Ask MetaFilter questions tagged with Mathematics

Business optimization eek!

nomnomnom — Sun, 22 Nov 2009 03:55:24 -0800

I've got these 2 math problems that are driving me crazy. Business optimization. Please help. I just can't grok this concept! Help me figure it out?

Q#1 A business consultant advises a client that by spending extra on advertising, the client will increase profits. For an increase of $x in advertising, profit will increase by 20 x²e^-.5x. What increase in expenditure will yield the greatest increase in profit? (x is the amount in 100s of dollars.)

Q#2 Fred has a business that makes two kinds of dining room suites. Model A takes 4 hours to assemble and 2 hours to finish. Model B takes 3 hours to assemble and 4 hours to finish. 3 employees assemble the suites and 2 do the finishing work. All employees work a 36 hour week.

Profit on Model A is $200, on Model B, $260. A minimum of 4 of each model has to be manufactured each week.
What production of each model will maximize profit? What is the maximum profit?

Help me learn to typeset equations like it was my job. (Why? Because it is.)

nebulawindphone — Wed, 04 Nov 2009 12:56:56 -0800

I am looking for a math typesetting style guide. By this I don't mean the kind of stylesheet for journal submissions that says "Be sure to use the blah-blah-blah LaTeX package and the XYZ equation environment, and our army of editorial assistants will tie up the loose ends and knock off the rough edges." (Why not? Because my advisor is involved in starting a new journal, and suddenly my labmates and I are that army of editorial assistants.) I am less interested in the technical details of mathematical typesetting. We've got our fonts chosen already, we're committed to using LaTeX and AMSMath which I speak pretty fluently, and we're distributing online so anything having to do with print is Not An Issue. In particular, I am not looking for another LaTeX user's manual — although if the advice I need happens to be buried in one, I'm okay with that. I'm also not particularly interested in simple questions of usage ("bigger parentheses or square brackets?" "~ or ¬ for negation?"), especially since a lot of those boil down to taste and convenience anyway.

I'm more interested in what you might call the visual semantics of it. (F'rinstance: How do you set a long equation so as to reveal its structure quickly and easily to the reader? How can spacing, line breaks, alignment and so on be used to produce that sort of clarity, and what other tricks are there that I'm not thinking of? What about a sequence of equations? A derivation or proof? How do you set a nonstandard symbol — an operator, function, etc. defined by the author;we get this a lot in my field — so that it's clear what its role in the equation is? This isn't a complete list of questions, but it's questions like that that I want to learn how to answer.) Aesthetic details — good spacing, good line breaks and page breaks, all-around symmetry and tidiness — are also important. The goal is to make these thorny and technical articles as easy and joyful to read as I possibly can.

Bonus points for a guide with good advice on the odd situations that come up in formal semantics and mathematical logic. (For instance, I've been unable to find any advice for laying out expressions in lambda calculus, or ones containing multiple quantifiers, and both of those are frequent sources of difficulty here.) But if that's asking too much, then I'm looking for general best practices that I can apply to the edge cases when they come up.

Rates of success?

rollick — Wed, 04 Nov 2009 09:46:36 -0800

Statistics question: is it possible to test sets of cumulative data for significant differences in rate? I have three cumulative percentage graphs, measuring the germination rates of three different seed types. Is there a way to compare them and see if there are any statistically significant differences?

The seed types were planted in triplicate, on three dishes each (nine overall). Every day for the past few weeks I've observed how many seeds on each dish have begun germinating -- so for an individual dish I would have " Day 1: 0 ... Day 7: 14 ... Day 14: 29" etc, with each day's score a cumulative total. (There are 100 seeds on each dish, so it works as a percentage rate as well)

In Excel, I've graphed the average germination rates of the replicates, for a graph that resembles this one. (with three lines plotted, and x-axis = time in days, y-axis = percent germinated).

So is there a way to compare these different rates statistically? I can use Excel, Minitab, SPSS, and R.

