tag:blogger.com,1999:blog-78210559941817667932024-03-12T22:01:43.513-05:00The ChalkboardWeblog of the Director of Undergraduate Studies of the Mathematics Department at Johns Hopkins UniversityRichard Brownhttp://www.blogger.com/profile/02890750341504212951noreply@blogger.comBlogger128125tag:blogger.com,1999:blog-7821055994181766793.post-79586912368231255442023-09-19T12:19:00.001-05:002023-09-19T12:19:51.061-05:00Shall we (again) begin...?<p>Going into hibernation is a lot like falling asleep. You never really know when it is happening unless you wake up out of it. And then at some point, you do wake up, and reflect on that sleep (in the past tense). </p><p>It has been a while since I wrote here, and will try yet again to start up and keep writing. </p><p>Let's see how I do this time, shall we?</p>Richard Brownhttp://www.blogger.com/profile/02890750341504212951noreply@blogger.com0tag:blogger.com,1999:blog-7821055994181766793.post-23666834821365609422018-07-23T10:08:00.002-05:002018-07-23T10:08:34.436-05:00Finding your Passion?As faculty (advisors, mentors), we are often telling undergraduates that they are in a good position to explore their future and "find their passion". You know, "Definitely take chemistry courses if you love the subject, but now is the time to also take that one class in a subject you were always curious about", or "well, if you are not happy with your studies, perhaps your focus is not what you would really love to pursue". We tend to strongly encourage students to use their undergraduate years as a means to "find" themselves. Tara Bahrampour of the Washington Post in the article<br />
<h3 style="text-align: center;">
<a href="http://bit.ly/FndPassion" style="font-weight: normal;"><span style="font-size: large;">'Find your passion'? That's bad advice, scientists say.</span></a></h3>
says that this may, in fact, be bad advice. Well, not so much bad advice, and incomplete advice. Developing a mindset of general growth, nurturing multiple interests, at least initially, may lead to a much more fulfilling and successful future path. Moreover, fixing the mindset on only a singular topic of study may stunt the pursuit of other interests.<br />
<br />
<br />
<blockquote class="tr_bq">
</blockquote>
<br />
<div style="-webkit-text-stroke-width: 0px; color: black; font-family: "Times New Roman"; font-size: medium; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px; orphans: 2; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">
I like the analysis. You should give it a read.</div>
Richard Brownhttp://www.blogger.com/profile/02890750341504212951noreply@blogger.com1tag:blogger.com,1999:blog-7821055994181766793.post-57603209389975261682018-03-14T15:22:00.000-05:002018-03-14T15:23:22.136-05:00Math in the Media: Arguing on Pi-Day I cannot say that we, as mathematicians, do not have our fair share of math-arguments and inside jokes and math puns and such. You know, stuff that the "outside" world would either groan at or simply walk away from in a head-shaking fashion. But Pi-Day, March 14, or 3/14, does seem to bring things like this to the surface....<br />
<br />
Here are two articles that have leaked out into the "real" world. The first is not a real debate or controversy, really..., but it is kinda fun in a strange sort of way. It is an argument for a better way to generally represent the constant that arises from comparing the diameter or radius of a circle to its circumference. Since pi radians represents only half a turn around a circle, why not have the universal constant simply be 2pi, representing a full turn around the circle. Call this number tau = 2pi. The article, in <a href="https://www.theverge.com/">the Verge</a>, is kind of a rant on pi's fame:<br />
<blockquote class="tr_bq">
<a href="http://bit.ly/2pee9MN">Stop Celebrating Pi Day and embrace Tau as the true circle constant</a></blockquote>
I am not sure about this one, but the accompanying "<a href="http://bit.ly/2HAgV6C">Tau Manifesto</a>" is a pretty good read. <br />
<br />
The other is really more of a comedy routine, designed to educate and highlight some real math. The sort of sweetened medicine you were forced to take as a child. Broadcast via <a href="https://www.motherjones.com/">Mother Jones</a>, the interview/debate<br />
<blockquote class="tr_bq">
<a href="http://bit.ly/2FVrpQU">What is the greatest number of all time?</a></blockquote>
is an argument between two mathematicians Tom Garrity and Colin Adams. Clever....<br />
<br />
Enjoy Pi-Day!!!Richard Brownhttp://www.blogger.com/profile/02890750341504212951noreply@blogger.com0tag:blogger.com,1999:blog-7821055994181766793.post-56684602369557862492018-02-26T09:34:00.001-05:002018-02-26T09:36:16.730-05:00...Back from hibernation....Sorry to all for the long lapse in communication. With other projects on the front burner (a textbook, now due on the shelf this summer), and local distractions right and left, this forum went dormant for a long while. It is now to be considered alive....<br />
<br />
Talk to you soon about math in teaching, education, recreation, etc. Richard Brownhttp://www.blogger.com/profile/02890750341504212951noreply@blogger.com0tag:blogger.com,1999:blog-7821055994181766793.post-47514035504977478252016-03-18T09:16:00.000-05:002016-03-18T09:16:23.188-05:00Math in the Media: The 2016 Abel PrizeAndrew Wiles, (well..., actually, Sir Andrew John Wiles), the British mathematician, currently at Oxford who is credited with solving the famous "Last Theorem" of Pierre de Fermat, has been awarded the 2016 <a href="http://bit.ly/1MecIGL">Abel Prize</a> for outstanding contributions to the field. From the Abel Committee of the Norwegian Academy of Science and Letters, <br />
<blockquote class="tr_bq">
[t]he prize is meant to recognize contributions of extraordinary depth and
influence to the mathematical sciences. Such work may have resolved
fundamental problems, created powerful new techniques, introduced
unifying principles or opened up major new fields of research. The
intent is to award prizes over the course of time in a broad range of
fields within the mathematical sciences.</blockquote>
One can easily say Professor Wiles is qualified, no? <br />
<br />
Congratulations, Professor! Read up on this amazing accomplishment here:<br />
<blockquote class="tr_bq">
<h3>
<a href="http://bit.ly/22rGf3C">Fermat's Last Theorem proof secures mathematics' top prize for Sir Andrew Wiles</a></h3>
</blockquote>
Richard Brownhttp://www.blogger.com/profile/02890750341504212951noreply@blogger.com1tag:blogger.com,1999:blog-7821055994181766793.post-65465974511052682962015-10-13T15:14:00.001-05:002015-10-13T15:14:47.938-05:00Math in the Media: The importance of Recreational Math? Math as a plaything is something most mathematicians take for granted. It is one of the main reasons we choose to study math as a discipline: Many of us "played" a lot when we were kids. We marveled at logic puzzles, looked for patterns and clues in complicated word problems, played tricks with the double meanings of words and phrases and generally devoured games that rewarded the player when one can uncover the proper strategy. Martin Gardner was a wonder at finding the mathematics hidden in playful puzzles and tricky games. His "Mathematical Games" series in Scientific American, something on the order of 300 columns from 1956 to 1986, is a true treasure trove of beautiful, yet playful mathematics. <br />
<br />
Now, Manil Suri, a professor in the Mathematics Department of the University of Maryland, Baltimore County, writes in the New York Times of this importance of the recreational side of mathematics, especially at the primary and secondary levels, citing Gardner's work. The piece is<br />
<blockquote class="tr_bq">
<a href="http://www.nytimes.com/2015/10/12/opinion/the-importance-of-recreational-math.html">The Importance of Recreational Math</a></blockquote>
