Ask MetaFilter questions tagged with math
http://ask.metafilter.com/tags/math
Questions tagged with 'math' at Ask MetaFilter.Fri, 15 Aug 2014 10:57:43 -0800Fri, 15 Aug 2014 10:57:43 -0800en-ushttp://blogs.law.harvard.edu/tech/rss60Statistics Book for an interested teen
http://ask.metafilter.com/266881/Statistics%2DBook%2Dfor%2Dan%2Dinterested%2Dteen
My teen aged niece has suddenly found a strong interest in statistics. What book would you recommend for a 14 year old who has good, but not advanced, math skills?tag:ask.metafilter.com,2014:site.266881Fri, 15 Aug 2014 10:57:43 -0800honestcoyoteHelp! Can I normalize statistical coefficients?
http://ask.metafilter.com/266739/Help%2DCan%2DI%2Dnormalize%2Dstatistical%2Dcoefficients
With deadline looming, stats consultant has bailed. Simple queries need resolution. Help?
I am working on a data graphic that involves statistical calculations about survival rates for startup businesses, correlated with certain tangible and intangible factors. The raw data (about survival/closure/merger outcomes) has already been investigated, and the original researchers (who are awesome) have generated some interesting correlations using univariate regressions and Cox regressions. For my output I am relying on their statistically significant findings, wanting to create comparisons among the univariate coefficients. Not sure my methods are kosher and would appreciate consultation. Avalanche inside. To make the information clearer to a lay audience, editors and I want to present the figures in a comparative framing. Ideally, we're aiming to say "firms with factor [foo] have a XX% greater likelihood of survival than firms with factor [not-foo1] and a YY% greater likelihood of survival than firms with factor [not-foo2]." <br>
<br>
Univariate: <br>
The factors are characteristics of the owner and/or firm that survives/closes/merges. Specifically, I have univariate coefficients for owner age (binned categorical), race (categorical) owner years of experience (continuous), owner's experience in same industry (dummy: yes/no), owner's college degree (dummy: yes/no), firm diversification (dummy: yes/no), possession of IP (dummy: yes/no), and startup capital (binned categorical). I have firms categorized as high-, medium- and non-tech.<br>
<br>
What I am hoping to do is normalize the coefficients. Simple example:<br>
<br>
female-owned: survive 8.5 close 17.81 merger or sale 12.09<br>
male-owned: survive 91.5 close 82.19 merger or sale 87.91 <br>
<br>
(If it matters, t-test was used to determine statistical significance; all of the above are stat-sig.)<br>
<br>
Can I say that female-owned businesses in this category are more than twice as likely to close as they are to survive [(17.81/8.5) = 209%]? And, similarly, 42.2% [(12.09 - 8.5)/8.5] more likely to merge or be sold than to survive?<br>
<br>
If I calculate similarly for male-owned businesses (89.8% as likely to close as to survive), can I compare the 209%-as-likely women's closure likelihood to the 89.8%-as-likely men's closure likelihood? <br>
<br>
And does the 89.8% comparative likelihood of closure mean that men's firms are actually 11% more likely to survive? Or do I need to use a different denominator in calculating that?)<br>
<br>
Cox - competing risks: <br>
With Cox regression tables, the researchers calculated the comparative likelihood of competing risks (closure vs. M&A -- both are considered business exits). <br>
<br>
It seems clear that these figures are meant to be compared in pairs - closure vs. M&A. As I understand it, the coefficients represent positive/negative correlation (with each type of exit) and the absolute value (intensity) of the influence...? <br>
<br>
For example: <br>
Duration regression analysis - Cox regression (competing risks)<br>
White-owned high-tech firms:<br>
closure 0.56/m&a 0.45<br>
<br>
White-owned medium-tech firms:<br>
closure 0.69/m&a 0.8<br>
<br>
White-owned non-tech firms:<br>
closure 0.67/m&a 0.64<br>
<br>
I suppose I can compare the closure figures to one another, but how? The scale is not necessarily -1 to 1, as some of these coefficients are upwards of 3 (for factors other than race, such as whether the business is a franchise). <br>
<br>
And given this type of info, can any information about survival likelihoods possibly be derived (via...umm...subtraction or something)? <br>
<br>
I feel a bit sheepish about these simple-minded queries, but for that reason I was sure they would be no-brainers for someone here. Sincere thanks to anyone who can shed some light.tag:ask.metafilter.com,2014:site.266739Wed, 13 Aug 2014 08:13:31 -0800GrammarMosesMath-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>
<br>
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 -0800aws17576Methods of approximation?
