Ask MetaFilter questions tagged with mathematics
http://ask.metafilter.com/tags/mathematics
Questions tagged with 'mathematics' at Ask MetaFilter.Tue, 09 Dec 2014 10:33:17 -0800Tue, 09 Dec 2014 10:33:17 -0800en-ushttp://blogs.law.harvard.edu/tech/rss60Online resources for brushing up on basic math skills?
http://ask.metafilter.com/272764/Online%2Dresources%2Dfor%2Dbrushing%2Dup%2Don%2Dbasic%2Dmath%2Dskills
What are some good, free online resources for an adult who needs to brush up on basic math operations such as working with fractions, percentages and ratios? Other than Khan Academy. The more interactive the better.tag:ask.metafilter.com,2014:site.272764Tue, 09 Dec 2014 10:33:17 -0800iamisaidSeeking advice about teaching maths
http://ask.metafilter.com/272150/Seeking%2Dadvice%2Dabout%2Dteaching%2Dmaths
I'm interested in teaching high school students mathematics through a tutoring agency. I have the required experience in mathematics, but very little in teaching. This doesn't seem to be a massive problem for many tutoring agencies, but I want to know: do you have any specific tips/advice about teaching mathematics? And more broadly, any advice about applying for and going to work for a tutoring agency? I'm a big fan of maths, and very interested in teaching it. I don't simply like it because 'there's only one right answer' etc, I like it for a frajillion reasons: the beauty of elegant proofs, the fun of problem solving, and the fact that it underlies the functioning of the universe as we know it. Heck, I do maths in my spare time. I make lame maths jokes. I am ready to accept that I am a fully-fledged maths nerd.<br>
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I understand that enjoying maths is not the same as being capable to teach it. I have gone through much of the high school maths syllabus (I am in Australia) and understand how to teach it from first principles.<br>
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Anything you can give me that would help me more ably engagingly teach mathematics to potential future students would be much appreciated.tag:ask.metafilter.com,2014:site.272150Wed, 26 Nov 2014 20:56:38 -0800QuilfordIn a multi-winner election, how many should I vote for?
http://ask.metafilter.com/270996/In%2Da%2Dmulti%2Dwinner%2Delection%2Dhow%2Dmany%2Dshould%2DI%2Dvote%2Dfor
Mathematically, in a 6-way race with 5 winners, should I vote for the 2 candidates I like, or all 5 who I don't hate? Details inside. There is a local race with 6 candidates, 5 of whom will take office. There are 2 candidates I actively like, 2 I actively dislike, and 3 I don't feel strongly about either way. I have no idea of the relative chance of any of the candidates to win, apart from an impression that one of the "eh" candidates who has been in office for over a decade is likely to continue to be in office. I can vote for up to 5 candidates. Mathematically, would I be more likely to have the most positive influence toward my A)Ideal situation, where one of the two candidates I dislike is the one who doesn't take office and B)Not a total lose situation, where the candidates I actively like both get on if I 1)Vote only for the two I like or 2)Vote for all 5 who I don't hate?tag:ask.metafilter.com,2014:site.270996Mon, 03 Nov 2014 20:15:34 -0800DebetEsseMath-related field trip destinations for Bay Area HS students?
http://ask.metafilter.com/266716/Math%2Drelated%2Dfield%2Dtrip%2Ddestinations%2Dfor%2DBay%2DArea%2DHS%2Dstudents
I teach math to high schoolers in the San Francisco Bay Area. I'd like to get them out of the classroom on a field trip to a local math-themed destination. Any suggestions? The destination doesn't need to be as completely all-about-math as the Museum of Math in NYC (though I would totally take them to the Museum of Math if it were nearby). Any place that can be tied in to a meaningful (and fun!) math lesson is fine. I'd rather it not be a theme park, though.<br>
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The students would be from math club and advanced classes (precalculus and up), so most are pretty sophisticated and enjoy math to begin with. It would be great to tie the trip in with something off the beaten path, curriculum-wise -- like if we could teleport to the Alhambra and try to <a href="http://britton.disted.camosun.bc.ca/alhambra/">spot as many symmetry groups as possible</a>. But we can't teleport to the Alhambra.tag:ask.metafilter.com,2014:site.266716Tue, 12 Aug 2014 18:36:31 -0800aws17576What are inter-disciplinary and atypical uses for math MSc?