It's a worthy topic to illuminate. Do take a look....Richard Brownhttp://www.blogger.com/profile/02890750341504212951noreply@blogger.com0tag:blogger.com,1999:blog-7821055994181766793.post-48219713036772436302015-04-15T16:20:00.001-05:002015-04-15T16:20:14.999-05:00Viral Math....So.... Have you figured out Cheryl's birthday yet? <br /><br />It's funny how so few people regard this puzzle as real math (as opposed to calculating a derivative or something.) In my mind, THIS is real math; taking a complicated situation, digging out and exposing the logical skeletal structure underlying it, studying that structure and abusing it to say something conclusive about the situation. Problem solving, in a nutshell, is mathematics. Or perhaps real math is learning how to synthesize and generalize the logical structure so that it can be used again in other puzzles, or situations. <br /><br />Either way.... This is real math. <br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRiG7ydsqspu8xLUyo-o0eWfH5Lsf9WqE2g93Fe_mvp6NIgmmMLDhL2nHMe2F5GroBmd7Rk6qeh89jHuBCCteoqUlL_I-zIcSUcNw_ZrjxcwVE3uhls3xRO8NdDduIB3HmTtGUSC4qDjSN/s1600/CherylsBirthday.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRiG7ydsqspu8xLUyo-o0eWfH5Lsf9WqE2g93Fe_mvp6NIgmmMLDhL2nHMe2F5GroBmd7Rk6qeh89jHuBCCteoqUlL_I-zIcSUcNw_ZrjxcwVE3uhls3xRO8NdDduIB3HmTtGUSC4qDjSN/s1600/CherylsBirthday.jpg" height="240" width="320" /></a></div>
<br />Richard Brownhttp://www.blogger.com/profile/02890750341504212951noreply@blogger.com1tag:blogger.com,1999:blog-7821055994181766793.post-61045226240580355842015-04-14T09:13:00.001-05:002015-04-14T09:13:36.227-05:00Math in the Media: The Best jobs of 2015?I keep telling you.... Math pays!! <br />
<br />
In the Business section of the online newspaper <a href="http://www.huffingtonpost.com/">The Huffington Post</a> sits an article by <a href="http://www.huffingtonpost.com/jenny-che/">Jennie Che</a> detailing the Best Jobs of 2015, a report prepared each year by <a href="http://www.careercast.com/">CareerCast</a>, ranking the top 200 jobs by work environment, income, stress and hiring outlook. <br />
<br />
And lo and behold, mathematics permeates most of the list, with the actual job of Mathematician, sitting at number 3 (Actuarial Scientist tops the list, with Statistics sitting at number 4). The HuffPost article<br />
<blockquote class="tr_bq">
<h3 class="title" style="text-align: left;">
<a href="http://huff.to/1yqIcm8">These Are The 10 Best Jobs Of 2015</a></h3>
</blockquote>
<div class="title" style="text-align: left;">
is a summary of the longer article posted directly in the CareerCast website:</div>
<blockquote class="tr_bq">
<h3>
<a href="http://bit.ly/1csneJH">The Best Jobs of 2015</a></h3>
</blockquote>
(always go to the source, right?) Personally, I've held position both in academia and in industry (NASA Goddard and Lincoln Laboratory, as well as in a private tech firm.) All were great work environments, with interesting people, work conditions, and colleagues. I certainly cannot argue with the conclusion that math is a great field to play in.<br />
<br />
Give the article a read! It's good stuff. <br />
<div class="title" style="text-align: left;">
<br /></div>
Richard Brownhttp://www.blogger.com/profile/02890750341504212951noreply@blogger.com0tag:blogger.com,1999:blog-7821055994181766793.post-16059649162912525662015-03-24T09:59:00.000-05:002015-03-24T09:59:25.200-05:00Math in the Media: NFL Mathematician??I am often asked what kinds of careers can a mathematician construct for themselves. There are many answers to this question, and in full generality, the list is long and very diverse. However, I recently found a new one: Professional American football player!! <br />
<br />
It seems that our very own <a href="http://bit.ly/1FzXO8Z">John Urschel</a>, a guard of the Baltimore Ravens ("our very own" because we are here in Baltimore after all), is a mathematician whose recent paper <a href="http://bit.ly/1C7yYcN">"A Cascadic Multigrid Algorithm for Computing the Fielder Vector of Graph Laplacians”</a> has been accepted for publication in the<a href="http://bit.ly/1DTzKNK"> Journal of Computational Mathematics</a>. Mr. Urschel received his Masters Degree in Mathematics from Penn State and was drafted by the Ravens last year.<br />
<br />
One can find mathematicians in the oddest of places, no? One just has to look carefully....<br />
<br />
...although in this case, it is not hard to see. Mr. Urschel's is on Twitter. His name??<br />
<br />
....@MathMeetsFball Richard Brownhttp://www.blogger.com/profile/02890750341504212951noreply@blogger.com0tag:blogger.com,1999:blog-7821055994181766793.post-87290975789954484662015-03-10T09:11:00.000-05:002015-03-10T09:12:17.015-05:00Math in the Media: Gender Bias in Teachers?Yes, it does take a village to raise a child.... (H/T to The Honorable Hillary Rodham Clinton.) But it seems it also takes a village to discourage girls from achieving their full potential in math and math-related fields.... (Sigh!)<br />
<br />
In a new study, headed by Edith Sand, an economist at the Bank of Israel and an instructor at the Tel-Aviv University’s Berglas School of Economics, teachers themselves contribute to the problem of too many female students shying away from higher-level math courses as they progress in their education. The study found a gender bias in performance evaluation; Teachers who knew the identities of their students tended to grade girls more harshly and boys less so on exams than teachers who did not have any information about the students. Unconscious or not, our influence as teachers on students always goes far beyond the content of our lectures and exercises. But this influence may not always be constructive. What care we need to always take.... <br />
<br />
The article, reported by Linda Carroll for Today, is here:<br />
<blockquote class="tr_bq">
<a href="http://on.today.com/1GBicXC">Teacher Bias May Help Discourage Girls from Math, Study Finds</a> </blockquote>
The study is published by the National Bureau of Economic Research in Cambridge, Mass.<br />
<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj63UMpqd63NJzaoLMOhi6bwSp1hSUlqb6w6LJHTyK1ohezo7PvjBPRhlTZLYdTDsnjd6z2bggUYONEo20dqCqE44lzNxgbWP_Nb9Yj5vTmpQtUdjHws18wRSGaPejmlziA0zK7_3ZdIgd0/s1600/knowledge_is_power_decal.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj63UMpqd63NJzaoLMOhi6bwSp1hSUlqb6w6LJHTyK1ohezo7PvjBPRhlTZLYdTDsnjd6z2bggUYONEo20dqCqE44lzNxgbWP_Nb9Yj5vTmpQtUdjHws18wRSGaPejmlziA0zK7_3ZdIgd0/s1600/knowledge_is_power_decal.jpg" height="200" width="200" /></a>Depressing...? Yes. Hopeful? Also. Knowing of an unconscious bias can contribute to its cure, eh? <br />
<br />
Remember School House Rock? "Knowledge is Power"Richard Brownhttp://www.blogger.com/profile/02890750341504212951noreply@blogger.com1tag:blogger.com,1999:blog-7821055994181766793.post-61443482921410755952015-03-04T09:49:00.000-05:002015-03-04T09:49:27.025-05:00Math in the Media: Homer vs. Pierre?<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh52Xf0qpzti3VrGeDpoCx3nK0zsvIfXqphCnHlixyNRIVaDMaM7gFSuOsYH-rn2AGoAdqEok6FvthlLrqI5AiUBX3p1lx4qhIOuod27MwxDdBPuHNGkXme28yw03bdazIK_P8TgfnO7wLm/s1600/The_Simpsons_3049738b.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh52Xf0qpzti3VrGeDpoCx3nK0zsvIfXqphCnHlixyNRIVaDMaM7gFSuOsYH-rn2AGoAdqEok6FvthlLrqI5AiUBX3p1lx4qhIOuod27MwxDdBPuHNGkXme28yw03bdazIK_P8TgfnO7wLm/s1600/The_Simpsons_3049738b.jpg" height="199" width="320" /></a>I just had the pleasure of watching a neat 8 minute video detailing some of the mathematics injected in to the Simpsons animations. Apparently, there are mathematicians among the creative staff who cannot help themselves throwing in a little math humor into the background every so often. <br />
<br />
The video, listed here on YouTube by <a href="http://bit.ly/1DUsQVR">Numberphile</a> is titled<br />
<blockquote class="tr_bq">
<h4>
<a href="http://bit.ly/1EgeQIC">Homer Simpson vs Pierre de Fermat</a></h4>
</blockquote>
Do give it a watch. It is always good to know where the subliminal messages about how cool math really is are lurking, no?Richard Brownhttp://www.blogger.com/profile/02890750341504212951noreply@blogger.com0tag:blogger.com,1999:blog-7821055994181766793.post-54140437261134544442015-02-11T10:04:00.000-05:002015-02-11T10:04:36.333-05:00What is Mathematics? Passages....So I was asked during the break between the semesters to take part in an Intersession course designed to bridge the void between the sciences and the humanities (mind the gap!) by having professors from all stripes discuss common topics to a diverse audience. The idea is that each professor sees the topic from the perspective of their chosen field and the same topic often looks quite different to different people. It is a wonderful idea hatched and developed by Dr. Kristin Cook-Gailloud, the Director of the Program in French Language and Culture here at Hopkins. This is the second year running this course and I thoroughly endorse it. Alas, due to scheduling issues, I did not participate this year. But a topic in this year's course, Passages, stuck in my head. The idea of movement from one state to another is something innate to a mathematician, if regarded as movement from a state of ignorance and confusion to clarity and enlightenment. <br />