Countdown

Blazecock Pileon — Fri, 30 Oct 2009 13:31:34 -0800

Is there an enumeration of complete chess games? Has anyone made an accurate (ideally, "closed form") count of possible chess games?

I found an older article via Google that does a very rough guess-timate of how many complete chess games are possible.

I'm curious if anyone has since tried to count all possible games, given standard FIDE rules, played to completion. Presumably, for example, it is not exponential because some moves will result in an end state ("checkmate" or "stalemate") faster than other moves.

Please do not offer speculation about the answer
Please do not link to Google search results (unless you have found something that answers the question as specifically framed)
Thanks!

Math Symbol Mystery

mazniak — Sun, 25 Oct 2009 20:19:54 -0800

I've never seen this mathematical symbol used this way before. Can anyone tell me what it means? Ok, my ignorance is on display for the world to see…

Please look at this image .

I'm referring to the parallel bars between the two resistances at the top. Obviously anyone who's taken 9th grade geometry knows that it is a symbol for describing a relationship as being parallel. But how does it fit here? How is it used to derive the final value of the voltage gain (3.82)?

Can I get into grad school in math?

tamaraster — Wed, 14 Oct 2009 20:31:11 -0800

Can I get into a funded Math Master's or PhD program? I'm graduating from a 4-year college with my B.S. this Spring, and I'm in my mid-30's. I have good GPA at this school (about a 3.6, up to about a 3.8 in math courses specifically) and good GRE scores (720 V / 780 Q), but I have dropped a lot of courses (I've worked full time over the years while getting my degree), and back in the mid-90's I flunked out of the first university I went to. Are there graduate math programs that would accept me and give me a TAship or RAship with stipend and free tuition? I have one publication (a not very good one in Computer Science from a regional conference) and will have decently good recommendations, but I haven't done anything brilliant.

I'd like to get a PhD but I'm certainly open to getting a Master's first. Is there an obvious way I should proceed here?

Uh...hang on, just give me a minute.

Demogorgon — Mon, 12 Oct 2009 10:34:31 -0800

What is the most important scientific question of our time? I volunteer at an observatory for a local amateur astronomers' society and one of the guests at a recent star party came up and asked, "What do you think is the most important question science has to answer right now?" Obviously, there is no right or wrong answer, but after the party was over a lot of us were still talking about this question and I ended up learning a great deal from my fellow club members that I might otherwise not have.
The next time this question gets asked I want to be prepared to offer a variety of answers from differing fields and opinions. I don't expect to represent every answer as an expert, but I'd like to be able to give a few more examples than I was able to, and then correlate them to some book recommendations from the answers in this thread about introductions to your field.
I also think it is important to frame the question in a way that can be meaningfully answered, i.e. "What is the most important scientific discovery about to be made?" or something like that.
Of course, I had my own answer in mind, but as a relative layperson to that branch of study I had a really hard time articulating why it was so important to "science." Therefore, if you are uniquely affiliated with a specific field that you think will produce a game-changer, feel free to get as technical as you're comfortable doing.

Thanks!

Calculating Probability Over Several Attempts?

WCityMike — Wed, 16 Sep 2009 09:39:58 -0800

How do you multiply probability across multiple chances? Let's say that every time you roll a die, you have a one-in-six chance of having five come up. What math would you perform to come up with the probability of five coming up at some point with the dice being rolled two times? Three? Five? Ten? (I'm using dice as a shorthand here: the actual probability figure I'm working with is 24%.)

Mutton dressed as lamb

Funmonkey1 — Tue, 15 Sep 2009 03:19:36 -0800

Is there a formula related to the statement "What's old becomes new again"? As middle age encroaches, it becomes harder and harder not to see history recycled and repackaged whether fashion, music, etc... Do marketers and and advertisers have a strategy backed by science or math? Or is this just my first sign of developing "Get off my lawn" syndrome?

Fourier series confusion and pre/post-integration substitution dilemmas.