http://ask.metafilter.com/265859/What%2Dare%2Dinter%2Ddisciplinary%2Dand%2Datypical%2Duses%2Dfor%2Dmath%2DMSc
I have just completed my MSc in mathematics in Europe. I do enjoy math, but I spent my uni years feeling like a autodidact hippie marooned on an island full of Mr and Mrs I-Want-A-Good-Job. My main interests revolve around humanities (literature/history/anthropology) and economics (but not finance), and instead of starting a "stable" well-paying career I dream about something inter-disciplinary. I am very open to earning little money and relocating just to do kind of work that engages those skills. What are some random uses of my degree? <strong>While I know that this might be kind of "have your cake and eat it too" scenario, I dream about utilising my core technical skills in an environment which doesn't stifle my humanistic interests but rather sees them as strengths.</strong> I am very open to studying more, but PhD programs that I find don't really cater to mathematicians who don't want to do pure math anymore. While this is very hopeful, math+analytic skills+statistics+coding are in-demand skills these days, so there must be opportunities there.<br>
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- I am mid-twenties. <strong>I am located in Europe</strong> (studied in Poland and Germany). I have no ties and can go anywhere, but highly US-specific info doesn't apply.<br>
- I saved money and <strong>only need to earn for basic living needs</strong>, which are low.<br>
- I am <strong>open to working short-term</strong>, half-time, trying as many new things as possible, <strong>travelling a lot to random places</strong>.<br>
- I did most of my studying on probability/statistics and graph theory. I loved game theory. I learn fast.<br>
- I have working experience in healthcare assessment (statistics) and I code (also in R and for web). It was pleasant, might do that some more, but I'd happily try something different.<br>
- I am useless at googling things, my ability to search for jobs/opportunities is non-existent and I'm haplessly clueless about all this "selling yourself" business.<br>
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<strong>So, in a nutshell: random, low-paying, humanities and soft/life sciences, uni work, weird places, inter-disciplinary PhDs (?).</strong><br>
Not my cup of tea: marketing, business, actuarial science, engineering, pure programming, big companies.<br>
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As a very dim example, I loved reading about Cliodynamics (historical modelling). My main inspirations (intellectually) are Jacob Bronowski and Douglas Hofstaedter. I adore Tyler Cowen's Marginal Revolution.<br>
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I realise this is a long shot, but it can't harm to ask and google around. You are welcome to be as random as you want.tag:ask.metafilter.com,2014:site.265859Mon, 28 Jul 2014 05:02:34 -0800desultory_banyanMath Careers
http://ask.metafilter.com/265554/Math%2DCareers
Non-obvious careers for someone with a B.S. in Applied Mathematics? I just graduated with an Applied Mathematics major and Computer Science minor, and I need a job ASAP. The thing is, I didn't think too much about what I was going to do when I finished school. All the career advice I've seen for people with my degree falls in only a couple different categories, most of which aren't really good options for me. I'm in need of some original suggestions for places I should be looking.<br>
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Things I DON'T want to hear: <br>
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+Grad school.<br>
+Actuarial Science.<br>
+Vague titles like "Mathematical Analyst." Which industries? What keywords can I search for?<br>
+Programming, unless you have tips on how to bridge the gap between the small projects I did in school and real-world development, or how to get hired with no experience. (Or you can reassuringly convince me that it's really not that hard.)<br>
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It's not necessarily that these are unappealing; I'm already aware of them, just looking for alternatives.<br>
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Is there anything I'm overlooking?tag:ask.metafilter.com,2014:site.265554Tue, 22 Jul 2014 15:28:13 -0800AnonymousCollegeFilter: How is one to choose without regret?
http://ask.metafilter.com/264167/CollegeFilter%2DHow%2Dis%2Done%2Dto%2Dchoose%2Dwithout%2Dregret
At the age of 24, I just completed my first year of undergraduate studies at a good public university. I am a strong student with a 4.0 GPA, but I feel that my interests are so broad and varied that I don't know how to narrow down on a specific path of study. Compound these problems with the ubiquitous financial and career concerns of the modern college student, and you have one confused student. How can I resolve this inner turmoil and structure a long-term plan that will bring me (at least some) peace of mind? I know this sort of a question is a dime a dozen, but any response is genuinely appreciated.<br>
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In an effort at brevity, let me concisely round out my background information: It has been a whirlwind of a year. College didn't work out for me after high school, and for years I pined for an opportunity at higher education. Now that I'm finally getting such an education, I feel overwhelmed with the decisions I need to make and the speed with which I need to make them. My original goal of studying social work and foreign languages quickly fizzled out once I learned the extensive education required for the social work field as well its measly financial return. If I had gone to college straight out of high school, I probably would have studied English or something similar. (It's taken so long to get into college due to family and financial reasons.) I have since veered towards philosophy, and I love it! I feel at home in the department and with the fellow students, and I thrive in the courses. However, I can't shake this grim adumbration of graduating with minimal earning prospects. <br>