http://ask.metafilter.com/266688/Methods%2Dof%2Dapproximation
I've never been very good at either math or at eyeballing things like weight or dimension, but was thinking recently about how to more or less accurately weigh things without using a scale. What good methods are out there to approximate other kinds of measurements? For weight, I figured the easiest way is to start with a known weight that can be easily divided (say a bag of sand), and that's heavier than what you're weighing. Compare it with what you want to measure. If it feels too heavy, divide it in half, set one half aside, and compare that. If it's too light, split the other half, set part aside, add that to your reference weight, and so on.<br>
<br>
I realize this is super basic stuff that was figured out a long time ago and is in some sense just using your hands as a scale, but it seems interesting how precise you could be as long as you were it accurately and knew how heavy the reference was to start. Also, the fractions you end up with at the end are easy to add up since they all have powers of two at the bottom. Is there a name for this kind of thing (continually splitting in half and adding back the fractional parts to get closer to what you want)? And is there a more generalized technique here that applies easily to estimating other kinds of things?tag:ask.metafilter.com,2014:site.266688Tue, 12 Aug 2014 09:34:45 -0800OverlappingElvisWhich algorithms changed the world?
http://ask.metafilter.com/266586/Which%2Dalgorithms%2Dchanged%2Dthe%2Dworld
A recent post to the blue proposed a set of <a href="http://www.metafilter.com/141814/Math-and-equations-are-fun">equations that changed the word</a>. As a computer professional, I'm curious, which algorithms transformed the world? I'm not necessarily looking for 'algorithms a computer programmer should know' or 'algorithms we should teach in CS 101.' An algorithm impact on the world should be the primary criteria, rather than pracitioner familiarity or pedagogical use.tag:ask.metafilter.com,2014:site.266586Sun, 10 Aug 2014 14:50:48 -0800pwnguinMath Camp for Economist help!
http://ask.metafilter.com/266560/Math%2DCamp%2Dfor%2DEconomist%2Dhelp
I'm basically teaching myself how to do pass an PhD economics placement test, and I'm looking for resources to learn these things that aren't books. I have A LOT of books, including the math camp notes for my school which I am currently unable to attend. But I'm looking for either video collections or forums to discuss these things and ask questions. We're using the book, Further Mathematics for Economic Analysis and I find it really useful. (I'm in a related social science program and looking to take econ classes down the line).<br>
<br>
I need to know how to do basic real analysis proofs, log-linearize some functions, tell if a formula is homogenous, homothetic, etc. Thanks!tag:ask.metafilter.com,2014:site.266560Sun, 10 Aug 2014 07:56:31 -0800MisantropicPainforestWhat 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>
<br>
- 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>
<br>
<br>
<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>
<br>
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>
<br>
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_banyan4x+y+2z=100, x>y, y>z, x+y+z=j, 3x+z=k, j>k, j+k=100.
