Springer-Verlag, 1998): "What should every aspiring mathematician know? The answer for most of the 20th century has been: calculus. . . . Mathematics today is . . . much more than calculus;…
on “Dismantling the calculus pyramid” ↗Stillwell is wrong, or at least not doing his homework, Have you read his book Numbers and Geometry, or any of Stillwell's other books? I actually think he takes the approach you advocate, but you haven't given me quite enough examples of the approach you think best for me to be entirely sure.
on “The Calculus Trap” ↗