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So I've considered picking up a second major, something more tangibly skill-oriented, e.g. computer science, mathematics, or economics. I'm particularly considering computer science or mathematics due to the love I had for a course in formal logic I recently took with the philosophy department. Alas, it's been years since I've done any post-algebraic math, so I would be getting a late start to the game. Hence such a decision would almost certainly result in an additional semester or two (four more years instead of three), not to mention the additional debt I would incur. (If I graduate within the next three years, I'll probably have around $20-30k in debt, maybe less depending on future scholarship opportunities.) Furthermore, although I'm a bright student and feel confident I <em>could</em> learn anything towards which I applied myself, the frank truth of the matter is that mathematics is not my <em>natural</em> strength. I have always had an intense love-hate relationship with it. However, as mentioned earlier, formal logic has opened my eyes to new understanding of the subject.<br>
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Truthfully, I want to study everything! In my spare time I read tons of psychology/psychiatry (viz., Jung, Maslow, Grof, etc.). I'm passionately interested in self-growth and social justice. I've gone through the entire list of majors offered by my university (multiple times), and it seems as if my mind changes month-to-month, week-to-week, and even day-to-day. One thing I <strong>do</strong> know for certain is that I'm unwilling to give up my philosophy major. It nurtures my soul, spirit, and mind, and it's the one field of study I feel totally comfortable in. That being said, I am also pretty certain that I do not want to pursue academia as a career choice.<br>
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My biggest fear is graduating at the age of 27 straddled with $25k in debt and unable to find a job. More specifically, I feel terrified I'll never be able to pursue all the things my soul craves: writing, music, art, languages, films, culture, all the myriad hobbies I pick up, et cetera. Maybe I'm overthinking this whole thing (I probably am), but I feel as though a whole lifetime's worth of ramifications sits heavily upon the decisions I'm making now. Needless to say, I feel pressured to make the right decisions.<br>
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So my questions are as follows:<br>
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1) Can someone with a liberal arts degree still enjoy prosperous careers?<br>
2) Are double-majors ever good ideas? What would be the best major to pair with one such as philosophy, especially for a student who is not necessarily interested in graduate-level studies?<br>
3) Perhaps most importantly, how can I begin to stop worrying so much about the future and instead enjoy this educational experience that is college? <br>
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So much for brevity. Again, I humbly thank anyone and everyone for reading and replying. I'm looking for opinions all over the spectrum. Tell me how it is.tag:ask.metafilter.com,2014:site.264167Wed, 25 Jun 2014 12:44:30 -0800fignewtonMathematical moments of wonder like Cantor's diagonal method
http://ask.metafilter.com/263238/Mathematical%2Dmoments%2Dof%2Dwonder%2Dlike%2DCantors%2Ddiagonal%2Dmethod
I've been reading <a href="http://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach">Godel, Escher, Bach</a> and I want to find more mind-expanding concepts that give the sense of understanding some fundamental truth. While I can't always follow the specifics of the mathematics in GEB I have experienced some jaw-dropping moments of understanding, e.g. when Cantor's diagonal <a href="http://en.wikipedia.org/wiki/Cantor's_diagonal_argument">argument</a> clicked into place. I want to find more mind-bending mathematical concepts like this, explained in a way that I as a non-specialist can understand (even if there is some work required). Books / websites / anything else welcome. Thanks in advance!tag:ask.metafilter.com,2014:site.263238Sun, 08 Jun 2014 15:57:27 -0800StephenFCalling all chem- physics- and math-philes!
http://ask.metafilter.com/259803/Calling%2Dall%2Dchem%2Dphysics%2Dand%2Dmath%2Dphiles
For the grad-level education I want, I need an understanding of chemistry, physics, and calculus at a minimum. I have a BA in a tangentially related field (or will in a couple months). What are the best resources for learning these subjects without spending even more time/money on tuition? I'm about to get my BA in Geography, but would really like to angle toward oceanography as a career. I have few qualifications for this as it stands now - the last time I took a math course was a 150 course in 2008, I haven't taken chemistry since high school, and I've never taken physics. I need a basis in chem, physics, and calc I & II before I can think about getting more into atmospheric science or environmental science.<br>
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Honestly, I'd just switch my major in a heartbeat to atmospheric science, but I'm 24 already and switching would mean at least three, maybe four more years of undergrad, and given how rigid the program is at my university, I'd have to give up on my no-loans streak to go full time, or else it would take me more like 5-6 years. Ack.<br>
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So, I'm starting now by watching CrashCourse Chemistry on Youtube, and will be taking a look at YaleCourses as well, particularly for physics. I find I learn best when I can add books to my lecture learning though, so I'm looking for suggestions for books, textbooks and otherwise, that I could take a look at.<br>
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Mathematics is probably going to be trickier. Complicating my learning of math is a history of high school teachers who destroyed my confidence years ago; this lack of confidence in math in general is pretty much the only reason I chose to get a BA and not a BS in the first place, and I'm only now realizing that I can probably do it after all and maybe my high school teachers were just wrong/didn't care enough to help me understand. So, in this case I'm looking for ways to simultaneously build up my confidence and my knowledge.<br>
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Bonus question: It's not strictly necessary, but while I'm at it I'd like to poke my nose a little farther into biology. I took some bio courses while I was getting my associate's degree back in 2007-2010, and I'd like to refresh my memory.<br>
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Thanks in advance for any and all assistance.tag:ask.metafilter.com,2014:site.259803Fri, 04 Apr 2014 13:01:16 -0800Urban WinterChance of event with small sample size, based on larger related sample?