http://ask.metafilter.com/265560/4xy2z100%2Dxy%2Dyz%2Dxyzj%2D3xzk%2Djk%2Djk100
4x+y+2z=100, x>y, y>z, x+y+z=j, 3x+z=k, j>k, j+k=100. WolframAlpha can only give me alternative forms or a solution involving 'real and imaginary parts of z'. Is there a solution I can count on my fingers? I wish to buy a thing. The thing I buy will have two desirable characteristics: j, and k.<br>
<br>
j comprises three sub-characteristics, while k comprises four sub-characteristics.<br>
<br>
I have three levels for ranking how important these sub-characteristics are to me - let's say 'super important', 'kinda important' and 'meh, whatever'. Obviously, they are of decreasing importance.<br>
<br>
I have rated the three sub-characteristics for j 'super important', 'kinda important' and 'meh, whatever'.<br>
<br>
I have rated three of the four sub-characteristics for k 'super important', and the fourth 'meh, whatever'.<br>
<br>
This means I have a total of four 'super important', one 'important', and two 'meh, whatevers'.<br>
<br>
Finally, j is a little bit more important to me than k. If further defining these variables help, then I think they'd be about a 60/40 split, though I'm flexible. They can be equal if that helps. At this stage I'd settle for k being less than j if it means a solution pops out.<br>
<br>
I would like to assign positive numbers to x, y and z, because I'm a bureaucrat, that's why.<br>
<br>
So, <br>
<br>
x>y (must)<br>
y>z (must)<br>
<br>
j = x + y + z<br>
k = 3x + z<br>
4x + y + z = 100 (per cent)<br>
j + k = 100 (per cent)<br>
<br>
I can't change the number of characteristics, sub-characteristics, or levels of importance. <br>
<br>
I could make k=2x+y+z, and so change the overall equation to 3x+2y+2z, but I'm not smart enough to know if that helps. It didn't help WolframAlpha.</j>tag:ask.metafilter.com,2014:site.265560Tue, 22 Jul 2014 18:07:45 -0800obiwanwasabiMath 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>
<br>
Things I DON'T want to hear: <br>
<br>
+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>
<br>
It's not necessarily that these are unappealing; I'm already aware of them, just looking for alternatives.<br>
<br>
Is there anything I'm overlooking?tag:ask.metafilter.com,2014:site.265554Tue, 22 Jul 2014 15:28:13 -0800AnonymousMath? College?
http://ask.metafilter.com/265440/Math%2DCollege
The best way to pursue my college goals given my situation. Last summer I went back to college and I took an Algebra and then A Pre-Calc course. I did well enough, A's in both. I never felt like I was really making any connections though. I started a career and as a result stopped pursuing school. I would now like to continue attending school on the side. I want to pursue more math and science courses but am not sure if it is a bad idea to try to take a Calc 1 class given the gap from the previous math courses last year. I am all for learning on my own, and am with several subjects, but math just does not seem like the kind of topic I can jump right into on my own and make any significant headway. Any suggestions on specific resources to get me up to speed or thoughts on what would be best in this case? I never really tried at the math and sciences when I was growing up and only gave it a shot for the first time last summer so I am not drawing on a significant base of knowledge. Thanks, I appreciate it.tag:ask.metafilter.com,2014:site.265440Sun, 20 Jul 2014 17:38:16 -0800mrdrummedCalculus Rabbit?
http://ask.metafilter.com/265439/Calculus%2DRabbit
Is there a game like <a href="http://www.mobygames.com/game/math-rabbit">Math Rabbit</a> out there, but for calculus? Specifically looking for something with lots of game-interface, not Khan Academy.tag:ask.metafilter.com,2014:site.265439Sun, 20 Jul 2014 16:41:00 -0800curious nuwhat percent will result from combining two types of milk?
