tag:blogger.com,1999:blog-3722233.post3949812920467956708..comments2024-11-03T06:24:21.294-06:00Comments on Computational Complexity: Inspiring a Love of MathLance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.comBlogger19125tag:blogger.com,1999:blog-3722233.post-55393842084974899342009-10-11T11:23:05.965-05:002009-10-11T11:23:05.965-05:00I'd like to recommend Conway and Guy's The...I'd like to recommend Conway and Guy's <b>The Book of Numbers</b>. It's not as entertaining as GEB, and requires a fair amount of patience to think and work through some of the problems. But I think it is rewarding as it gives multiple approaches to answering questions about why some results are true. For example, as to the question what is the pattern of 1, 1+3, 1+3+5, ..., they give both algebraic and geometric formulations of the problem.<br /><br />I am not a theorist, but I sometimes write about my (often frustrating) experiences with theory in the "problem solving" and "learning" memories of my LJ.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-85404293267925865602009-09-27T12:59:29.405-05:002009-09-27T12:59:29.405-05:00Many thanks to Chris. I had totally forgotten abou...Many thanks to Chris. I had totally forgotten about "The I Hate Mathematics! Book". I think it was the only math book in my elementary school's library. I definitely remember learning about Moebius strips and googleplexes from it!ryanwhttps://www.blogger.com/profile/09644595632189419277noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-48653822153521528962009-09-26T17:49:14.193-05:002009-09-26T17:49:14.193-05:00I second the Art of Problem Solving recommendation...I second the Art of Problem Solving recommendation, and I think that the forum is a specially good source, in the sense that it is easy to find there very diverse problems, in terms of both breadth and depth.<br /><br />I don't find GEB to be a good book to learn about math, and I don't like most of its references, although maybe I might have liked them when I was younger, and, well, of course different people can have different experiences about it.Anoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-19568414159268354402009-09-26T12:40:41.924-05:002009-09-26T12:40:41.924-05:00No one has mentioned science fiction (in the class...No one has mentioned science fiction (in the classic SF sense). The short stories of Cordwainer Smith had a big influence on me ... these stories characterically combine complexity theory, game theory, evolutionary biology, politics, and morality, in the context of wonderful narratives.<br /><br />Two stories that come to mind are <i>Alpha Ralpha Boulevard</i> and <i>The Burning of the Brain</i> (hope I remembered the titles correctly!)John Sidleshttp://www.mrfm.orgnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-33945520054036778302009-09-26T12:14:40.705-05:002009-09-26T12:14:40.705-05:00Books with lots of information in them, along with...Books with lots of information in them, along with lots of fun problems to explore, might be good. Two stand out in my mind:<br /><br />Mathematical Journeys, by Schumer<br /><br />Excursions in Calculus, by Young<br /><br />I'm not particularly good at judging what level reader these (or any other) texts are appropriate for. But I like both of these.sumidiothttps://www.blogger.com/profile/14998929191458452400noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-39172675732616651492009-09-26T11:13:14.029-05:002009-09-26T11:13:14.029-05:00You might want to see if there are any "math ...You might want to see if there are any "math circles" nearby or otherwise any small learning groups for math (often related to training for math contests). There is a book on the topic of math circles, written by some people who started some, which is pretty interesting from the perspective of teaching, and the philosophy of exploring math, called <a href="http://www.amazon.com/Out-Labyrinth-Setting-Mathematics-Free/dp/0195147448/sr=8-1/qid=1167859040/ref=sr_1_1/002-8958891-7740062?ie=UTF8&s=books" rel="nofollow">Out of The Labyrinth</a>. <br /><br />Also, try letting your child pick the material if you haven't already. When I was much younger I found a surprising amount of value in going to high school/local/university libraries and book stores, and just browsing the math section.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-9441420205450190772009-09-26T04:08:37.127-05:002009-09-26T04:08:37.127-05:00Physics was my first love as a kid. I was fascinat...Physics was my first love as a kid. I was fascinated by the possibility of answering many big questions (life, universe and all that) through the scientific approach. At the time, I knew very little 'real math' and I was mainly reacting to the excellent popular writings of Gamow, Feynman, etc.<br /><br />As I have grown up and looked at some real math, I find that one of the most fantastic things about it is its utility in the description and analysis of phenomena that would otherwise seem too vague. Perhaps it is not a bad idea to introduce children to this idea (in conjunction with the notion of pure math as the ultimate form of entertainment).Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-85734705235989290572009-09-26T00:42:09.986-05:002009-09-26T00:42:09.986-05:00The thing that got me into math was a love of puzz...The thing that got me into math was a love of puzzles. I always kind of liked math somewhat but the Junior Waterloo Math Contest problems for grades 9-11 (and the MAA contest) really hooked me - multiple choice problems on a varied range of combinatorics, simple algebra, geometry, and logic. I would work on copies of old contests during my other classes.<br /><br />The funny thing is that though these math contests got me into the field, I now have little patience for doing math puzzles of the sort where someone else already knows the answer.Paul Beamenoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-87224030891606798582009-09-25T17:35:25.054-05:002009-09-25T17:35:25.054-05:00I loved A.K.Dewdney's The Planiverse . Like F...I loved A.K.Dewdney's <a href="http://www.amazon.com/Planiverse-Computer-Contact-Two-Dimensional-World/dp/0387989161" rel="nofollow"> The Planiverse </a>. Like Flatland, it looks at life in a two dimensional universe, but goes way beyond Flatland in terms of exploring what engineering, physics, biology, and chemistry would look like in a two dimensional world. How would you play volleyball in a two dimensional world? What sorts of vehicles can you build? How does a two dimensional body with a digestive track avoid falling apart?<br /><br />Flatland was written as a social satire and, even with that in mind, can be hard to stomach at times. Parents whose kids read Flatland will need spend significant time explaining the satire, as opposed to the mathematics, including the extreme sexism and social hierarchy of the Flatland society. The satire has its value, but is not necessarily what readers expect when they pick up a book that is famous now almost entirely for its mathematical content.Unknownhttps://www.blogger.com/profile/09358937783900380398noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-84193663805727057792009-09-25T15:19:23.108-05:002009-09-25T15:19:23.108-05:00Physics was (and is) my main motivation for math, ...Physics was (and is) my main motivation for math, though there is a lot of neat pure math as well. <br /><br />In <a href="http://scottaaronson.com/blog/?p=410" rel="nofollow">this post by Scott Aaronson</a>,he links to and discusses <a href="http://www.maa.org/devlin/LockhartsLament.pdf" rel="nofollow">a paper by Paul Lockhart</a>, of which I have only read the first few pages, and it is more about what is wrong with math than how to do it right (I think). Still, like all good science, it can be great to know all the things that don't work.codyhttps://www.blogger.com/profile/11407919985914326282noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-89322980219499017562009-09-25T12:22:33.024-05:002009-09-25T12:22:33.024-05:00I grew up in Africa and was home schooled from gra...I grew up in Africa and was home schooled from grade 8 to 12. I was an average student in Mathematics in grade 6 and 7 (and I had a very lazy math teacher, who hardly got up from his chair!) My interest in Math was sparked by a British grade 10 mathematics textbook called "O-Level Additional Mathematics" by Michael Browne. It was a delightful textbook. At University, I was lucky to have professors who were excellent Mathematics teachers and kept my interest in MathematicsAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-67588432336846342492009-09-25T09:58:40.570-05:002009-09-25T09:58:40.570-05:001) (ME) In 4th grade I wanted to find out how many...1) (ME) In 4th grade I wanted to find out how many seconds were in a century so I figured it out<br />(I think I didn't count leap years--- oh well.)<br />I doubt this is that interesting to anyone nowadays with computers so prevalent.<br /><br />2) (ME still) 9th grade--- the fact that you could PROVE the quadratic formula I thought was fascinating, and I decided RIGHT THEN to become a math major to find out why you could not solve a quintic equation.<br />(I doubt my thoughts were quite so clear as I remember them, but that was my general sense.)<br /><br />3) For YOUR kid, I AGREE<br />with prior posters-- I also read Martin Gardner<br />in high school and thought that was great.<br /><br />4) For more recent books--I recently wrote a BOOK REVIEW of several<br />books of the type you may be looking for. Its<br />at <br />www.cs.umd.edu/~gasarch/bookrev/bookrev.html<br /><br />5) Here are some math things that have amused my great nieces and nephews (ages 9-11).<br /><br />a) NIM games: here is one,<br />there is more information on the web.<br />There are n stones on the table. Each player can remove 1,2 or 3 stones.<br />Whoever removes the last stone wins. For which values of n does player I wins.<br />(could be more concrete at first- have 10 stones on the table)<br /><br />b) FIND THE NUMBER- I am<br />thinking of a number between 1 and 100. You can<br />ask questions about it.<br />Try to find it in as few questions as usual.<br /><br />c) Look at the sums of odd number<br /><br />1<br /><br />1+3<br /><br />1+3+5<br /><br />etc. Try go guess what the<br />pattern is.<br /><br />d) Same for sums of evens.