<br />
So I wrote an essay to clarify my idea of passage in mathematics. It is here:<br />
<blockquote class="tr_bq">
<h4>
<a href="http://bit.ly/1E95tGS">Passages in Mathematics</a></h4>
</blockquote>
Enjoy and do let me know what you think....Richard Brownhttp://www.blogger.com/profile/02890750341504212951noreply@blogger.com0tag:blogger.com,1999:blog-7821055994181766793.post-83965164470388310932015-02-04T10:51:00.001-05:002015-02-04T10:51:40.538-05:00Math in the Media: Stereotype Threat?How often we are in Mathematics faced with the fact that our profession was, and still is, quite female-starved; that boys and men are thought to be better at math than girls and women (an amazingly ridiculous thought, given my view up here!). So many recent studies seem to point decidedly at the dangerous effects of a person's perceptions of ability at the moment of evaluation and how easily they can affect performance. For example, reminding students of a stereotype they conform to just before taking a math test tends to degrade performance. This slow drip of research exposing the damaging effects of culture bias and preconceptions on lack of ability can only have a good effect in the long run. And I do see here at Hopkins some light in the form of a general welcoming attitude and positive outreach to students studying higher mathematics regardless of gender. But it does seem that this huge ship turns only very slowly. <br />
<br />
Over at the online newspaper, the Huffington Post, <a href="http://huff.to/1CZ88Ve">Cailin O’Connor</a>, a Professor of the Philosophy of Science at the<a href="http://uci.edu/"> University of California, Irvine</a>, details some of the evidence that runs contrary to the notion of an innate gender bias in mathematical ability here:<br />
<blockquote class="tr_bq">
<b><a href="http://huff.to/1z9N34m">Are Women Worse at Math? It's Time to Stop Asking</a></b></blockquote>
Her take? Perhaps it is time to stop focusing on looking for innate differences between the genders in mathematical ability and start simply addressing the cultural barriers that keep the gender balances way too tilted to one side. <br />
<br />
I agree, but still love seeing the rising tide of evidence condemning the idea that math is more a male thing. Geez!<br />
<br />
<br />Richard Brownhttp://www.blogger.com/profile/02890750341504212951noreply@blogger.com2tag:blogger.com,1999:blog-7821055994181766793.post-87130079130718229822014-12-22T14:19:00.000-05:002014-12-22T14:19:25.135-05:00Math in the Media: Prime Gaps....I am always amazed at how some of the most vexing, curious and fascinating puzzles in mathematics can be stated so simply, even as they evade solution or even complete understanding for centuries. It is one of the more alluring aspects of this trade. <br />
<br />
Here's one: Just how big can the gaps between consecutive pairs of prime numbers get as one traverses the natural numbers out toward infinity? <br />
<br />
One would expect the gaps to get larger and larger and also tend toward infinity in the long run, no? But showing this, and providing some sort of measure of the growth of the size of the gaps as one goes "out there" has been remarkably elusive. <br />
<br />
I'll let you read this nice article by <a href="https://www.quantamagazine.org/authors/erica-klarreich/">Erica Klarreich</a> in <a href="http://www.quantamagazine.org/">Quanta Magazine</a>, to "see" that progress has recently been made, and there is promise of more progress coming. <br />
<blockquote class="tr_bq">
<a href="http://bit.ly/1E3Bgxe"><b>Mathematicians Make a Major Discovery About Prime Numbers</b></a></blockquote>
Will math ever cease to amaze.... <b><br /></b><br />
Richard Brownhttp://www.blogger.com/profile/02890750341504212951noreply@blogger.com0tag:blogger.com,1999:blog-7821055994181766793.post-51296892520396232812014-12-03T10:10:00.000-05:002014-12-03T10:10:18.692-05:00Math in the Media: Mathematics is Evil?There is an old saying (really, I just made this up): If you are looking for immortality, you have two choices. Become famous, or become infamous. Either way, you will not soon be forgotten....<br />
<br />
A professor here is uncovering an interesting conjecture. The fictitious, evil mastermind and arch-nemesis of Sherlock Holmes, <a href="http://en.wikipedia.org/wiki/Professor_Moriarty">Professor James Moriarity</a>, was modeled by Sir Arthur Conan Doyle on a mathematics professor here at Hopkins. The similarities are quite striking, detailed here by current professor Carl McTague<br />
<blockquote class="tr_bq">
<h4>
<a href="http://bit.ly/11U0JYF">Moriarity at Hopkins</a></h4>
</blockquote>
Give it a read. Nice idea, eh? Richard Brownhttp://www.blogger.com/profile/02890750341504212951noreply@blogger.com1tag:blogger.com,1999:blog-7821055994181766793.post-88205058135254773892014-09-26T17:24:00.001-05:002014-09-26T17:25:54.511-05:00Math in the Media: Return on Investment in a Math Degree?So I would up devoting my life to the study of Mathematics because I absolutely love the subject. It is inherently beautiful, surprisingly counter-intuitive, and seems to exhibit a logical framework for all that is in a way that I find ever intriguing.<br />
<br />
However..., the study of math at a high level is also quite lucrative!!<br />
<br />
Here is an article from <a href="http://www.businessweek.com/">Bloomberg Business Week</a>, from June:<br />
<blockquote class="tr_bq">
<a href="http://buswk.co/1pwRcuF">Undergrad Business Majors Don't Get the Career Payback Math Majors Do</a></blockquote>
You must love this title from my perspective. The article highlights a measure of the lifetime worth of different college majors in term of a return on investment of time and effort. Some majors are harder than others, I am sure. And why they decided to include math and computer science together is a mystery to me (perhaps that is how the business world sees us? As the studiers of logic?<br />
<br />
In any case, they make a good case for choosing math as a major while here in the Ivory Tower. Call that reason number..., what... 132 in the countably infinite number of reasons why someone can benefit from choosing math as a major? (BTW, have you heard that over 80% of statistics are made up on the spot?)<br />
<br />
Give it a read. I will await your change-of-major form.... ;-) Richard Brownhttp://www.blogger.com/profile/02890750341504212951noreply@blogger.com2tag:blogger.com,1999:blog-7821055994181766793.post-91259963130123522492014-08-18T15:54:00.000-05:002014-08-18T15:54:32.695-05:00Real Mathematics!I am gearing up for the fall semester here at Hopkins. This fall, I am teaching our version of vector calculus (aka multivariable calulus), 110.202 Calculus III. It is a great course, beautifully visual and quite subtle in many ways. Good stuff! <br />
<br />
I sent out a "hello" email to my 300+ students, inviting them to check out the webpage and generally welcoming them to the course. In this email, I say near the end:<br />
<!--[if gte mso 9]><xml>
<o:OfficeDocumentSettings>
<o:AllowPNG/>
</o:OfficeDocumentSettings>
</xml><![endif]--><br />
<!--[if gte mso 9]><xml>
<w:WordDocument>
<w:View>Normal</w:View>
<w:Zoom>0</w:Zoom>
<w:TrackMoves/>
<w:TrackFormatting/>
<w:PunctuationKerning/>
<w:ValidateAgainstSchemas/>
<w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid>
<w:IgnoreMixedContent>false</w:IgnoreMixedContent>
<w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText>
<w:DoNotPromoteQF/>
<w:LidThemeOther>EN-US</w:LidThemeOther>
<w:LidThemeAsian>X-NONE</w:LidThemeAsian>
<w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript>
<w:Compatibility>
<w:BreakWrappedTables/>
<w:SnapToGridInCell/>
<w:WrapTextWithPunct/>
<w:UseAsianBreakRules/>
<w:DontGrowAutofit/>
<w:SplitPgBreakAndParaMark/>