http://ask.metafilter.com/265223/what%2Dpercent%2Dwill%2Dresult%2Dfrom%2Dcombining%2Dtwo%2Dtypes%2Dof%2Dmilk
If I add 1/100 to 2/100, I get 3/100 or 3%. But if I add one hundred apples, one of which is red, to one hundred apples, two of which are red, I will have 3/200 or 1.5%. I'm very confused now as to what percent milk fat my milk will be if I combine the two types of milk (1% and 2%) together.tag:ask.metafilter.com,2014:site.265223Wed, 16 Jul 2014 09:49:50 -0800windykitesConverting math to code
http://ask.metafilter.com/264616/Converting%2Dmath%2Dto%2Dcode
Wanting to code. Can't read calculus. Kinda stuck. Help? As I spend more and more time coding (just as a hobby, mostly in C and C++,) I keep running into a specific limitation of mine. I'm totally fine with the math, both conceptually and programmatically, but I can't understand much of the research that's in (what looks to me like) calculus. For example, the Wikipedia page that talks about <a href="http://en.wikipedia.org/wiki/Filter_(signal_processing)">signal filters</a> talks about transfer functions, and points to the Wiki page on <a href="http://en.wikipedia.org/wiki/Transfer_function">transfer functions</a>. That page makes no sense to me.<br>
<br>
But, when someone explains something like filters through non-calculus means (for example, <a href="http://christianfloisand.wordpress.com/tag/comb-filter/">this page</a> uses English and flow charts), I can totally follow it and create code based on that explanation.<br>
<br>
Some of the areas that I'm exploring aren't common enough to have English explanations of the calculus. So I'm stuck.<br>
<br>
Is there a way to learn enough calculus to conceptually read it? I don't need to do any math in calculus. I just need to be able to understand what a function expects me to do with it. Basically, how to read a function so that I can implement the idea in code.<br>
<br>
<small>In case it isn't clear, I don't need code samples for filters. I have plenty, and that's not where I typically get stuck. I need resources on deciphering calculus functions.</small>tag:ask.metafilter.com,2014:site.264616Thu, 03 Jul 2014 14:46:12 -0800ericcMath Filter: What is Calculus?
http://ask.metafilter.com/264607/Math%2DFilter%2DWhat%2Dis%2DCalculus
My son would like to know: Is there more to calculus than functions, examples of functions, various formats for presenting functions, and so on? That is, does calculus have unique to it other tools that are not just variations on functions? I dropped out of calculus my first quarter in college at age 18. I am in over my head. Please hope me, serious math geeks.<br>
<br>
Thanks!tag:ask.metafilter.com,2014:site.264607Thu, 03 Jul 2014 12:49:29 -0800Michele in CaliforniaMath book recommendations?
http://ask.metafilter.com/264105/Math%2Dbook%2Drecommendations
Years ago I read John Derbyshire's <em>Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics</em> and loved it. Now I'm studying formal theory/real analysis and I'm finding it really it interesting, but would like to be able to spend my downtime reading about the background of math and also explains some of the concepts. Thanks!tag:ask.metafilter.com,2014:site.264105Tue, 24 Jun 2014 14:09:10 -0800MisantropicPainforestMaximum sum of numbers, one from each set, with constraints
http://ask.metafilter.com/264069/Maximum%2Dsum%2Dof%2Dnumbers%2Done%2Dfrom%2Deach%2Dset%2Dwith%2Dconstraints
Working on a personal project, I am running into a number of math problems of the kind described within. I am not a math expert, so I don't know what to call these kinds of problems, so I don't know how to search for information about them. Here is an example of the kind of problem I am trying to find the answer to.<br>
<br>
There are ten sets of numbers with three numbers each (X, Y, Z).<br>
I want to find the greatest possible sum of (for example) 4 Xs, 2 Ys, and 1 Z<br>
BUT: (for example) If an X is chosen from a set, the Y and Z value from that set cannot be chosen.<br>
<br>
My questions are:<br>
Is there a name for these kinds of problems?<br>
Is there a general method to make sure I always find the greatest possible sum, that will work even when the details change? Sometimes I have more sets, sometimes there are more numbers within each set, sometimes more than one number can be taken from inside a set, each problem is different, but I am always trying to calculate the greatest possible sum.<br>
<br>
If I haven't been clear, please ask questions, and I will do my best to explain.tag:ask.metafilter.com,2014:site.264069Mon, 23 Jun 2014 22:16:30 -0800moonroofHelp Me Learn Math!
http://ask.metafilter.com/263592/Help%2DMe%2DLearn%2DMath
I will be returning to school in the fall to start prerequisite courses for a Physical Therapy program.
