I have a 12 year old cousin who loves math but finds it so easy as to be boring. She would like it if I found a book of higher math that she could go through herself, to play around with. She has probably taken geometry and algebra.
Are there any good books that do calculus, linear algebra, etc. using examples that use real-world, practical examples of where one might use a particular calculation, but could be understood by someone young? I saw this book:
However, I’m not sure that it’s reasonable to equate all examples to pizza. For someone who is 12, I think it would be better to use scenarios that are useful in daily life and where the math is the clear solution to arriving at the answer, than presenting a complete study. If there aren’t any practical uses of certain problems outside of partical physics, that’s okay to skip. This is just for her to have fun with, not to pass any tests.
Also, not concerned with practical applications, but full of the joy of mathematical discovery: David Flannery’s The Square Root of Two, and Hiroshi Yuki’s Math Girls.
Also, many young readers have had their interest in math piqued or nurtured by Martin Gardner’s books on recreational mathematics (such as his “Aha!”books and his collections of columns from Scientific American.
Are you sure the nature of her interest in math is specifically in terms of “real-world, practical examples”, “scenarios that are useful in daily life”, “practical uses”, etc.? I was once a 12 year old who loved math, with my interest in it having very little to do with such applications.
How about game theory? Stuff like the prisoner’s dilemma, zero sum games, etc. are incredibly useful things to know, and it can be taught in a fun way without invoking all kinds of jargon and weird notation. I mean, hell, there’s even a manga that’s pretty much serial, weekly game theory. Not too hard to make this stuff accessible. I see some books on Amazon like this and this. I’ve no idea how good they are.
Calculus can be useful in basic mechanics (differentiating a position function to get velocity, etc.), which can lead to some fun times (in high school, our physics teacher had us form teams to build trebuchets to toss stuff across the football field), but you really need trig first to have a full go of it, and trig is pretty dry. This is why I particularly remember—and loathe—one particular moment from Star Trek: TNG in which a child, roughly ten years old, was complaining to his father about his calculus class. Calc really does require that full algebra, geometry, and trig (my school called that class “Precalculus”) background. IME, elementary game theory doesn’t require anything like that, even though it’s not generally taught except in college-level sciences-and-engineering kinds of contexts (I didn’t have a formal introduction to it until Introduction to Artificial Intelligence).
By the way, don’t discount twelve year olds and particle physics. One of my very first adult pop-science books was Leon Lederman’s The God Particle when I was 13 or 14, and I loved (and still love) that book. Awfully outdated by now—the book refers to the SSC in the future tense—but Dr. Lederman has a great sense of humor, and I really credit it with being an accessible introduction to a very complicated topic, and it probably directly led to one of the most fun moments of my life, my ten week internship at Fermilab during the summer between sophomore and junior years at college.
My thoughts exactly. I’m very much interested in applications these days, but I did not start out that way, and I don’t really know of anyone who does. I’m going to second the recommendation for any of Martin Gardner’s works; he’s probably the most influential mathematician of the 20th century simply by virtue of the number of people he brought into the field.
Thirding Martin Gardner. His books as well as Isaac Asimov’s (the non-fiction especially) helped make me the nerdy engineer I am today. Web based resources: I highly recommend Vi Hart’s videos as a starting point for all sorts of mathematical stuff. There’s also Numberphile, Khan Academy, Better Explained, etc. I think at that age, it’s best to get exposed to a variety of fields before beginning a slog through Tipler’s Physics for Science and Engineers.
Gödel, Escher, Bach by Hofstadter is part of what sparked my initial interest in mathematics; Metamagical Themas, a book of his articles he wrote for Scientific American’s “Mathematical Games” column when he took it over from Gardner, is perhaps more digestible if the more philosophical themes of Gödel, Escher, Bach leave her cold.