<w:EnableOpenTypeKerning/>
<w:DontFlipMirrorIndents/>
<w:OverrideTableStyleHps/>
</w:Compatibility>
<w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel>
<m:mathPr>
<m:mathFont m:val="Cambria Math"/>
<m:brkBin m:val="before"/>
<m:brkBinSub m:val="--"/>
<m:smallFrac m:val="off"/>
<m:dispDef/>
<m:lMargin m:val="0"/>
<m:rMargin m:val="0"/>
<m:defJc m:val="centerGroup"/>
<m:wrapIndent m:val="1440"/>
<m:intLim m:val="subSup"/>
<m:naryLim m:val="undOvr"/>
</m:mathPr></w:WordDocument>
</xml><![endif]--><!--[if gte mso 9]><xml>
<w:LatentStyles DefLockedState="false" DefUnhideWhenUsed="true"
DefSemiHidden="true" DefQFormat="false" DefPriority="99"
LatentStyleCount="267">
<w:LsdException Locked="false" Priority="0" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Normal"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="heading 1"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 2"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 3"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 4"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 5"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 6"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 7"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 8"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 9"/>
<w:LsdException Locked="false" Priority="39" Name="toc 1"/>
<w:LsdException Locked="false" Priority="39" Name="toc 2"/>
<w:LsdException Locked="false" Priority="39" Name="toc 3"/>
<w:LsdException Locked="false" Priority="39" Name="toc 4"/>
<w:LsdException Locked="false" Priority="39" Name="toc 5"/>
<w:LsdException Locked="false" Priority="39" Name="toc 6"/>
<w:LsdException Locked="false" Priority="39" Name="toc 7"/>
<w:LsdException Locked="false" Priority="39" Name="toc 8"/>
<w:LsdException Locked="false" Priority="39" Name="toc 9"/>
<w:LsdException Locked="false" Priority="35" QFormat="true" Name="caption"/>
<w:LsdException Locked="false" Priority="10" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Title"/>
<w:LsdException Locked="false" Priority="1" Name="Default Paragraph Font"/>
<w:LsdException Locked="false" Priority="11" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtitle"/>
<w:LsdException Locked="false" Priority="22" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Strong"/>
<w:LsdException Locked="false" Priority="20" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Emphasis"/>
<w:LsdException Locked="false" Priority="59" SemiHidden="false"
UnhideWhenUsed="false" Name="Table Grid"/>
<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Placeholder Text"/>
<w:LsdException Locked="false" Priority="1" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="No Spacing"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 1"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 1"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 1"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 1"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 1"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 1"/>
<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Revision"/>
<w:LsdException Locked="false" Priority="34" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="List Paragraph"/>
<w:LsdException Locked="false" Priority="29" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Quote"/>
<w:LsdException Locked="false" Priority="30" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Quote"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 1"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 1"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 1"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 1"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 1"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 1"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 1"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 2"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 2"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 2"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 2"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 2"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 2"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 2"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 2"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 2"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 2"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 2"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 2"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 2"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 3"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 3"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 3"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 3"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 3"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 3"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 3"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 3"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 3"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 3"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 3"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 3"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 3"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 3"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 4"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 4"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 4"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 4"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 4"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 4"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 4"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 4"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 4"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 4"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 4"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 4"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 4"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 4"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 5"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 5"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 5"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 5"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 5"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 5"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 5"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 5"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 5"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 5"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 5"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 5"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 5"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 5"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 6"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 6"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 6"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 6"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 6"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 6"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 6"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 6"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 6"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 6"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 6"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 6"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 6"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 6"/>
<w:LsdException Locked="false" Priority="19" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Emphasis"/>
<w:LsdException Locked="false" Priority="21" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Emphasis"/>
<w:LsdException Locked="false" Priority="31" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Reference"/>
<w:LsdException Locked="false" Priority="32" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Reference"/>
<w:LsdException Locked="false" Priority="33" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Book Title"/>
<w:LsdException Locked="false" Priority="37" Name="Bibliography"/>
<w:LsdException Locked="false" Priority="39" QFormat="true" Name="TOC Heading"/>