I don't know math.
The last time i took math was in high school, and it was basic geometry.
I would like to teach myself primarily, so that i can test into higher classes. The goal is to be able to test into pre-calc, so that i can also qualify for the physics classes as well.
Any suggestions? I don't really care about the method. I was thinking about buying a textbook, but i was unsure of which ones to get.
Thanks.tag:ask.metafilter.com,2014:site.263592Sat, 14 Jun 2014 19:31:10 -0800hiddenknivesHelp Building a Gameplan For a Career In Market Research Analysis
http://ask.metafilter.com/263483/Help%2DBuilding%2Da%2DGameplan%2DFor%2Da%2DCareer%2DIn%2DMarket%2DResearch%2DAnalysis
So, I’ve been doing a lot of thinking about how to land a career in market research analysis. Below are the steps I’ve laid out for myself. Could you tell me if this is a good game plan to get where I want to go? 1. Take a market research class to see if I like it<br>
<br>
2. Get major/minor set up correctly<br>
<br>
3. Figure out LinkedIn and how to network<br>
<br>
4. Follow the advice from the following link https://www.linkedin.com/groups/How-Break-into-Market-Research-1772348.S.84150355<br>
<br>
5. Get an internship in market research<br>
<br>
6. Figure out if a masters is needed and if so how to get it<br>
<br>
7. Get masters<br>
<br>
8. Look for job, using steps 3, 4, 5, and 7 as selling points in my resume.<br>
<br>
9. Get job<br>
<br>
About me:<br>
I’m 25, I’ve never really had a job more serious than a first job kind of job (This summer I’m going to be getting a job at a Dollar General as a sales associate… a job that a 15 year old could do). <br>
<br>
I’ve been in college off and on since 2007 trying to find myself and figure out what the heck I should do with my life. Don’t worry though: I was in community college (and paid as I went) up until Fall 2013, which was my first semester at Texas State University in San Marcos under the major of psychology. <br>
<br>
Combining my entire college career, I have a GPA of 3.10 with 95 earned hours (hours that are unfortunately all over the place). But just in my time at Texas State University under the major of psychology, I have a GPA of 3.88. I don’t know which GPA counts.<br>
<br>
Unfortunately, I have so many random hours that to get a marketing/statistics degree I would have to surpass 120 earned hours, and after you get past 120, you are charged out of state tuition. There is no way I can afford to pay that, so I’m stuck with my major of psychology. My minor right now is in English, which I need to change into something useful. I don’t know whether a minor in statistics or marketing would get me to where I need to be to land a career in market research analysis.<br>
<br>
The reason I’m leaning towards market research analysis is because I am good at math (in that I have never gotten less than an A in a college math class - I’ve taken classes in college algebra, intro to statistics, and just last semester, behavioral statistics). I thoroughly enjoyed my sociology class (got an A in that too) but it was a bit on the easy side, so I don’t know if I’d enjoy it as much if I had a boot camp style professor. I research everything that I buy and cross research it, so I think I may have the right mentality to do research. The reason I chose psychology was to understand people and how they think, which is a big component (just not on an individual scale) in figuring out who will buy what and why. Additionally, I have a knack for writing (my writing may not be the best right now as I’m a little tired).<br>
<br>
Are these good enough reasons?<br>
<br>
A couple of problems/concerns I have about market research analysis.<br>
<br>
I’m a little slow. Obviously, I’ve been fast enough to finish my work and get an A in every math class, but I have to work longer and harder than most people, it seems. But this is how I am with everything… I’m just a slow but steady person. I don’t know if it’s a side effect of my high functioning autism or my perfectionist nature, but it’s just a reality of who I am. I don’t know if this will get in the way too much in my job as I’d be working under tight deadlines.<br>
<br>
Secondly, what if I burn out? I know it’s a hectic career, and I don’t handle stress too well. I enjoy numbers, formulas, and data because they are always predictable and reliable in a world full of crazy chaos, but I don’t know whether or not I could spend the rest of my life hunched over a computer compiling numbers. I may be able to, I don’t know. I know there is more to the job, but this is the heart of it, correct?<br>
<br>
I apologize if that was too long of a question, but I just have a lot to ask and I’m not the best at condensing my thoughts!tag:ask.metafilter.com,2014:site.263483Thu, 12 Jun 2014 18:30:57 -0800ggp88Can you answer this question before my traffic court at 9 am?