http://ask.metafilter.com/258957/Chance%2Dof%2Devent%2Dwith%2Dsmall%2Dsample%2Dsize%2Dbased%2Don%2Dlarger%2Drelated%2Dsample
Can/how can one improve the estimate for a chance of an event with a small historical sample size by utilizing the chance of a related event with a large historical sample size? Example and half-assed guess inside. A baseball-related example (for the purposes of this question, please forget about complicating factors like lefty/righty splits, home/away splits, the fact that a particular player might be better or worse now than he was in the past, etc.):<br>
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Joe has had 1000 at bats. He has gotten a hit in 270 of those 1000 at bats.<br>
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Of those 1000 at bats, 10 were against the pitcher Fred. In those 10 at bats against Fred, Joe got six hits.<br>
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Clearly we can say "Joe is a .600 hitter against Fred". But also clearly, that doesn't really have any meaningful predictive power for Joe's future at bats against Fred. If we want to guess what the chance of Joe getting a hit off of Fred is, 27% is almost certainly a much better guess than 60%.<br>
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But can we use <i>both</i> pieces of information to get a guess that's better than "27%"?<br>
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I have a half-assed guess, which I'll describe momentarily, but it occurs to me that this is probably a problem which has been thought about rigorously by mathematicians. So does anyone know if there's a "real" answer to this problem?<br>
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My half-assed guess is something along these lines:<br>
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Joe has 10 at bats against Fred, and 6 hits in them. But Joe has 1000 at bats total (with 270 hits). Let's assume that if Joe had had 1000 at bats against Fred, 10 of them would have gone as they did, and the other 990 would have been as if against an average pitcher. So Joe would have gotten:<br>
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6 + 990 * 270 / 1000<br>
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= 6 + 267.3<br>
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= 273.3<br>
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So we guess that in his upcoming at bat against Fred, Joe has a 27.33% chance of getting a hit.tag:ask.metafilter.com,2014:site.258957Thu, 20 Mar 2014 07:20:36 -0800FlunkieWhy do we have order of operations in arithmetic?
http://ask.metafilter.com/258530/Why%2Ddo%2Dwe%2Dhave%2Dorder%2Dof%2Doperations%2Din%2Darithmetic
Why do we have order of operations rules in arithmetic instead of just strictly evaluating expressions from left to right (possibly with parenthesis for grouping if we really wanted to change the order)?tag:ask.metafilter.com,2014:site.258530Tue, 11 Mar 2014 11:49:07 -0800Reverend JohnWhat are the best ways to teach mathematics to elementary age children?
http://ask.metafilter.com/257919/What%2Dare%2Dthe%2Dbest%2Dways%2Dto%2Dteach%2Dmathematics%2Dto%2Delementary%2Dage%2Dchildren
What do you do to teach your children math (or maths)? My kids are in kindergarten now and they do a bit of mathematics every week, but not every day, and really they aren’t learning anything new. In the first grade in our district, there are no math text books or workbooks, which seems weird. I’m comfortable with what the common core demands, but I’m not convinced that the teachers will be. I suspect that I will have to supplement my children’s mathematics education just to keep up with Common Core standards. <br>
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What are the best practices? What are the best curriculum? What are the best picture books? How about homeschoolers and unschoolers? How do you make sure that you aren’t missing essential math elements?tag:ask.metafilter.com,2014:site.257919Fri, 28 Feb 2014 09:11:09 -0800mearlsGetting back to higher math
http://ask.metafilter.com/257562/Getting%2Dback%2Dto%2Dhigher%2Dmath
I'd like book/course suggestions to do a slow gentle study of higher Math by myself. I did a bachelor's degree in Math (and Economics) several years ago by myself as an external course (from the Univ of London and LSE), on the side of a whole lot of other things. I did reasonably well, enjoyed parts of it very much, but I've forgotten most of it now. I taught high school Math for a couple of years after that but now work in a totally different field (communication design). I love my work, but miss the brainwork Math required. I'd also like to slowly internalise more Math vocabulary and the structure of the subject, which didn't happen during my Bachelors. I'd be especially happy with a sort of gentle book that doesn't plunge too deep right at the start. I loved number theory and my entire abstract math course when I studied it. After a certain point, advanced calculus threw me off a little, but I didn't have enough time to study it thoroughly at that point.tag:ask.metafilter.com,2014:site.257562Fri, 21 Feb 2014 19:03:39 -0800miaowWhere can I find advice for returning to school?
