{"id":2509,"date":"2009-05-30T15:33:57","date_gmt":"2009-05-30T07:33:57","guid":{"rendered":"http:\/\/www.intmath.com\/blog\/?p=2509"},"modified":"2009-06-07T11:14:19","modified_gmt":"2009-06-07T03:14:19","slug":"intmath-newsletter-wolfram-alpha-point-of-inflection","status":"publish","type":"post","link":"https:\/\/www.intmath.com\/blog\/letters\/intmath-newsletter-wolfram-alpha-point-of-inflection-2509","title":{"rendered":"IntMath Newsletter - WolframAlpha, point of inflection"},"content":{"rendered":"<p>In this Newsletter:<\/p>\n<p>1. Math tip (a) - Studying for math exams<br \/>\n2. Math tip (b) - Wolfram Alpha<br \/>\n3. Math tip (c) - Point of Inflection and house prices<br \/>\n4. From the Math Blog<br \/>\n5. Final thought - who are your real friends?<\/p>\n<hr \/>\n<h2>1. Math tip (a) - Studying for math exams<\/h2>\n<p>Many of you are facing final math exams at this time of the year. Here are some articles that may help you:<\/p>\n<ul>\n<li><a href=\"https:\/\/www.intmath.com\/blog\/how-to-learn-math-formulas\">How to learn math formulas<\/a><\/li>\n<li><a href=\"https:\/\/www.intmath.com\/blog\/how-to-understand-math-formulas\">How to understand math formulas<\/a><\/li>\n<li><a href=\"https:\/\/www.intmath.com\/blog\/ten-ways-to-survive-the-math-blues\">Ten Ways to Survive the Math Blues<\/a><\/li>\n<li>And for some light relief: <a href=\"https:\/\/www.intmath.com\/blog\/videos\/friday-math-movie-how-to-use-the-quadratic-formula-by-hector-the-battle-droid-1248\">Friday Math Movie - How To Use the Quadratic Formula by Hector the Battle Droid<\/a><\/li>\n<\/ul>\n<p><b>Summer:<\/b> And how will you use your summer (those of you in the Northern hemisphere)? I suggest that you consider doing a bit of math here and there during your holidays. You will beat the <a href=\"https:\/\/www.intmath.com\/blog\/letters\/intmath-newsletter-overcoming-fear-of-math-tests-free-calculus-book-2318#forgetting-curve\">forgetting curve<\/a>, which is very important for future math success. <\/p>\n<p>See also <a href=\"https:\/\/www.intmath.com\/blog\/learn-math\/the-summer-math-brain-drain-754\">The summer math brain drain<\/a>.<\/p>\n<hr \/>\n<h2>2. Math tip (b) - Wolfram Alpha<\/h2>\n<p><a href=\"http:\/\/www.wolframalpha.com\/\">WolframAlpha<\/a> is a new online tool can show you how to do math &mdash; and much more.<\/p>\n<p>It is a \"computational knowledge engine\", based on the <i>Mathematica<\/i> computer algebra system and it is one of the most significant recent online offerings.<\/p>\n<p>Their <a href=\"http:\/\/www.wolframalpha.com\/about.html\">aim<\/a> is to <\/p>\n<blockquote>\n<p>... make it possible to compute whatever can be computed about anything<\/p>\n<\/blockquote>\n<p>Wolfram Alpha has a search function, but it has more <a href=\"https:\/\/www.intmath.com\/blog\/mathematics\/google-calculator-handy-but-not-always-correct-1314\">math capabilities than Google's<\/a>:<\/p>\n<blockquote>\n<p>As of now, Wolfram|Alpha contains 10+ trillion of pieces of data, 50,000+ types of algorithms and models, and linguistic capabilities for 1000+ domains.<\/p>\n<\/blockquote>\n<p>Those algorithms can help math students the most.<\/p>\n<p>Enter something like \"<a href=\"http:\/\/www.wolframalpha.com\/input\/?i=graph+sin+x\">graph sin x<\/a>\" and it will provide you with 2 plots showing different domains (first from -2pi to +2pi and the other from -20 to 20.)<\/p>\n<p>Another example: If you enter \"x<sup>2<\/sup> + 3x &minus; 2\", it will give you a wealth of useful information:<\/p>\n<ul>\n<li>The graph of the function (ie y = x<sup>2<\/sup> + 3x &minus; 2 using 2 different domains)<\/li>\n<li>A description of the curve (\"a parabola\")<\/li>\n<li>The roots of the expression (that is, the solution for <span style=\"white-space:nowrap\">x<sup>2<\/sup> + 3x &minus; 2 = 0)<\/span><\/li>\n<li>The derivative, indefinite integral and the minimum value<\/li>\n<li>And assorted other bits of information<\/li>\n<\/ul>\n<p>Two plots of y = x<sup>2<\/sup> + 3x &minus; 2:<\/p>\n<p style=\"margin-left:50px;\"><img loading=\"lazy\" src=\"\/blog\/wp-content\/images\/2009\/05\/wolfram-alpha-01.gif\" alt=\"wolfram-alpha-01\" title=\"wolfram-alpha-01\" width=\"331\" height=\"303\" \/><\/p>\n<p>The solutions for x<sup>2<\/sup> + 3x &minus; 2 = 0:<\/p>\n<p style=\"margin-left:50px;\"><img loading=\"lazy\" src=\"\/blog\/wp-content\/images\/2009\/05\/wolfram-alpha-02.gif\" alt=\"wolfram-alpha-02\" title=\"wolfram-alpha-02\" width=\"143\" height=\"109\" \/><\/p>\n<p>Minimum value of the function:<\/p>\n<p style=\"margin-left:50px;\"><img loading=\"lazy\" src=\"\/blog\/wp-content\/images\/2009\/05\/wolfram-alpha-04.gif\" alt=\"wolfram-alpha-04\" title=\"wolfram-alpha-04\" width=\"273\" height=\"64\" \/><\/p>\n<p>Calculus of the function f(x) = x<sup>2<\/sup> + 3x &minus; 2:<\/p>\n<p style=\"margin-left:50px;\"><img loading=\"lazy\" src=\"\/blog\/wp-content\/images\/2009\/05\/wolfram-alpha-03.gif\" alt=\"wolfram-alpha-03\" title=\"wolfram-alpha-03\" width=\"330\" height=\"148\" \/><\/p>\n<p>It gives the steps for the integral of x<sup>2<\/sup> + 3x &minus; 2:<\/p>\n<p style=\"margin-left:50px;\"><img loading=\"lazy\" src=\"\/blog\/wp-content\/images\/2009\/05\/wolfram-alpha-05.gif\" alt=\"wolfram-alpha-05\" title=\"wolfram-alpha-05\" width=\"332\" height=\"336\" \/><\/p>\n<p><b>Will it do my math homework for me?