http://ask.metafilter.com/263325/Can%2Dyou%2Danswer%2Dthis%2Dquestion%2Dbefore%2Dmy%2Dtraffic%2Dcourt%2Dat%2D9%2Dam
I'm due in traffic court at 9 am. Help me use math to prove I didn't do it. Long story short: officer says I went from 0 mph to 29 mph within a distance of about 200 feet. There is no way I got my little Honda Fit up to that speed within that distance.<br>
<br>
Is there any science: simple math about acceleration; or somehow using the Honda Fit's 0 to 60 speeds (2007 Honda Fit Sport 0-60 mph 8.9 Quarter mile 16.6) to use SCIENCE! to help me be persuasive that I didn't do this.tag:ask.metafilter.com,2014:site.263325Tue, 10 Jun 2014 04:41:06 -0800anastasiav2 problems of combinations and permutations.
http://ask.metafilter.com/263055/2%2Dproblems%2Dof%2Dcombinations%2Dand%2Dpermutations
How many unique ways are there to put X rocks into Y boxes?
(Given two different sets of attributes for both the rocks and the boxes.) Apologies in advance for what is probably some pretty non-standard notation; I am a very amateur mathematician, and I've not studied set theory.<br>
<br>
I'm working on a table of formulas for figuring out various combinations/permutations. The table is missing two formulas, which I've not yet been able to figure out.<br>
<br>
There are a few ways to describe these sorts of problems, but I'm going to use the following metaphor for each of them: How many unique ways are there to put X rocks into Y boxes?<br>
<br>
(In the examples, the rocks are labelled X1, X2, etc., if they are distinct from each other, and simply X if they are not. Likewise for the boxes.)<br>
<br>
.....<br>
<br>
<strong>PROBLEM 1:</strong><br>
How many unique ways are there to put X rocks into Y boxes?<br>
·Every rock is unique. Every rock can be used up to one time.<br>
·The boxes are not unique. Every box can hold an unlimited number of rocks. The minimum number of rocks per box is zero.<br>
<br>
<strong>EXAMPLE 1-1:</strong><br>
If X=2 and Y=2, there are 5 unique combinations:<br>
01. Y() Y()<br>
02. Y(X1) Y() <br>
03. Y(X2) Y()<br>
04. Y(X1) Y(X2)<br>
05. Y(X1,X2) Y()<br>
<br>
<strong>EXAMPLE 1-2:</strong><br>
If X=3 and Y=3, there are 15 unique combinations:<br>
01. Y() Y() Y()<br>
02. Y(X1) Y() Y()<br>
03. Y(X2) Y() Y()<br>
04. Y(X3) Y() Y()<br>
05. Y(X1) Y(X2) Y()<br>
06. Y(X1) Y(X3) Y()<br>
07. Y(X2) Y(X3) Y()<br>
08. Y(X1) Y(X2) Y(X3)<br>
09. Y(X1,X2) Y() Y()<br>
10. Y(X1,X3) Y() Y()<br>
11. Y(X2,X3) Y() Y()<br>
12. Y(X1,X2) Y(X3) Y()<br>
13. Y(X1,X3) Y(X2) Y()<br>
14. Y(X2,X3) Y(X1) Y()<br>
15. Y(X1,X2,X3) Y() Y()<br>
<br>
.....<br>
<br>
<strong>PROBLEM 2:</strong><br>
How many unique ways are there to put X rocks into Y boxes?<br>
·The rocks are not unique. Every rock must be used exactly once.<br>