http://ask.metafilter.com/256249/Where%2Dcan%2DI%2Dfind%2Dadvice%2Dfor%2Dreturning%2Dto%2Dschool
Dropped out of school several years ago, drifted for a bit, but now I want to return and get AT LEAST a BS in mathematics. What sources are there for someone returning to school? Should I bite the bullet and pay for college counseling, or are there good free resources I'm missing? My first attempt at a university education (a mid-tier UC) ended 6 years ago with me dropping out. I had a 2.9 GPA, a transcript littered with Ws, and I'm honestly not sure if I'd even attained junior standing, owing to the number of classes I'd dropped. I decided that higher education just wasn't for me and there was zero point in ever trying again.<br>
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Fast-forward to today. I have a decent income doing web marketing in Los Angeles, but it's not at all what I love. I've done a lot of thinking over the past year or so and I came to the realization that I want to go back to school. I want to at the very least attain a BS in mathematics - and would absolutely relish the opportunity to earn a masters or even a PhD. My wonderful GF is incredibly supportive of my plan and I'm extremely eager to realize my full potential.<br>
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So far, I've been taking steps to get back into the learning process. I wanted to make sure I had a strong foundation with math (I took calculus back in college - my performance was mediocre, probably a C+ average over the entire three-course sequence) so I started taking pre-calc at my local community college, plus another GE. I earned straight As my first semester, something I've literally never done in my life, and I'm taking a bunch more classes this semester. I'm planning on beginning calculus again this summer and the rest of my math/sci classes in 2014-15.<br>
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I feel so enthusiastic about the process, but I have to confess I'm a little nervous about my direction. Aside from aiming to fulfill the IGETC curriculum for transfer, I don't have a lot of guidance on the task I'm undertaking. I have a lot of questions about the transfer process:<br>
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-Which colleges I should apply to/have a reasonable chance of getting into<br>
-What deficiencies I should be addressing in my application right now<br>
-Timeline for when I can begin applying to schools<br>
-How realistic my plan is (kick ass and get a BS in mathematics, then go to a top 20 school for a PhD in pure or applied math) (I'm especially concerned about this as I am so interested in going to grad school and I don't want to hobble myself with a not-so-great undergraduate institution.)<br>
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So what I'm looking for is 75% information, 25% "You can do it!" exhortation.<br>
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Are there any especially useful sources for this kind of advice? I'm looking for anything that can help. I've considered going to a college counseling service; they seem kind of rip-off-ish but I figure spending a couple hundred bucks now at the start of this process could be super useful. I've also been looking for books on returning to school, and I've been hovering around my CC's transfer center. I've also been to my school's counseling office, though since I don't have enough credits through them to get an official transcript evaluation until after this semester I have yet to receive really firm advice from them. I've even read a bunch of threads on AskMefi, which have done a decent job making me feel more confident about this whole endeavor.<br>
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Does anyone have any advice on where I could get what I'm looking for? I want to make this second trip through higher education really count for something. Thanks in advance for all of your responses.tag:ask.metafilter.com,2014:site.256249Thu, 30 Jan 2014 13:01:43 -0800miltthetankIs there a name for this property of a data series?
http://ask.metafilter.com/254951/Is%2Dthere%2Da%2Dname%2Dfor%2Dthis%2Dproperty%2Dof%2Da%2Ddata%2Dseries
I have a series of physical data with a fairly straightforward property: it follows a path in space. If I plot a bunch of successive (x, y) values from the data, they follow a curving, looping line rather than randomly jumping all over the plot. More formally, if I have a point (x[t], y[t]) at time t and (x[t+1], y[t+1]) at time t+1, there is an upper limit on the distance between these two points (and this limit is small relative to the overall variation in the data). Is there a well-defined technical term for this property? If the variation were random I'd call it a random walk. But it's governed by a bunch of complex physical processes that aren't relevant to the analysis I'm trying to do: the only thing I'm currently interested in is the "walk" property. Of course it's easy to give an ad-hoc formalization as I did above, but I'm sure there must be some standard terminology for this, and maybe some general results on series with these properties. I've skimmed several works on random walks and time-series analysis without finding a suitable term. I'm sure that this wheel has been invented before; what have I missed? Links and references very welcome.tag:ask.metafilter.com,2014:site.254951Wed, 08 Jan 2014 05:40:38 -0800pontEducational mathamatics apps for adults that will work on an iPhone?
http://ask.metafilter.com/252478/Educational%2Dmathamatics%2Dapps%2Dfor%2Dadults%2Dthat%2Dwill%2Dwork%2Don%2Dan%2DiPhone
I am looking for adult-oriented iOS apps that will help improve my math skills. I'm looking to improve in two areas:<br>
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1.) Basic mental math: + - / *. <br>
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My skills in this area are lacking, to say the least. I also tend to play an unhelpful mental soundtrack whenever I make an attempt, "You're going to screw this up and have to do it three more times. You can't trust yourself to do this without a calculator." and etc. <br>
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I thought that maybe with enough repetition, I could make certain things more automatic and help overcome some of this. Even leaving the mental stuff aside, I could use practice. <br>
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2.) A grade 9 - 12 review<br>
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I was pushed into math courses in high school that, in retrospect, were probably too advanced for me. They certainly weren't required for what I would eventually pursue in university. As result, I did quite poorly, and I'm fairly certain the passing grade in my final year was more out of pity than ability. <br>
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I much more interested now, and would like to review the things I mostly avoided learning in the past. Is there something that would let me review the equivalent of a high school curriculum's worth of math? <br>
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I'd like to practice using my iPhone (at least initially) because the barrier to entry is so low. I always have my phone with me, and I could practice whenever I have downtime. For reference, I am aware of the resources available with Khan Academy, and plan to use them, but would like to have something more mobile as well. <br>
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Thanks everybody!tag:ask.metafilter.com,2013:site.252478Sat, 23 Nov 2013 13:02:13 -0800Gin and ComicsMathematics for the innumerate
http://ask.metafilter.com/247100/Mathematics%2Dfor%2Dthe%2Dinnumerate
I'm developing a Data Design curriculum for Art college students, and I'd like to teach some basics of maths and statistics in ways that the non-numerically inclined will understand. For this, I need some simple explanations for complicated ideas. The idea is to equip Arts majors with the skills needed to translate at least some of the requirements of analysts, statisticians, scientists and developers when creating data applications. My goal is that students learn to express narratives with numbers in a way that is both mathematically correct and effective as communication.<br>
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So, Mefites, what key numerical concepts does an aspiring data designer with little or no formal math training need? Do you know some great explanations for things like exponents and logarithmic scales? Standard distributions? Trigonometry? Matrix transformations? What brilliantly simple ways of communicating these ideas can you think of, visually and verbally? Do you have examples? <br>
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<small>(Note that I myself have a pretty solid foundation in applied mathematics so don't be afraid to hit me with calculus etc if you see fit.)</small>tag:ask.metafilter.com,2013:site.247100Thu, 22 Aug 2013 07:07:42 -0800Elizabeth the ThirteenthApplying to some kind of math grad program with no research experience?