</w:LatentStyles>
</xml><![endif]--><!--[if gte mso 10]>
<style>
/* Style Definitions */
table.MsoNormalTable
{mso-style-name:"Table Normal";
mso-tstyle-rowband-size:0;
mso-tstyle-colband-size:0;
mso-style-noshow:yes;
mso-style-priority:99;
mso-style-parent:"";
mso-padding-alt:0in 5.4pt 0in 5.4pt;
mso-para-margin:0in;
mso-para-margin-bottom:.0001pt;
mso-pagination:widow-orphan;
font-size:10.0pt;
font-family:"Calibri","sans-serif";
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;}
</style>
<![endif]-->
<br />
<blockquote class="tr_bq">
<div class="MsoPlainText">
Even though one may think of calculus as simply a math
course where one learns some techniques for solving physics and statistics
problems, it actually is much more than this. Instead of simply learning
techniques, we will be learning how and why the techniques even exist, what
they say about the structure of mathematics like calculus, and how to think
analytically and reason deductively and abstractly. THIS is the real
mathematics. The techniques will come along for the ride. You will
learn those also. </div>
</blockquote>
<blockquote class="tr_bq">
<div class="MsoPlainText">
Perhaps the best way to drive this point home is the
following:<span style="mso-spacerun: yes;"> </span><span style="color: blue;">It does not matter what your
current and/or future major is or will be.<span style="mso-spacerun: yes;">
</span>You are here at Hopkins to train to be a scholar at something.<span style="mso-spacerun: yes;"> </span>Part of that training includes proficient and
efficient understanding of the abstract logical structural framework found in
all complex ideas and constructions.<span style="mso-spacerun: yes;">
</span>This is really what mathematics is.<span style="mso-spacerun: yes;">
</span>We typically use numbers and operations on those numbers to study and
exhibit mathematical ideas because they provide the self-consistent framework
needed for the study.</span><span style="mso-spacerun: yes;"><span style="color: blue;"> </span> </span>I will say a lot
more about this on the first day of class. </div>
</blockquote>
Perhaps this is one of my personal definitions of mathematics. But I like it. Make sense?<br />
Richard Brownhttp://www.blogger.com/profile/02890750341504212951noreply@blogger.com0tag:blogger.com,1999:blog-7821055994181766793.post-50377668170475547772014-08-14T16:06:00.000-05:002014-08-14T16:06:31.544-05:00Math in the Media: Finally!! A female Fields Medalist....Well, I am back and in time for a new semester here at Hopkins. And I am back with some very nice news. <br />
<br />
The next recipients of one of our field's top honors, the Fields Medal, includes <span class="caption-text">Maryam Mirzakhani, an Iranian born mathematician at <a href="http://www.stanford.edu/">Stanford University</a>. She is a dynamicist (a mathematician whose field of study is dynamical systems) and the first woman to receive this prize since its inception in 1936. She shares the prize this year (the prize is given out every four years) with three other mathematicians, listed in this article in the <a href="http://www.nytimes.com/">New York Times</a>, </span><br />
<blockquote class="tr_bq">
<a href="http://nyti.ms/1l7uoGI"><span style="font-size: small;">Top Math Prize Has Its First Female Winner.</span></a></blockquote>
<span style="font-size: small;">And while there should be nothing special about a woman receiving the prize (math is hardly a gender-specific endeavor), I do have sort of a glass-ceiling-breaking-moment feeling here. Congratulations, Professor and Professors! Here's to more outstanding math research.</span><br />
<span style="font-size: small;"><br /></span>
<span style="font-size: small;">And <a href="http://stanford.io/1sHlQIN">here </a>is another nice write up of this event and her contributions to mathematics.</span>Richard Brownhttp://www.blogger.com/profile/02890750341504212951noreply@blogger.com0tag:blogger.com,1999:blog-7821055994181766793.post-92020459443533151512014-06-24T13:56:00.003-05:002014-06-24T13:56:56.562-05:00Math in Film: NUMB3RSSo I finally got around to watching he pilot for the series <a href="http://en.wikipedia.org/wiki/Numbers_%28TV_series%29">NUMB3RS</a>. Yeah, I know, the show is way old and quite dead now (it ran from 2005-2010). But I tend to avoid shows that have mathematicians as main characters. Hollywood (and environs) understand so little about our practice that they rely on stereotypes rather than seek to educate or play straight. My son, however, found the pilot, watched it, and promptly told me that the show actually gets some genuine features of mathematicians. So, armed with his endorsement, I jumped in.<br />
<br />
For those who do not know, the show is a crime drama centering around an FBI agent who winds up using his brother's help and expertise to solve very complicated crimes in LA. The brother is said to be a young, genius, mathematician (professor at Stanford). The brother's mathematical insight and ideas are a central aspect of the show. I suspect that in each episode, they are crucial to the solution of the case. I have only watched the one introductory episode so far. But they is some merit here.<br />
<br />
For the most part, mathematicians are considered brilliant but weird, fascinating but off-putting, playful but socially awkward to the point that people do not really know what to do with them. I must admit that this is a fairly accurate portrayal even from the inside. NUMB3RS gets this part right, and the character mathematician has the right zest for life and obsession with the logical structure of everything that he can easily make his way around a conference unnoticed. <br />
<br />
What works is (1) "his work is his life is his work" aspect of how he approaches new puzzles, (2) the idea that there is an elegant solution to every problem and the trick is to simply find it, (3) the notion that everything is mathematical in that everything has a logical structure which, once understood, can be exploited, (4) the absolute certainty of results once proved, and lastly (5) the idea that mistakes are merely foundations for building more enlightened theory. All seemingly fresh, given other depictions I have seen in film and TV. I guess this idea in future episodes, like in this one, would be a single big lesson taught in each case, and each lesson would be different. <br />
<br />
What didn't work for me? Well..., the acting was generally very wanting. The pilot was a bit like the many CSI-type crime dramas where a team is working together to solve a crime. Every scene with the team has each member saying one line which is crucial to the case (so that they all contribute), and there is little wasted banter. Too unrealistic for me. Also, the idea that mathematicians only deal with equations, and to them everything is an expression. In this idea, mathematicians can only work when their ideas are rendered into equations. This is not true at all. That was, I suspect a simplification to mesh with the stereotype. <br />
<br />
In any case, it was refreshing to see a depiction much closer to reality than is usual. Give it is shot.Richard Brownhttp://www.blogger.com/profile/02890750341504212951noreply@blogger.com0tag:blogger.com,1999:blog-7821055994181766793.post-9270414219575562822014-04-01T17:34:00.000-05:002014-04-01T17:35:22.021-05:00Playfully Serious Math: A glimpse at Vi Hart and FibonacciI am often struck by just how repulsive mathematics is to some people when, in my eyes, it is all an absolute kaleidoscope of color, art and logical splendor. But it is not always easy to get someone else to see what you see. This is what education is all about, I guess. One step at a time....<br />
<br />
I was recently turned on to an absolutely wonderful math and science educator whose videos would do well to provide the backbone of the next generation of the Common Core, at least in math education. Vi Hart is a videographer (is that what one would call someone who makes videos) who specializes in a playful, though very serious approach to expose and illustrate complicated science concepts and techniques. One of her series, entitled Doodling in Math Class, exposes the rich, playful and beautiful structure inherent in every math class but lost in the tedium of sterile, and solely utile function. Below is a three part video explaining why and how the Fibonacci Sequence (not a series, really) shows up so often in nature. It is mind-boggingly well done, IMHO:<br />
