Ask MetaFilter questions tagged with math

150 to around 120, which bpm is best for pitch?

semaphore — Thu, 23 May 2013 08:23:47 -0800

I have a song at 150 bpm, perfectly in tune. I want to repitch it down to around 120 by slowing it down. At which bpms will the notes be at pitch?

How do I go from one kind of nerd to another?

vernondalhart — Tue, 21 May 2013 17:08:39 -0800

What steps should I take to switch to the aerospace industry from the academic world? I am currently a post-doc in pure mathematics (in Canada), with a background in mathematical physics; that said, even the physics I did was theoretical, so I don't really know any practical skills from that.

I've been thinking more and more that I might like to do a drastic shift in careers and move into the aerospace industry, but I honestly don't have the foggiest clue how to do that.

My naive guess would be that I need to go back to school into either an engineering program or into a heavy-on-applications-to-space physics/computer science program, but I don't know if this is the best way or not. If it is, how does ? It seems that going back for an undergraduate degree wouldn't make sense (it'd be a little funny to have to take an engineering calculus class, for instance, since I've taught those...), but having glanced around a little bit I'm not sure what graduate programs to look into either. I'm also worried that regarding graduate programs, that I don't have sufficient background in practical applications.

I guess my main questions are the following:

If I need to go back to school, where should I go? What universities within North America (or even Europe, I guess) have good programs that would move job in the space industry?

What other advice can you suggest for someto make this leap?

How to pronounce an equation in English.

misozaki — Tue, 30 Apr 2013 20:22:40 -0800

Please help me pronounce this formula related to projectile motion as it would be spoken out loud: L = v0^2 sin2θ / g Please don't laugh at me for wasting a question on this.

How can I relearn high school subjects?

Grandysaur — Thu, 25 Apr 2013 13:49:56 -0800

I want to relearn algebra, chemistry, basic mechanics, and basic physics this summer. For free? I was an excellent student in high school but haven't taken a math or science class in about five years (yay liberal arts!)

I know I have the capacity to know this stuff, and to relearn it, but show me the quadratic equation and all I can muster is "yup, that's a thing."

So how can I brush up on what should be basic knowledge this summer? I'm looking for high school, advanced high school or "101" type of information. How should I go about redoing high school, preferably for free?

I'd also love any general tips for successful self-guided study.

Any and all suggestions welcome, for any and all of the subjects I'm looking to learn.

Tweak my study habits.

squirtle — Wed, 10 Apr 2013 08:47:32 -0800

I'm taking Calc II at a community college and I'm not getting the grades I want. Studying 10 hours everyday a week in advance only got me an 84% on the first test. It is clear that I'm doing something wrong, but what is it? Help me tweak my study habits before the second test! When I took Algebra, Trig, and Pre-Calculus, there was a positive correlation between the amount of time I studied and the grades I received. Studying all day, everyday, in advance was the trick for me. However, I'm dismayed at why this isn't working anymore. Perhaps the subject got harder and I need even more time to study? Or maybe I need to be wiser about how I study instead of blindly throwing more time into studying?

To get a more spot-on answer, let me tell you how I go about it. My professor assigns a ton of homework from the textbook. It takes me a day to finish one section of homework and each consists of a few easy problems, some intermediately hard problems, and some incredibly difficult special case problems that he doesn't even lecture on and probably won't test. I painstakingly do every problem and utilize the campus' free tutoring. I figure if I could do the hard stuff, I can do anything. Right?

So I do my homework for the majority of the week. Then a few days before the test I redo them to make sure I got this stuff down step-by-step via memory. I work on the study guide right before the test. And then I take the test. To my delight, my professor's testing style is surprisingly simple. He only tests the bare basics. No bells and whistles. The homework was way harder so I thought I was going to ace this until I started taking it.

I lacked some basic understanding, but how? I legibly did the damn homework twice and reviewed the material! When I got my test back, I loss 4% to careless mistakes despite triple-checking. The fact that I put incredible effort and time into this makes me feel even more stupid. Maybe all that homework hinders me instead of help and I should bullshit them to make time for studying basic concepts. Maybe all that tutoring and homework gave me a false sense of security so I overlook things. I'm in distress and I don't know how to proceed. I need permission to change the study habit that worked so well in the past. Any thoughts?

Algebra: exotic identity values?

knz — Mon, 08 Apr 2013 01:48:30 -0800

[mathfilter] please give me some example algebraic structures that are not commutative, with exotic identity values. I am creating an inventory of example algebraic structures of one operator that feature associativity, commutativity, identity values and all combinations thereof. My table is nearly full but for three entries:

- non-associative, non-commutative with different left and right identities

- non-associative, non-commutative with both left and right identities, where both identities are equal

- associative, non-commutative, with either a left or right identity but not both

(For clarity: a left identity is a value 0l such that 0l . x = x for all x, and a right identity is a value 0r such that x . 0r = x for all x. They may not be both present / the same if the structure is not commutative.)