·The boxes are not unique. Every box can hold an unlimited number of rocks. The minimum number of rocks per box is one.<br>
<br>
<strong>EXAMPLE 2-1:</strong><br>
If X=3 and Y=3, there is 1 possible combination:<br>
01. Y(X) Y(X) Y(X)<br>
<br>
<strong>EXAMPLE 2-2:</strong><br>
If X=8 and &=3, there are 5 possible combinations:<br>
01. Y(XXX) Y(XXX) Y(XX)<br>
02. Y(XXXX) Y(XX) Y(XX)<br>
03. Y(XXXX) Y(XXX) Y(X)<br>
04. Y(XXXXX) Y(XX) Y(X)<br>
05. Y(XXXXXX) Y(X) Y(X)tag:ask.metafilter.com,2014:site.263055Wed, 04 Jun 2014 18:49:18 -0800CustooFintelMortgage shenanigans?
http://ask.metafilter.com/261820/Mortgage%2Dshenanigans
We have an excessive interest rate on our home. We tried to refi, and the appraisal came in a good $40,000 less than it needed to in order to qualify. So some of our more numerically-talented friends ran some numbers for us in an attempt to find alternative solutions and found a weird discrepancy that makes it appear we owe $15,000 more on the loan than we do... My husband bought the house in 2001 before I lived with him. He's always paid the mortgage on time, but the attractive (<em>for investors! not us!</em>) interest rate means it's been resold a kajillion times to multiple mortgage holders. It's currently with (<em>shudder</em>) Ocwen after GMAC failed. <br>
<br>
What steps do we take to determine if something hinky has happened along the way? Do we start by adding up a decade of mortgage payments and saying hmm, that totals <strong>xxx</strong>? Or what? Is there any way of tracking all the companies that have ever held the loan and demanding records?<br>
<br>
(For the purposes of this situation, assume my husband pays everything online and that we don't have paper bills for every mortgage payment made). Thanks in advance, hive mind!tag:ask.metafilter.com,2014:site.261820Tue, 13 May 2014 07:06:18 -0800bitter-girl.comPythagorean Theorem in the original Greek
http://ask.metafilter.com/261768/Pythagorean%2DTheorem%2Din%2Dthe%2Doriginal%2DGreek
I'm looking for a textual version of <em>a</em><sup>2</sup> + <em>b</em><sup>2</sup> = <em>c</em><sup>2</sup> that is as old as possible, among all the Greek sources. I am looking for the earliest statement of the Pythagorean theorem in Greek. I want it to be as text, hopefully something like "the sum of the squares on the sides is equal to the square on the hypotenuse". <br>
<br>
- It's probably not stated that way, but that's fine.<br>
- Greek text is a requirement.<br>
- Older is better.<br>
<br>
I've gotten some indication that I should look in Euclid's <em>Elements</em>, but haven't managed to track that down. I thought there might be some MeFi classicists who had this at their fingertips. Thanks.tag:ask.metafilter.com,2014:site.261768Mon, 12 May 2014 10:57:31 -0800benito.straussHow do I calculate combined percentages?