<blockquote class="tr_bq">
<h1 class="yt" id="watch-headline-title">
<span style="font-size: large;"><b><span style="font-weight: normal;"><span class="watch-title long-title yt-uix-expander-head" dir="ltr" id="eow-title" title="Doodling in Math: Spirals, Fibonacci, and Being a Plant [1 of 3]"><a href="http://bit.ly/1lmpodq">Doodling in Math: Spirals, Fibonacci, and Being a Plant</a> </span></span></b></span></h1>
</blockquote>
The other two parts follow immediately from this one. Give them a look!<br />
<br />
BTW, THIS is what mathematics is really about. Vi's money quote (at the end of the third part):<br />
<blockquote class="tr_bq">
This is why science and math are so much fun. You discover things that seem impossible to be true, and then you get to figure out why it is impossible for them not to be true.</blockquote>
Richard Brownhttp://www.blogger.com/profile/02890750341504212951noreply@blogger.com0tag:blogger.com,1999:blog-7821055994181766793.post-37282784164788456502014-03-19T09:26:00.000-05:002014-03-19T09:26:33.229-05:00Math in the Media: TEDx and me....Late last year, I was asked to give a TEDx talk (the 'x' means locally organized) for the inaugural TEDx event here at Hopkins (called <a href="http://www.tedxjohnshopkinsuniversity.com/">TEDxJohnsHopkinsUniversity</a>). I gladly accepted, seeing it as a chance to say something I've been wanting to say for a while: I wanted to give a talk on what mathematics means to me and why I chose it as a lifestyle. On February 22, 2014, here on campus, I gave the talk, entitled "Why Mathematics?". <br />
<br />
Here it is in full:<br />
<blockquote class="tr_bq">
<a href="http://bit.ly/OwkleQ">Why Mathematics?</a> </blockquote>
It was a great experience, and the organizers did an excellent job. I hope you find the talk interesting. Richard Brownhttp://www.blogger.com/profile/02890750341504212951noreply@blogger.com0tag:blogger.com,1999:blog-7821055994181766793.post-13766588433430105942014-02-17T17:35:00.001-05:002014-02-17T17:36:39.407-05:00Math in the Media - Perhaps the Matrix is....Here is an article filed under the category "Thoughts to Ponder": <a href="http://math.berkeley.edu/~frenkel/">Edward Frenkel</a>, a mathematician from Berkeley, posits that the university perhaps is just a giant simulation and we are simply participants. How would we know? Can we detect if we were? The article is an OpEd in the <a href="http://www.nytimes.com/">New York Times</a>, and can be found here:<br />
<blockquote class="tr_bq">
<a href="http://nyti.ms/1gXfvQi"><span style="font-size: large;">Is the Universe a Simulation?</span></a></blockquote>
Frenkel gives some sense to this idea by differentiating (no pun intended) mathematical ideas (manuscripts, really) from literary ones in the following way: Mathematical ideas are somewhat universal. The laws and constructions of Pythagorus, Euclid, Newton, etc., would surely have been created (discovered?) even if these greats had never existed. It may have taken longer for someone else to develop them. But the structure of mathematics (its logical framework) exists as it is whether we discover it or not. Try that with a sonnet sans Shakespeare....<br />
<br />
It is a very nice read, this article, and again, gives a sense for how mathematics seems different from other disciplines of study. Frenkel mentions that many mathematicians consider themselves Platonists, believers that everything exists in the ideal, and what we perceive in this world is simply real versions of that ideal. It works for me. I would believe that it would work for most all mathematicians, really. <br />
<br />
Frenkel even goes so far as to say that the giant computer simulation that we exist in is, like all computer simulations, not entirely without anomalies, coding inaccuracies that render the coding conspicuous. Perhaps all of our logic in mathematics is simply facets of the coding that can be detected "from within"<span style="font-size: small;">?</span><br />
<br />
<span style="font-size: small;">Certainly a "thought to ponder".... </span> Richard Brownhttp://www.blogger.com/profile/02890750341504212951noreply@blogger.com0tag:blogger.com,1999:blog-7821055994181766793.post-55650964709606541452014-02-14T18:27:00.000-05:002014-02-14T18:27:45.814-05:00Beauty in MathMathematicians often talk about their craft in emotional terms. We get excited by elegant, beautiful, clever constructions and the hidden insight in the logical relationships we uncover. We can easily be stunned into awe when our intuition leads us astray, and something we did not expect pops out of our reasoning. And when we see a formula or other type of mathematical construction that not only looks aesthetically pleasing, but contains meaning far beyond its simple symbolic patterns, we treat it as something that should be hanging in the Louvre....<br />
<br />
Beauty has profound meaning in mathematics, at least to us.<br />
<br />
Not sure you believe me? Well, a paper just published in the journal <a href="http://bit.ly/1ezSoIb">Frontiers in Human Neuroscience</a> may just change your mind. Researchers use Functional Magnetic Resonance Imaging (fMRI) to map the brain activity of mathematicians as they viewed various mathematical formulae and constructions that they have rated on an ugly-beautiful scale. That part of the brain that is activated when people see beautiful art, or hear beautiful music (yes, there is a specific place)? Evidently, that place lights up when we view math that we see as beautiful. At least to us, it is real. <br />
<br />
Give it a read (H/T to CG!!): <br />
<blockquote class="tr_bq">
<h2 class="heading newsitemheading">
<a href="http://bit.ly/1fnkqrh"><span style="font-size: small;">Mathematical beauty activates same brain region as great art or music</span></a></h2>
</blockquote>
BTW, the most beautiful formula of the study: Why <a href="http://en.wikipedia.org/wiki/Euler%27s_identity">Euler's Identity</a>, of course! Can you see the beauty?<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhuzLjSR7Uo54cCU_sHR1sZLSbbOvBcvTErGt-KtTfzscw73n2AxrTbfjdG-AAkzLOyF-JX8jjjRdh50-_er8bWeKzSREXWDcc5PTtORTgEJ8gm7WmIcOgqaL6v2P_RkiYHNd0vsBE9PvSJ/s1600/Beautiful_formula__square_jpg.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhuzLjSR7Uo54cCU_sHR1sZLSbbOvBcvTErGt-KtTfzscw73n2AxrTbfjdG-AAkzLOyF-JX8jjjRdh50-_er8bWeKzSREXWDcc5PTtORTgEJ8gm7WmIcOgqaL6v2P_RkiYHNd0vsBE9PvSJ/s1600/Beautiful_formula__square_jpg.jpg" /></a></div>
Richard Brownhttp://www.blogger.com/profile/02890750341504212951noreply@blogger.com0tag:blogger.com,1999:blog-7821055994181766793.post-46779278881879001332014-02-03T15:56:00.000-05:002014-02-03T15:56:25.326-05:00The importance of mathematical "error"?I recently participated in an intersession course here at Hopkins (a short, three week course offerd between our fall and spring semesters) called "Thinking though the Fields, A Round Table on Bridging Science and the Humanities at Hopkins" (sound like a title in need of an acronym, eh?) The course was run by Dr. Kristin Cook-Gailloud. It was a wonderful experience, with a topic of the day presented in a short talk by a few academics in diverse fields, and then a general discussion about the different interpretations and experiences. I talked about the importance of puzzles and game playing in mathematics and mathematical research. Neat.<br />
<br />
A short time afterwards, I received a request from some of the students in the class. They were doing a class project to compile a booklet on topics of a similar capacity. They asked me to answer a few questions about how mathematicians use error in their work. My answers are below. Enjoy:<br />
<br />
<!--[if gte mso 9]><xml>
<o:OfficeDocumentSettings>
<o:AllowPNG/>
</o:OfficeDocumentSettings>
</xml><![endif]--><br />
<!--[if gte mso 9]><xml>
<w:WordDocument>
<w:View>Normal</w:View>
<w:Zoom>0</w:Zoom>
<w:TrackMoves/>
<w:TrackFormatting/>
<w:PunctuationKerning/>
<w:ValidateAgainstSchemas/>
<w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid>
<w:IgnoreMixedContent>false</w:IgnoreMixedContent>
<w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText>