PuGZ — Sun, 13 Sep 2009 01:10:41 -0800

Asking for a friend: With the use of Fourier series, I'm trying to solve an ODE of the form L*y'' + R*y' + y/C = r(x), where r(x) = 1 - x^2 for |x| <= 1, i.e. has a period of 2. To do so I need to represent 1 - x^2 as a Fourier series. In doing so I have to integrate e^(-n * i * pi * x), but I've reached a stumbling block. I'm stuck because I noticed that substituting n = 0 before the integration yielded a different result to substituting post-integration (ie. Divide by zero). What am I doing wrong? Both in regards to what I'm trying to achieve overall and as a stand alone problem, how would I deal with the such integrals when substituting in for the case n = 0?

You ate ALL MY PIZZA!

contessa — Fri, 04 Sep 2009 11:58:49 -0800

Is there a mathematical, economic, logical or game-theory name/description for the following scenario? Let's say you have two pairs of people: Pair A and Pair B.

Both pairs are ordering pizza. Pair A will not eat meat toppings, whereas Pair B wants meat toppings. Collectively all four decide to order two pizzas: one with no meat toppings (pizza #1) and one with meat toppings (pizza #2).

When the pizzas arrive, Pair A of course will only eat pizza #1. But Pair B are not committed carnivores; in addition to pizza #2 (which only they prefer) they also want to eat slices from pizza #1.

At the end of the meal, Pair A have had to struggle to get a "fair" share of pizza #1, whereas Pair B have helped themselves to both pizzas.

What's this called? (Besides "being jerks"?)

(3Excel)(2Help)(1Please)

Nanukthedog — Fri, 28 Aug 2009 08:41:37 -0800

MathFilter, NumericSimplificationFilter, RecursionFilter, ExcelFilter: Where X_1,X_2,...,X_n can be any number, is there a name, simplified series, or equation to describe: (X_1)+(X_1+X_2)+(X_1+X_2+X_3)+...+(X_1+X_2+...+X_n) ? Seriously seriously insane exel implementation question inside. The prior question probably gives me enough information that I can do some research on the implementation of what I'm asking below. Effectively I'm doing an accumulation of data in Excel.

For each data set, I have a row containing distinct quantities
We'll say that says{A1:D1} contain the values {100 | 500 | 200 | 300 }
What I need {A2:D2} to say is the cumulative value of the prior cells, plus the cumulative value of the prior cumulative values

This means {A2:D2} = {100 | 700 | 1500 | 2600 } is my desired result.

METHOD 1.
{A2} =Sum($A1:A1)
{B2} =Sum($A1:B1,A2)
{C2} =Sum($A1:C1,B2)
{D2} =Sum($A1:D1,C2)

METHOD 2.
I could also represent each of these as
{A2} =Sum((A1*1))
{B2} =Sum((2*A1),(B1*1))
{C2} =Sum((3*A1),(B1*2),(C1*1))
{D2} =Sum((4*A1),{B1*3),(C1*2),(D1*1))

Now here's the thing I'm not doing this to D2, I'm doing this more likely to {BB2}. I need a way (preferably without macros) to get a cleaner table. Is there a relatively simple expression so that I could generate {BB2} without generating {A2:BA2}? With the amount of data I'm performing this on, METHOD 1 requires a lot of cell real estate, and METHOD 2 results in an insanely long, quasi recursive forumula that doesn't lend itself to copying and re-use.

Understand the portability of copying and re-use are the big needs, as I don't do this once, I do this a couple hundred times on data sets of varying length.... generally for 63+ columns and 200-300 entry rows...

I'm hoping that by getting a better name and notation for the series that I can figure out a better way to implement this. Also, eventually this gets ported to SQL, so while recursive realities are nice, the DB admin hates 5 hour tablebuilds...

What can I do with a Master's in math?

Earl the Polliwog — Sun, 09 Aug 2009 23:59:02 -0800

I have been attending graduate school in mathematics for the last 3 years, in hopes of getting a Ph.D. It hasn't exactly worked out - I'm taking my Master's and getting out of here. What can I do now? The main reason the program hasn't worked for me is that no one here studies what I want to do - computability, information theory, computer sciencey math. I only figured out my real interest after I sent out apps, and it has come back to bite me. I was trying to tough it out but the mean time-to-Ph.D here is 7 years and I realized I would be miserable if I forced myself spend that much time slaving over something that I didn't genuinely find exciting.