http://ask.metafilter.com/246199/Applying%2Dto%2Dsome%2Dkind%2Dof%2Dmath%2Dgrad%2Dprogram%2Dwith%2Dno%2Dresearch%2Dexperience
I plan on applying to graduate mathematics programs for the 2014-2015 school year and I'm starting to get a little nervous about my chances at landing a spot in a funded program. My major concern is that I have absolutely zero research experience from my undergrad years, and am having trouble focusing in on what kind of work I would be interested in anyways, and I don't know where to start! And the research papers that do seem interesting to me are so specialized, I have trouble understanding them! I'm a 25 year old woman with a Bachelor's of Music in Music Composition, and a minor in Mathematics. I'm glad I studied music, but I've decided that I want to go back to school for mathematics because I'm better at it and it makes me very happy. I've always been pretty interdisciplinary - I've a lot of computer music and technology-based sound installations as well. <br>
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My overall GPA was around 3.6, and about 3.8 for my mathematics courses. I've taken and done very well in Calculus 3, Differential Equations, Real Analysis, Linear Algebra and Abstract Algebra. I pretty much did all of the mathematics major requirements, but was missing an elective or two so I ended up with a minor instead of a major. I'm very good at doing well in classes and taking tests, so I'm confident that my general GRE scores will be competitive and that I won't horribly botch the Math Subject GRE, for which I've been rigorously studying. <br>
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It has been about 4 years since I graduated, but I'm pretty sure I'll be able to get good/great recommendations from at least two math professors. <br>
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However, I'm totally lost as to how I should develop and focus my research interests. I have the feeling that I can make up for having a degree in music by showing that I am independently focused, but journals and articles and theses make me feel dizzy. I am definitely interested in the intersections of mathematics and music and have found a number of relevant articles...but I feel totally clueless as to how to develop a statement of intent around a bunch of articles that I'm struggling to understand. There seems to be a huge gap between my ability to do well in classes/tests and how to understand and pursue specialized applications and subjects. <br>
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Is this normal/acceptable for an incoming graduate student? <br>
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Am I just psyching myself out by reading profiles of other graduate applicants on grad school forums?<br>
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Should I be targeting Applied Math programs over Pure Math? Statistics is also a possibility. <br>
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What can I do to get better at answering the question, "So, what would you like to accomplish here at So-and-So University?". Because right now, the best answer I can give is "Well, I love taking classes and if you tell me what to do I'll do it, and I'm interested in the mathematical analysis of sound and music and music informatics sounds really cool but I really can't wrap my head around any of these super specific papers I've seen in fancy journals and I just don't know where to start!"<br>
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So....at this point, where do I start? <br>
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Funding is pretty necessary for me. Universities I am considering include but are not limited to: UMass Amherst, UNC Chapel Hill, University of Maine. I haven't picked out too many yet because I'm not sure how competitive of an applicant I am and what exactly I should be looking for. Program recommendations welcomed!tag:ask.metafilter.com,2013:site.246199Wed, 07 Aug 2013 09:56:35 -0800supernaturelleI'm having trouble understanding likelihood ratios and diagnostic tests.