http://ask.metafilter.com/261686/How%2Ddo%2DI%2Dcalculate%2Dcombined%2Dpercentages
Mathfail: I'm considering supplementing my cat's food with plain meat. I'd like a rough idea of how much it would bump percentage of calories from protein and fat. Here are the numbers I'm working from:<br>
<br>
Total calories: 215<br>
<br>
Canned food calories: 180<br>
% calories from protein: 32%<br>
% calories from fat: 59%<br>
<br>
Meat calories: 35<br>
% calories from protein: 77%<br>
% calories from fat: 8.5%<br>
<br>
If I combine these together, what are the combined calories from fat and protein?<br>
<br>
I'm looking at a couple of canned foods, and would be grateful if you could walk me through the calculation. I feel dumb asking this - I'm sure I learned how to do this at some point in my life, but my math skills are rusty.<br>
<br>
(For the curious: this is to compare numbers of cheaper food + meat to more expensive food.)tag:ask.metafilter.com,2014:site.261686Sat, 10 May 2014 13:40:14 -0800moiraShould my math student have some Unix skills?
http://ask.metafilter.com/261436/Should%2Dmy%2Dmath%2Dstudent%2Dhave%2Dsome%2DUnix%2Dskills
I think my son, who is on an AP math trajectory in high school, would benefit from getting some familiarity and basic programming skills in the Unix world. I've noticed math depts in some universities include study of these skills in early years. Are there some tutorials we could use in the OS X environment to get a leg up? He is competent with computers but has no programming or command line experience.tag:ask.metafilter.com,2014:site.261436Mon, 05 May 2014 21:02:47 -0800Mei's lost sandalWhat Major and Career Should I Look At If I Enjoy Math?
http://ask.metafilter.com/261370/What%2DMajor%2Dand%2DCareer%2DShould%2DI%2DLook%2DAt%2DIf%2DI%2DEnjoy%2DMath
In studying for my Behavioral Statistics final (it’s a statistics class dealing with psychology research methods) I’ve realized something. I actually kind of enjoy math. As long as I don’t have to memorize formulas (as long as they are right there as I’m going through the work) it’s actually kind of comforting and fun. In fact, every math class I’ve taken in college (I’ve taken two remedial algebras, college algebra, and regular statistics before this class) I’ve enjoyed and made an A in.
I’m really struggling about what I want to major in (I’m in psychology but I don’t have it in the gas tank to get a PhD), but I know that a lot of people don’t like math. They don’t get it. I do, so I’ve got something there, right?
The only problem is, I don’t know what to do with it. These are the parameters… maybe you can think of something that fits? -I’ve been in college since 2007 floundering around in terms of what I want as a major. At the VERY MOST, I am willing to get a masters, but I’d rather just get a bachelors.<br>
<br>
-I want to make around 60-70k a year at the least.<br>
<br>
-I like people, and the idea of working in teams, but sometimes I suffer from social anxiety. I don’t want some high-pressure sales job.<br>
<br>
-I like math because of its formulaic, step-by-step, one-thing-leads-to-another nature. It’s predictability in a world of chaos. I’m not a big fan of unpredictability and that’s why it’s comforting.<br>
<br>
-I like discovering new things, but I’m not a trailblazer… I work as a follower, a team member.<br>
<br>
-I’d rather not be behind a cubicle working on mundane paperwork. I want to do something that has meaning and excites me.<br>
<br>
-I want to have time for my other hobbies such as family, friends, and being outside. <br>
<br>
-It would be very nice if the job were in demand and not some extremely highly competitive field. I value security very very much, and the idea of graduating college and being lost again is terrifying.<br>
<br>
-I know that every job can be stressful and unfun at times, but I’d prefer this job to be on the low-stress end of the spectrum. I don’t deal very well with stress.<br>
<br>
I may be just being too picky here, and perhaps such a job that fits all of those requirements does not exist. But maybe there are careers out there that fit pretty well, if not perfectly.<br>
<br>
The most important aspects are the salary, not getting the PhD, and a non dog-eat-dog gladiator ring of a competitive field. And I’d rather it be fun and engaging, not boring and soul-draining.<br>
<br>
Does anyone have any ideas?tag:ask.metafilter.com,2014:site.261370Sun, 04 May 2014 17:18:24 -0800ggp88