<w:DoNotPromoteQF/>
<w:LidThemeOther>EN-US</w:LidThemeOther>
<w:LidThemeAsian>X-NONE</w:LidThemeAsian>
<w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript>
<w:Compatibility>
<w:BreakWrappedTables/>
<w:SnapToGridInCell/>
<w:WrapTextWithPunct/>
<w:UseAsianBreakRules/>
<w:DontGrowAutofit/>
<w:SplitPgBreakAndParaMark/>
<w:EnableOpenTypeKerning/>
<w:DontFlipMirrorIndents/>
<w:OverrideTableStyleHps/>
</w:Compatibility>
<m:mathPr>
<m:mathFont m:val="Cambria Math"/>
<m:brkBin m:val="before"/>
<m:brkBinSub m:val="--"/>
<m:smallFrac m:val="off"/>
<m:dispDef/>
<m:lMargin m:val="0"/>
<m:rMargin m:val="0"/>
<m:defJc m:val="centerGroup"/>
<m:wrapIndent m:val="1440"/>
<m:intLim m:val="subSup"/>
<m:naryLim m:val="undOvr"/>
</m:mathPr></w:WordDocument>
</xml><![endif]--><!--[if gte mso 9]><xml>
<w:LatentStyles DefLockedState="false" DefUnhideWhenUsed="true"
DefSemiHidden="true" DefQFormat="false" DefPriority="99"
LatentStyleCount="267">
<w:LsdException Locked="false" Priority="0" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Normal"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="heading 1"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 2"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 3"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 4"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 5"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 6"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 7"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 8"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 9"/>
<w:LsdException Locked="false" Priority="39" Name="toc 1"/>
<w:LsdException Locked="false" Priority="39" Name="toc 2"/>
<w:LsdException Locked="false" Priority="39" Name="toc 3"/>
<w:LsdException Locked="false" Priority="39" Name="toc 4"/>
<w:LsdException Locked="false" Priority="39" Name="toc 5"/>
<w:LsdException Locked="false" Priority="39" Name="toc 6"/>
<w:LsdException Locked="false" Priority="39" Name="toc 7"/>
<w:LsdException Locked="false" Priority="39" Name="toc 8"/>
<w:LsdException Locked="false" Priority="39" Name="toc 9"/>
<w:LsdException Locked="false" Priority="35" QFormat="true" Name="caption"/>
<w:LsdException Locked="false" Priority="10" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Title"/>
<w:LsdException Locked="false" Priority="1" Name="Default Paragraph Font"/>
<w:LsdException Locked="false" Priority="11" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtitle"/>
<w:LsdException Locked="false" Priority="22" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Strong"/>
<w:LsdException Locked="false" Priority="20" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Emphasis"/>
<w:LsdException Locked="false" Priority="59" SemiHidden="false"
UnhideWhenUsed="false" Name="Table Grid"/>
<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Placeholder Text"/>
<w:LsdException Locked="false" Priority="1" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="No Spacing"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 1"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 1"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 1"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 1"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 1"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 1"/>
<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Revision"/>
<w:LsdException Locked="false" Priority="34" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="List Paragraph"/>
<w:LsdException Locked="false" Priority="29" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Quote"/>
<w:LsdException Locked="false" Priority="30" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Quote"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 1"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 1"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 1"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 1"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 1"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 1"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 1"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 2"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 2"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 2"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 2"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 2"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 2"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 2"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 2"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 2"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 2"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 2"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 2"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 2"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 3"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 3"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 3"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 3"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 3"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 3"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 3"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 3"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 3"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 3"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 3"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 3"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 3"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 3"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 4"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 4"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 4"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 4"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 4"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 4"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 4"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 4"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 4"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 4"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 4"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 4"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 4"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 4"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 5"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 5"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 5"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 5"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 5"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 5"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 5"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 5"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 5"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 5"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 5"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 5"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 5"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 5"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 6"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 6"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 6"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 6"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 6"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 6"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 6"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 6"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 6"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 6"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 6"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 6"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 6"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 6"/>
<w:LsdException Locked="false" Priority="19" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Emphasis"/>
<w:LsdException Locked="false" Priority="21" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Emphasis"/>
<w:LsdException Locked="false" Priority="31" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Reference"/>
<w:LsdException Locked="false" Priority="32" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Reference"/>