I might want to go back and get the Ph.D if I can find the right school. But that's not on the table for at least one year. I need the break, and my undergrad girlfriend has a couple years left here too.

So, what jobs are looking for people with a Master's in math? I have already applied for a lecturing position at the local community college. I have also been looking through the job pages of the AMS and a couple other big math sites, and the standard job sites like Monster. I just want to know if I am missing something.

Math? Maths? Mathesises? Mathelesalizes? Mathematisessizes?

fishmasta — Sat, 11 Jul 2009 20:21:17 -0800

When did "Maths" change to "Math" in American English? Or is it the other way around? I'm curious to know more about the origin of the math/maths break in the English language. Growing up in the United States, the shortening of mathematics to "math" has always sounded correct to me. But I know in the UK that "maths" tends to be more common. What I'm wondering is how/when/why this shift happened? Is it based on the long form spelling of "mathematics"? Is it based on the sound when pronounced (and is a teacher of other subjects with the "s" sound treated in a similar manner (e.g. a Sciences teacher rather than a Science teacher))? Or is it just one of those weird differences with no explanation other than that is how it's always been done? Any background you can provide is appreciated. Information on how other slight changes between our English forms happened is also welcome. Not as interested in total word differences (lorry/truck, lift/elevator, etc.) so much as the same word with slight variance.

Learning General Relativity

DU — Mon, 06 Jul 2009 06:06:12 -0800

What textbook can I use to learn General Relativity, including the associated math? What I have so far

I'm pretty firm on calculus and basic physics (and of course Euclidean geometry, etc). Less firm or polished, but technically familiar with vector calculus. I recognize words such as "laplacian" from electromagnetics, but really only have a vague understanding of the actual concepts.

What I'm interested in

I'd like to learn GR. And of course to learn GR, I need to learn some of the underlying mathematics such as differential geometry. I'm also interested in learning perhaps 10% more diff geo than is strictly required for GR.

The field

I have access to a largish technical library covering stuff from math to programming to astronomy to thermodynamics to engineering. "Classics" are probably in the catalog, but may be permanently checked out.

The requirements

Requirement 0 is really more of a guideline: I'd like something that teaches both GR and the needed math together. However, if there are N books that otherwise qualify and teach the subjects separately, I'm open to the idea.

1) Not overly formalized. I prefer a conversational, readable textbook.
2) Good problem sets. (I.e. not just one or two per chapter)
3) Answer key.
4) Not a "bible" or an "elegant reformulation". I need to be able to learn from it, not marvel at the comprehensiveness or elegance from a position of already knowing the subject.

An example of a nearly great suggestion is Gravity: An Introduction to Einstein's General Relativity by James Hartle. Why only "nearly" great? No answer key. Unfortunately, as perfect as the book otherwise appears, this renders it useless to me.

Some examples of actually great suggestions, but on different topics. If you know (of) these books, you will know the kind of thing I'm looking for:

Fundamentals of Physics by Halliday, Resnick and Walker
Div, Grad, Curl And All That by Schey.

Economics' greatest hits? ... or... Where's the science in economics?

zaebiz — Tue, 23 Jun 2009 12:54:37 -0800

As a former scientist, help me gain some faith in economics. What were the great successes of economics as a tool for making better decisions in the last 100 years? The Queen of England said it best for me : Why did none of the big shot economists see this crisis coming?

Having been scientifically trained, I have always had this belief that economics is a mostly mathematical rationalisation of events after-the-fact with the same predictive capabilities as astrology and whose validity decreases as more people believe in it. Why am I wrong? what demonstrable uses has it had? Also interested in any books or papers discussing either side of this debate.

Do I need the PhD to work in industry?

alligatorman — Sun, 14 Jun 2009 09:42:47 -0800

I want a PhD in Mathematics, but I do not want to stay in academia. Is it worth it? I would like to go into industry immediately after getting my PhD.