http://ask.metafilter.com/245816/Im%2Dhaving%2Dtrouble%2Dunderstanding%2Dlikelihood%2Dratios%2Dand%2Ddiagnostic%2Dtests
I'm struggling to understand likelihood ratios (LR) in the context of diagnostic tests, and why a positive LR is influenced by the sensitivity of the test. I know that:<br>
<ol><br>
<ul>1. its a tool to get from a pre-test probability to a post-test probability</ul><br>
<ul>2. it is defined as the (percentage of people with the disease who test positive) divided by (the percentage of people without the disease who test positive).<br>
</ul><br>
<ul>3. Or, alternately, a positive LR is equal to sensitivity/ (1-specificity).<br>
</ul><br>
</ol><br>
</ul><br>
What I don't understand is <strong>why is a positive LR dependant on the sensitivity of the test?</strong><br>
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For example, lets say I want to diagnose someone with Hairy Face Syndrome, and my diagnostic test is that the clouds open up, and God comes down from the heavens and tells me "this man has hairy face syndrome!"<br>
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This is, understandably, a very *specific* test, but very poorly sensitive. <br>
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The way I've always understood likelihood ratios is that the positive likelihood ratio helps you interpret what to do with a positive result, not how useful searching for a positive result is likely to be.<br>
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Therefore, why does the low sensitivity of waiting for an act-of-god negatively impact the likelihood ratio and, consequently, your interpretation of it when it does, miraculously happen?tag:ask.metafilter.com,2013:site.245816Thu, 01 Aug 2013 08:48:46 -0800cacofonieMathematics-related accessories and clothing for women
http://ask.metafilter.com/244700/Mathematicsrelated%2Daccessories%2Dand%2Dclothing%2Dfor%2Dwomen
I'm learning to accessorize! I'd like to find some little mathematics-related accessories, kind of like the women's equivalent to a (relatively subtle) mathematics tie or cufflinks, that are work (think secondary school educator) appropriate. Simple and relatively understated is preferred. I'm also interested in clothing that would be work-place appropriate (not t-shirts!). I had a lot of fun with my regex skirt from XKCD a few years ago. Categories I'm interested in:<br>
- jewelry (necklaces or earrings, NO bracelets, anklets, or rings)<br>
- scarves<br>
- knit items (patterns would be most welcome)<br>
- other suggestions welcome<br>
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I did like the Pi necklace listed <a href="http://www.etsy.com/people/Graphmagics/feedback?type=from_buyers">here</a> (scroll down), but it looks like its no longer available. I did see a golden spiral necklace earlier, which looked nice. <br>
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I have knit myself some math-related hats, but am looking for something I could wear inside, on a regular basis, possibly even to interviews. I do have a pattern for a lace Sierpinski triangle shawl and plan to try it out. <br>
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What I'm not looking for: <br>
- charm bracelets or necklaces<br>
- cutesy items<br>
- rings, bracelets, anklets<br>
- collage-type pins or broaches<br>
- ties and/or cufflinks (not a good look for me)<br>
- text pendants<br>
- "math is fun/awesome/wonderful" type slogans<br>
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Thank you!tag:ask.metafilter.com,2013:site.244700Sun, 14 Jul 2013 18:58:21 -0800wiskundeiPad math apps for a 10-year-old?
http://ask.metafilter.com/243543/iPad%2Dmath%2Dapps%2Dfor%2Da%2D10yearold
My son is 10 years old and going into 5th grade in the fall (but he usually does 6th grade math). He likes <a href="https://itunes.apple.com/us/app/stack-the-states/id381342267?mt=8">Stack the States</a>, and we're looking for a math app with similar appeal. We already have <a href="https://itunes.apple.com/us/app/sushi-monster/id512651258?mt=8">Sushi Monster</a> and his younger sister loves it, but I'd like something more challenging for him.tag:ask.metafilter.com,2013:site.243543Tue, 25 Jun 2013 08:45:32 -0800The corpse in the libraryFind standard deviation in Excel, but first develop a labor-saving trick
http://ask.metafilter.com/243333/Find%2Dstandard%2Ddeviation%2Din%2DExcel%2Dbut%2Dfirst%2Ddevelop%2Da%2Dlaborsaving%2Dtrick
Help me with statistics and Excel. Especially help me if you know any labor saving methods. I want the median, mean and standard deviation for the average price of all items sold, but my spreadsheet-full-of-data doesn't tell me the price of each sale -- just the average price per store, and the number sold at that store. Something like this: <pre>Store # sold Avg price per item<br>
A 72 $16,824<br>
B 208 $13,133<br>
C 269 $15,190<br>
...</pre><br>
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So I think I need to count store A's price 72 times and store B's price 208 times, etc. It's pretty each to figure out algebra that will allow me to calculate mean treatment price given this information ("# of items sold at A" times "Avg. price at A"+"# of items sold at B" times "Avg. price at B" ... etc.) divided by (sum of # of items sold at all stores). <br>
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Is there a formula or other approach I can use in Excel that will also allow me to calculate the median and standard deviation relatively easily? Or do I need to re-create my spreadsheet so it reads <br>
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<pre>Store Avg price per item<br>
A $16,824<br>
A $16,824<br>
A $16,824<br>
... (etc, a total of 72 times)<br>
B $13,133<br>
B $13,133<br>
... (etc., etc.)</pre><br>
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There are 30-some stores, 99 distinct items and roughly 39,500 unique sales of those items across all the stores, so I'd *really* prefer not to have to copy and paste onto a new line to represent each individual item sold.tag:ask.metafilter.com,2013:site.243333Fri, 21 Jun 2013 12:54:25 -0800croutonsupafreakHelp me understand fractions
http://ask.metafilter.com/243209/Help%2Dme%2Dunderstand%2Dfractions