<w:LsdException Locked="false" Priority="33" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Book Title"/>
<w:LsdException Locked="false" Priority="37" Name="Bibliography"/>
<w:LsdException Locked="false" Priority="39" QFormat="true" Name="TOC Heading"/>
</w:LatentStyles>
</xml><![endif]--><!--[if gte mso 10]>
<style>
/* Style Definitions */
table.MsoNormalTable
{mso-style-name:"Table Normal";
mso-tstyle-rowband-size:0;
mso-tstyle-colband-size:0;
mso-style-noshow:yes;
mso-style-priority:99;
mso-style-parent:"";
mso-padding-alt:0in 5.4pt 0in 5.4pt;
mso-para-margin:0in;
mso-para-margin-bottom:.0001pt;
mso-pagination:widow-orphan;
font-size:10.0pt;
font-family:"Times New Roman","serif";}
</style>
<![endif]--><b><span style="color: black; mso-fareast-font-family: "Times New Roman";">In relation
to your field, how do you define error?</span></b><span style="font-family: "Calibri","sans-serif"; mso-fareast-font-family: "Times New Roman";"> </span>
<br />
<ul type="disc">
<li class="MsoNormal" style="color: #282828; mso-list: l3 level1 lfo2; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; tab-stops: list .5in;"><span style="font-family: "Calibri","sans-serif"; mso-fareast-font-family: "Times New Roman";">In
Mathematics, we define or use error in many ways. Perhaps two
important ones are: (1) As a means to study levels of inaccuracy in
estimation and approximation, and (2) as a means to address falsity in
claims of truth, like proofs. For (1), mathematics is the study of
the logical structure of complicated things. Many times, these complicated
things are systems defined by equations involving numbers. When used
to model something physical, we must accept that our model might not be
completely accurate, due to the fact that we cannot properly account for
some influential effects in our model. Think how a model of a
pendulum may take into air resistance when predicting its position at some
future time, but possibly not that the humidity of the air may affect the
constant that we use for air resistance. Instead of trying to account
for everything, we make an approximation and hope that we are fairly
accurate in the end, accepting the errors that will accrue, but hoping
that they are small. Also, when modeling mathematics on a computer,
another kind of error we see is the fact that computers cannot be precise
in the way that we are when doing arithmetic. For example, there is
really no such thing as zero on a computer. When defining arithmetic
on a computer, and assigning numbers to variables we must determine a
level of precision (number of bits to devote to a number.) This works well
for normal calculations, but when doing high precision work, if one were
to multiply an extremely small number to a very very large one, the result
may be inaccurate, since the very small number may only be accurate to a
finite degree and the multiplication may bring some of the inaccuracies up
to the range of what we consider normal numbers. There is a field of
mathematics that studies errors in calculation like these, call numerical
analysis. For (2) , any new mathematical structure or concept or
theorem is an abstract idea that must be proven to be consistent with all
other mathematical ideas. Many times, a new idea is claimed to be
proven, but under scrutiny by other mathematicians, it is shown to not be
proven completely. There is an error in the proof. Either the
claim is wrong, or the claim is not fully justified as proven. At
this point, the idea is NOT a fact, and dangerous to try to use to help
prove other possible facts. All mathematical ideas claimed to be
proven are scrutinized extremely carefully by the mathematical community,
either in research paper review, or by other independent
verification. It is a strength of the field that nothing is really
proven until verified fully. </span></li>
</ul>
<br />
<b><span style="color: black; mso-fareast-font-family: "Times New Roman";">How do you
deal with and interpret error in your field of work</span></b><br />
<ul type="disc">
<li class="MsoNormal" style="color: #282828; mso-list: l5 level1 lfo4; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; tab-stops: list .5in;"><span style="font-family: "Calibri","sans-serif"; mso-fareast-font-family: "Times New Roman";">Mostly,
the above answer works here also. For (1), we deal with errors in
accuracy by trying desperately to manage it and/or minimize it.
Typically, on a computer, decreasing error means increasing computational
time and effort. Hence there is often a trade off between how
accurate you want your answer to be and how long you want the computer (or
you) to spend trying to compute the answer. For (2), when a new idea
seems to be proven, a mathematician will immediately go to colleagues and
collaborators to have them assess the value, correctness and completeness
of the proof. Errors are often found and arguments (statements of
the proof) are changed to address the criticisms. Once a research
paper with some new result (proof) is submitted, there is a formal review
process where independent mathematicians with knowledge in a particular
field assess the correctness of the proof. Papers are deemed
unacceptable for publication when not correct, and must be reworked or
abandoned, depending on the nature of the errors. Sometimes, when a
paper is published with an error, the error must be fixed either with an
addendum to the original paper, or with withdrawal of the paper from the
journal. There are no instances where errors are tolerated in
mathematical proof. </span></li>
</ul>
<b><span style="color: black; mso-fareast-font-family: "Times New Roman";">During your
career has erroneous findings led to any key or luminous findings?</span></b><span style="font-family: "Calibri","sans-serif"; mso-fareast-font-family: "Times New Roman";">
</span>
<ul type="disc">
<li class="MsoNormal" style="color: #282828; mso-list: l4 level1 lfo6; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; tab-stops: list .5in;"><span style="font-family: "Calibri","sans-serif"; mso-fareast-font-family: "Times New Roman";">In my
work personally, no. Although some work has not been published due
to errors unseen in the original drafts. However, so much beautiful,
amazing mathematical ideas have come from initial errors. The famous
Fermat's Last Theorem, proved only recently but stated 300 years ago, was
a simply stated idea that was claimed to have a simple proof by Pierre de
Fermat. Alas, he never wrote down his proof, and the community has
been trying to find it for 3 centuries. The idea is now a fact
(theorem), but the recent proof is not simple at all. However, two
things come out of this: (a) So much beautiful math has been developed
in the search of this proof, and (b), it is now basically universally
believed in the mathematics community that if Fermat indeed had an idea
for a simple proof, it had an error. We will never know,
but.... And in the 70's, Stephen Smale claimed to prove that Chaos
(the theory of unpredictability in deterministic mathematical models) does
not exist in mathematics. His proof was in error, and this was shown
by another mathematician who produced a counterexample (a single example
of something that shows that a supposed fact is incorrect.) Smale
set out to prove he was indeed correct, and in doing so, developed a new
branch of mathematics called hyperbolic dynamics, centered around his
famous "Smale Horseshoe". Alas, he only really proved he
was originally mistaken, but the error is considered a beautiful one due
to what came out of it! </span></li>
</ul>
<br />Richard Brownhttp://www.blogger.com/profile/02890750341504212951noreply@blogger.com0tag:blogger.com,1999:blog-7821055994181766793.post-29969615358266394512014-02-03T11:28:00.001-05:002014-02-03T11:28:56.495-05:00I'm back....I must apologize for my lack of communication over the last few months. I enjoy my time here at Hopkins and try to take an active role in the community. However, adding activities tends to take attention away from other activities. And this blog took a hit, unfortunately. <br />
<br />
I recently was inspired to jump back in and write on the Chalkboard (so here I am..., H/T to AE!)<br />
<br />
Talk to all of you soon.Richard Brownhttp://www.blogger.com/profile/02890750341504212951noreply@blogger.com0