My question is: Is it worth it? Will having a PhD give me opportunities that I can never have otherwise?

My interests are in discrete mathematics: combinatorics, graph theory, algorithms, etc. I've been told by someone who works in the computer tech industry that he knows of a lot of companies that hire mathematicians for work in algorithms, optimization and other things that I wouldn't mind doing.

Would I be wasting my time going for a PhD? Could I ultimately be doing work that a PhD does with just a Masters (ideally funded by the company) and some experience? If so, would I even be able to land a position with such prospects with just a Bachelors degree and no related work experience?

I want to continue to do mathematics that I find interesting, but I don't want to go through what's necessary to become a tenured professor.

Any advice would be greatly appreciated.

The science of suckiness

handybitesize — Mon, 08 Jun 2009 10:07:15 -0800

I want to calculate the mean of a matrix, but I don't want a value, I want co-ordinates. The following math question has lots of terminology that I'm not qualified to use i.e. most of it is wrong. I hope you can see through this and help me. I will be using the words matrix, mean and transformation without fully understanding them. For this I apologize. Imagine a 10x10 matrix of integers, I wish to find the 'point of balance'. That is, if the integers were weights and the matrix a sheet of plywood, it is where I would place a pivot for the sheet to remain in balance (assume the plywood has no weight).

I don't want to work it our mechanically (using trig and moments and things of that ilk, besides the weight thing is an analogy, I'm looking at luminosity), I want to apply a matrix transformation if possible.

However my knowledge doesn't even let me begin to search on the type of transformation I need.

I have played with the mean of the rows and cols. In a 2x2 matrix for example

10,20
4,200

x = ((1 * 10) + (2 * 20) + (1 * 4) + (2 * 200)) / (10 + 20 + 4 + 200) = 1.94017094
y = ((1 * 10) + (2 * 4) + (1 * 20) + (2 * 200)) / (10 + 20 + 4 + 200) = 1.87179487

which looks right, but doesn't feel right. I'm sure we are missing something.

Any pointers/equations/corrections are very appreciated.

(The 'suckiness' in the title refers to the larger integers "sucking" the balance point towards them, not that I suck at science, which I do)

How to keep material organized while teaching?

madcaptenor — Fri, 15 May 2009 08:00:46 -0800

How do I keep track of things I want to cover in the future in the course I'm teaching? I'm a graduate student in math, hopefully (crossing my fingers!) a year away from getting my PhD. This summer I'll be the sole instructor for a course, and I'm worried about planning. What sort of system do those of you who teach use to keep track of things you might want to talk about in class in the future?

Some background about the course: The course is titled "Ideas of Mathematics", thirty or so students, mostly sophomore and juniors, various (mostly non-technical) majors. This meets a distribution requirement at my university, so they don't necessarily want to be there, but there are courses which are less mathy that satisfy the requirement, so I can assume they don't totally hate math. I can't assume any prerequisites beyond the fact that they got into my (top 10? in the US) university. The course is in turn not a prerequisite for anything else, so there's no particular material I am required to cover. I plan to cover some basic number theory and combinatorics, fractals and chaos, probability, and game theory; I'm using the textbook The Heart of Mathematics by Burger and Starbird, which came recommended by a colleague who has used it twice for this course.

Some background about me: I have TA experience (mostly in calculus courses), which has gone reasonably well (I've gotten above-average but not award-winning evaluations). I actually taught a calculus class three summers ago, before I had any TA experience, which was a bit of a disaster; let's pretend that never happened. From experience as a TA, I'm confident about my ability to do the "little things" in teaching -- answering questions that students ask, grading homework and exams, and so forth. It's the larger-scale things that I'm worried about.

finding a good book is hard

Brennus — Thu, 07 May 2009 13:45:24 -0800

I need a good statistics book! I an looking for a good probability and statistics book (or multiple, if necessary). I have a good math background (math undergrad, engineering grad school) but my statistics background is lacking. I want a book that is relatively accessible but does cover all the major topics, preferably with proofs. I want to gain a solid understanding of applying t tests, ANOVA and the like while understanding the fundamentals. The library is full of books but most don't seem right. Which book would you recommend?