Dear math people: please help me understand fractions and ratios <em>intuitively</em>. I feel really embarrassed about this, but I must have missed a fundamental period when I was learning fractions as a child because I have a really hard time with understanding them intuitively. I am hoping someone can help me to see where my understanding breaks down and how I can make it more intuitive.<br>
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I know what fractions are and I fully understand addition and subtraction of fractions. I can also convert fractions (thought I don't remember the term for this). I think this is because I like to bake so when I think of adding or subtracting fractions, I always imagine cups of flour or something. So 2 1/2 + 1/3 makes perfect sense to me because I can picture it. I know that I need to find a common measurement (denominator) and the easiest way (but not the only way) to do that is to multiply both denominators. So, I would convert so I have this:<br>
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5/2 + 1/3<br>
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make them have common denominators:<br>
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15/6 + 2/6 = 17/6 = 2 5/6<br>
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That part is easy for me! Makes total logical, intuitive sense. <br>
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Multiplying and dividing fractions make no sense (maybe because I never have to do it in real life??). So I have to rely on remembering the "rules" (which I can never remember). I guess (because I looked it up) that to multiply you just multiply both numerators and then multiply both denominators. But to divide you have to flip one of the fractions and then multiply across. Anyway, I get that the rules are simple but this doesn't make logical sense to me (like why you would flip the fraction). <br>
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So to bring this into real life matters where it is really bothering me is something like the P/E ratio. Here are the "rules" I know about it:<br>
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- market value of share divided by earnings per share<br>
- a higher P/E means people think the company has better potential for future earnings growth<br>
- PE ratios are only comparable to similar companies<br>
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What I don't understand is the logic. So if someone asks me - "what happens to the PE ratio if a company's earnings per share falls?" I see this as what happens to the fraction itself if either the numerator or denominator or both rises or falls. The ONLY way I can figure this out is literally by trial and error using normal numbers. This is literally what I do:<br>
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20/5 = 4<br>
20/4 = 5 <br>
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So if the <strong>numerator falls</strong>, the fraction solution <strong>rises</strong>. So if the above were a PE ratio, the PE ratio would go up, which means the market thinks the company has better future growth prospects than it did before (extrapolating, if the EPS has gone down but the share price stays the same, the market thinks the lower EPS is temporary, but still has faith in the company because the share price hasn't changed and the EPS doesn't fully reflect the value of the company or whatever. THIS PART DOESN'T REALLY MATTER FOR THE PURPOSES OF MY QUESTION).<br>
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Another example would be financial/balance sheet ratios where understanding intuitively how fractions work and what it means when the numerator or denominator changes is super important to understand the balance sheet and the company. So if I wanted to look at net profit margin, the ratio is:<br>
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Net income/revenue<br>
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And if someone asked what decreased revenue means for a company's net profit margin, I would like a way to understand this intuitively through my understanding of fractions (and not my understanding of how companies and economies work) without having to use my manual trial and error divisions of twenty that I used above, Does that make sense? To make it perfectly clear:<br>
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Variable A/Variable B = Bigger Picture XYZ<br>
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What are the implications for Bigger Picture XYZ if Variable A changes?<br>
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PLEASE HELP. Where is my understanding of fractions breaking down???tag:ask.metafilter.com,2013:site.243209Wed, 19 Jun 2013 16:34:52 -0800AnonymousEducate me on modern mathematics!
http://ask.metafilter.com/242605/Educate%2Dme%2Don%2Dmodern%2Dmathematics
My math knowledge ends just past Newton. What books provide a good, relatively general-audience introduction to the past 150-250 years of problems and developments in mathematics? Ideally, I'm looking for something (1) that's accessible to a relatively knowledgeable layperson (comfortable with practical math through calculus/elementary analytic geometry, no real background in theoretical math at all), and (2) that blends serious explanations of the actual math with some "softer" historical background about interesting personalities, wider societal influences, etc. A bouquet of books that fall on one side or the other would be fine, too, though, as would some books that treat more specialized topics within that very broad umbrella (like just geometry or just arithmetic, just the early nineteenth century, whatever.) What should I be reading on the beach this summer?tag:ask.metafilter.com,2013:site.242605Mon, 10 Jun 2013 07:25:08 -0800gallusgallusWhy might some mathematical truths be unknowable?
http://ask.metafilter.com/238910/Why%2Dmight%2Dsome%2Dmathematical%2Dtruths%2Dbe%2Dunknowable
For all we know, some mathematical truths might be unknowable. E.g., for all we know Goldbach's conjecture (or its negation) is this way. Yet, if there are unknowable mathematical truths, why might this be?
Here are some initial considerations/hacks in the dark: (a) Presumably any computing device would have a finite number of parts. Maybe this would limit its processing power in some relevant way; (b) maybe some of the proofs are too long.tag:ask.metafilter.com,2013:site.238910Wed, 10 Apr 2013 17:03:30 -0800Eiwalker