<\/b> As long as you know what to ask Wolfram Alpha, there is a good chance it will do most of your homework.<\/p>\n<p>But is that a good thing? This is a great tool but it can be dangerous. There is a good chance your math skills will deteriorate if you use this too much and begin to rely on it. <\/p>\n<p>My suggestion is to do your homework questions first and later check your solutions using Wolfram Alpha.<\/p>\n<p>That link again: <a href=\"http:\/\/www.wolframalpha.com\/\">WolframAlpha<\/a>. Try some of their \"sample inputs\" when you get there.<\/p>\n<hr \/>\n<h2>3. Math tip (c) - Point of Inflection<\/h2>\n<p>Have we reached a \"point of inflection\" when it comes to house prices?<\/p>\n<p><img loading=\"lazy\" src=\"\/blog\/wp-content\/images\/2009\/05\/pt-inflection-house-prices5.gif\" alt=\"pt-inflection-house-prices5\" title=\"pt-inflection-house-prices5\" width=\"233\" height=\"280\" \/><\/p>\n<p>In the UK it appears that house prices have bottomed, but not so in the USA yet.<\/p>\n<p>In this special article for this Newsletter, we learn what a <b>point of inflection<\/b> really means and why it is important for your future job. It's also a good introduction to the concepts of maximum, minimum and rate of change graphs.<\/p>\n<p>Go to: <a href=\"https:\/\/www.intmath.com\/blog\/mathematics\/point-of-inflection-for-house-prices-2619\">Point of inflection for house prices?<\/a><\/p>\n<hr \/>\n<h2>4.  From the math blog<\/h2>\n<p>a) <a href=\"https:\/\/www.intmath.com\/blog\/mathematics\/will-the-djia-follow-the-nikkei-down-2576\">Will the DJIA follow the Nikkei down?<\/a><br \/>\nWill the DJIA follow Japan's Nikkei? The conditions are eerily similar to Japan's situation in the early 1990s.<\/p>\n<p>b) <a href=\"https:\/\/www.intmath.com\/blog\/videos\/friday-math-movie-kinetic-wave-sculptures-2562\">Friday Math movie - Kinetic Wave Sculptures<\/a><br \/>\nHere's some kinetic (moving) art based on trigonometry.<\/p>\n<p>The following 2 articles are mentioned above:<\/p>\n<p>c) <a href=\"https:\/\/www.intmath.com\/blog\/mathematics\/point-of-inflection-for-house-prices-2619\">Point of inflection for house prices?<\/a><br \/>\nHave UK house prices reached a turn around? What does \"point of inflection\" mean, anyway?<\/p>\n<p>d) <a href=\"https:\/\/www.intmath.com\/blog\/mathematics\/wolframs-alpha-a-computational-knowledge-engine-2584\">Wolfram's Alpha - a computational knowledge engine<\/a><br \/>\nHere's a free online tool that will do algebra, calculus and trigonometry problems, as well as tell you what day of the week you were born!<\/p>\n<hr \/>\n<h2>5. Final Thought - who are your real friends?<\/h2>\n<p>Oprah Winfrey has inspired many people to live a better life. Her enthusiasm for reading, learning and teachers shows in everything she does. She has built a school in Africa and continually tries to help reduce the dropout rate in American schools.<\/p>\n<p>This quote from Oprah is relevant for all students, especially math students:<\/p>\n<blockquote>\n<p>Surround yourself with only people who are going to lift you higher.<\/p>\n<\/blockquote>\n<p>Avoid the people who tell you math sucks, is useless and is a waste of time. They will only bring you down. Instead, surround yourself with people who love learning and are curious. Your life will be so much richer.<\/p>\n<p>Until next time.<\/p>\n<p class=\"alt\">See the <a href=\"https:\/\/www.intmath.com\/blog\/letters\/intmath-newsletter-wolfram-alpha-point-of-inflection-2509#comments\" id=\"comms\">8 Comments<\/a> below.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In this Newsletter:<br \/>\n1. Math tip (a) - Studying for math exams<br \/>\n2. Math tip (b) - Wolfram Alpha<br \/>\n3. Math tip (c) - Point of Inflection and house prices<br \/>\n4. From the Math Blog<br \/>\n5. Final thought - who are your real friends?<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mo_disable_npp":""},"categories":[104],"tags":[],"_links":{"self":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/2509"}],"collection":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/comments?post=2509"}],"version-history":[{"count":0,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/2509\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/media?parent=2509"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/categories?post=2509"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/tags?post=2509"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}