I need a free and robust math worksheet generator

booksherpa — Tue, 28 Apr 2009 04:37:56 -0800

I need a free and robust math worksheet generator, and don't care whether or not it's a script, web-based, or software. It should produce addition, subtraction, multiplication and division problems; create addends, minuends, subtrahends, multiplicands, multipliers, divisors and dividends with as many digits as I specify, within reason; and ideally, export to Excel, or at least cut and paste accurately to there. Being able to throw decimals in would be nice, but I'll pen them in before I photocopy the sheet if I have to.

There's a number of worksheet generators online, but it's hard to find ones that go beyond 4 or 5 digits. Right now I use some online generators, and make up the rest of the problems myself, using Excel as the framework for placing numbers in columns. Excel's random number generator doesn't work the way I need it to for this - I have each digit of the problem in its own column for alignment. For the tougher problems I make the grid behind the worksheet visible and let it serve as graph paper - it helps the students line up their work, particularly partial products and long division.

Can anyone point me to some page I've missed in my extensive Google searches?

Python and Math

alligatorman — Tue, 14 Apr 2009 15:22:10 -0800

Is it worth learning Python for combinatorial mathematics research? I need to (re-)learn a programming language for some future research I plan on doing in combinatorics and discrete mathematics, and the elegance of Python is drawing me towards it.

How much efficiency/speed would I lose by not using a lower level language, like C++?

I know this question is very vague, but I do not know exactly what type of problems I plan on tackling. I just want to know if Python can efficiently handle heavy data.

I've read about the excellent math packages for Python, and Sage looks very neat.

Any (discrete) mathematicians out there use Python on a regular basis? Am I better off re-learning C++? (I'd rather not!)

Math question

dydecker — Tue, 14 Apr 2009 03:33:09 -0800

Math problem with shipping rates. Can a maths whiz point me in the right direction? Let's say a post office charges two rates, depending on the dimensions of the box you are sending. If your box is smaller than 350mm x 200mm x 30mm, it's calculated at rate X, if it's bigger, it's rate Y.

Now let's say we know the exact dimensions of all the individual products that will go in a box, and we just want to know if the total volume of the order is bigger than the cutoff or not. How can I work this out?

Answers in English, computer language, or just a general pointer would be appreciated. Also: is this an insanely difficult math problem? (it is for me, but I'm kind of a maths neophyte). Cheers

Learn Math Via Programming?

fightoplankton — Mon, 13 Apr 2009 16:59:39 -0800

I have always been horrible at math, but somehow a great programmer. I have found that writing a computer program that demonstrates a certain mathematical concept enables me to better understand the concept. I'm a psych major and I brought this up once in the research lab I've been working in. My prof said he recalls that someone did research and/or created a system in which a student writes a computer program that is pertinent to a certain mathematical concept and upon completion is given the regular math problem (as it would appear in a math class). This enables the student to better understand the math problem, solve, and learn math. Has anyone heard of this or anything similar? A learning system such as this would be a blessing to my education. Thanks.

Euler's map of the 7 Bridges of Königsberg

tnygard — Tue, 07 Apr 2009 16:31:51 -0800

Do you know good sources for historical mathematics images, specifically the Bridges of Königsberg by Leonhard Euler? Hi all, Euler's map of the 7 Bridges of Königsberg, which were all to be crossed once without crossing any twice is considered to be the first directed graph in the history of mathematics. I am trying to find a high quality reproduction of it, preferably on the internet. Does anyone know where to find such a thing? I would especially like to find one that is close to the original, rather than a later redrawing. This is for some writing that I am doing on the history of mathematics. I did some searches on google books, but did not find a wonderful PDF. Unfortunately I am not a mathematician, so I am probably unaware of the best math websites. Thanks in advance for your thoughts.