<br /><br />bill gasarchbill gasarchnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-63912796184125011992009-09-25T09:46:26.710-05:002009-09-25T09:46:26.710-05:00>> I remember asking myself whether our scho...>> I remember asking myself whether our school's computer with its fixed amount of memory could eventually print all the digits of π (no it can't).<br /><br />Why not? I always thought it could. Given sufficient time it could print *any* digit of Pi you want :)Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-48294365932029383692009-09-25T08:44:57.731-05:002009-09-25T08:44:57.731-05:00You read Godel, Escher, Bach as a child? Umm. I re...You read Godel, Escher, Bach as a child? Umm. I read it as an undergrad and I still thought it was heavy reading at the time. <br /><br /><a href="http://www.artofproblemsolving.com/" rel="nofollow">Art of Problem Solving</a> is a website that promotes a number of books for kids who are really into math. Their tagline is "Is math class too easy for you? Looking for a greater challenge? You've come to the right place."Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-68710270633855068422009-09-25T08:28:35.257-05:002009-09-25T08:28:35.257-05:00You didn't say how old your son was. =)
Let m...You didn't say how old your son was. =)<br /><br />Let me second the Martin Gardner recommendation. And he has so many books that one can go years without exhausting them all.<br /><br />You may also want to look at math competitions, which start as young as 6th grade (or younger?). Whether your child actually "competes" or not, you can download the exams from the web to give him something challenging to work on.<br /><br />If he's interested in fundamentals of computers you can try "Elements of Computing Systems..." by Nisan. Surely other can recommend for TCS-focused books.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-23158714120270826252009-09-25T08:20:11.552-05:002009-09-25T08:20:11.552-05:00For the young student who is just starting out in ...For the young student who is just starting out in math, I can't recommend two books highly enough: "The I Hate Mathematics! Book" and its somewhat more advanced sequel "Math for Smarty-Pants".<br /><br />I <i>devoured</i> these books in early elementary school. They are full of zany comics, fun activities/experiments/puzzles/magic tricks with surprising mathematical depth, and great concepts that they don't teach in school: Mobius strips, perfect numbers, "huge" numbers (e.g., googol and googolplex), the Josephus problem, etc.<br /><br />The book also poses problems, some of which end up being very deep. (Some have even been open for centuries!) I remember thinking about whether all perfect numbers are even, and that led to all kinds of independent explorations and discoveries in number theory. I can't praise these books highly enough.Chrishttps://www.blogger.com/profile/03327470068256472110noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-3919956840606177282009-09-25T08:06:52.115-05:002009-09-25T08:06:52.115-05:00Many math-loving people got their start reading Ma...Many math-loving people got their start reading Martin Gardner.<br /><br />The Art of Problem Solving books make me wish I had learned from them when I was younger http://www.artofproblemsolving.com/<br /><br />Like Lance, I had no idea what real math was like or that I could do it until partway through undergrad. The key for me was not "big" inspiring questions but rather learning that I could solve "small" ones with just a little flash of insight, and it was only a lot of solving little questions that gave me the confidence to pose my own. This is not something that I would have figured out how to do on my own, or even if my parents had handed me a book or two (though that might have helped).<br /><br />Your child may enjoy learning to program, in which case something like http://projecteuler.net/ might be fun (but a bit much for junior high math).Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-3612653312990353292009-09-25T07:58:28.459-05:002009-09-25T07:58:28.459-05:00I was a perfectly capable math up until my first g...I was a perfectly capable math up until my first go-round as an undergraduate. Then it all seemed so horribly unmotivated, and so consequently was I. I went into math related fields because I was 'supposed to'. It ended badly.<br /><br />In my second go-round, I had the good fortune of taking quantum mechanics from a very smart guy, and that is when I got my first real taste of math as a rich and expressive medium. So, for me it wasn't love at first sight, but it grew on me like moss.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-1911598814258625982009-09-25T06:15:11.931-05:002009-09-25T06:15:11.931-05:00Gödel, Escher, Bach is a very special book about G...Gödel, Escher, Bach is a very special book about Gödel's uncompleteness theorem, not everybody will like the lots of logic it contains. I would suggest <a href="http://www.amazon.com/Music-Primes-Searching-Greatest-Mathematics/dp/0060935588/ref=sr_1_1?ie=UTF8&s=books&qid=1253877138&sr=8-1" rel="nofollow">The Music of the Primes</a>: a really fascinating account of the human side of Number Theory…Yannis Haralamboushttp://omega.enstb.org/yannisnoreply@blogger.com