Do you know of example functions in these three categories?

Masters in maths? Difficulty level: Have bachelors in graphic design

Cat Set Go — Sun, 31 Mar 2013 11:08:49 -0800

Dear Mefites, a long time ago I got a degree in graphic design but never worked in the industry. Along the way I somehow (don't remember how or why or when) became interested in math and I finished a graduate diploma in maths as a distance learning course in my free time. I am considering applying for masters programmes in maths or related subjects but ... can I? Should I? To give a little more background, I'm interested in what I perceive as stuff related to applied maths: meteorology, language processing, cryptography, etcetera. But I'm also wondering how I can relate these sorts of interests to jobs or careers ...

I've seen center for women in mathematics and LEAP but I'm not a US citizen and I can't afford to attend those. Also, I have no access to education I'm interested in where I live, hence I'm considering becoming an international student in the EU. I have some savings but by no means can I afford to get a second bachelors degree ...

I've also tried looking for work in related fields so I could get a feel for them but right now I'm just stuck at an awful data entryish job that I hate so much.

And also sometimes I feel like I'm so stupid that I just shouldn't be attempting this at all ... argh!

I'd appreciate any advice! Thank you!

Wearable expressions

firstbest — Thu, 28 Mar 2013 18:22:41 -0800

What is the math (physics?) going on in this very cool-looking, equations-as-art necklace?

I can say with 99% confidence that this class is killing me

ActionPopulated — Thu, 28 Mar 2013 11:53:40 -0800

I'm struggling hard in my statistics class right now. Some of it comes from not grasping the concepts, but a bigger part is the ridiculous level of anxiety I've developed about my grades, and catastrophizing about what a low grade means. Help me attack both aspects of the problem. I'm taking stats at my local community college right now, as a pre-requisite for eventual nursing and public health degrees. I have a previous BA and took a stats class as part of that, and just managed to scrape by with a C.

I decided to retake the class this time to improve my grade and get a better handle on the concepts, but I'm still floundering and pulling Cs. A large part of this, I think, is my anxiety and complete lack of math study skills. I was one of those students who skated through most classes with a bare minimum of work just by having good writing skills; in stats I've hit the wall of "thing I am not naturally good at and can't write my way out of, but need to be successful at anyway." (I identify with this comment about building your identity around intelligence a whole hell of a lot.) Plus, I was a qualitative social science major the last time I did school; the skills you need to study for essay tests and research papers are completely different from problem sets.

But the thing is, I badly need my grade to be good, and I badly want to understand the material. As a person who wants to do public health work, I know full well how important stats are going to be in my future, both for school admissions and for work. Although this class doesn't present it well, the actual process of study design is fascinating to me. When I get a low grade on a test or don't understand a problem in class, though, I immediately start catastrophizing to "shit, I will never get into nursing school, I will never get into public health school, what am I going to do with my life now?" At least one of the local programs I'm looking at requires a B in stats for admission, and that's not even the most competitive one.

The more I catastrophize, the more I shut down and can't concentrate on studying, the less I study, the less I understand, and the more likely I am to blank out and forget entire concepts on tests. Repeat vicious cycle. It's specifically about this class and about my understanding of statistics/math more broadly, not generalized test anxiety--I'm acing biology right now, but in stats, even on lecture days, I'm always on the verge of an anxiety attack.

I got a low C on my first test in the class, and a higher C (just a few points under a B) on the second one. My average is about five points under a B. I have two more tests and a final to bring my grade around. How can I make sure I study the concepts well and work on the anxiety issues?

Things I am already doing:
-Supplementing class lectures with Khan Academy/other youtube videos.
-Studying sometimes with a classmate who understands the material better than I do.
-Mining another textbook for practice problems. (Our official class textbook is shit.)
-Telling myself things like "A C really means average, it doesn't mean you're stupid, it doesn't reflect poorly on you as a person"
-Going to therapy

Things that won't work:
-The school doesn't offer any additional tutoring resources specifically for stats; several of my classmates have already asked about this, and apparently the tutors just aren't there.
-I don't have the money for a private tutor

Hope me please! Thanks everyone!

I can't do basic math, but my competence is in other things...Help?

OmieWise — Thu, 14 Mar 2013 07:54:12 -0800

We want to assess a list of vendors in two domains: Accessibility and Cost. We have two tools that we are using to essentially score them in each of these domains separately. The Accessibility assessment tool totals 110 points; the Cost tool totals 90 points. We want a final score for each vendor that combines the domains and is out of 100. We want the Accessibility score to "count" about 20% more than the Cost score in the final because it is more important to us. How do we do this? Were both domain scores out of 100 this would be easy: we would simply multiply Accessibility by 0.55 & Cost by 0.45.

Some folks are proposing that because there are already about 20% more points in the Accessibility section, we simply add both together and average. (The two sections add to 200 points.) I know from brute arithmetic that this does not work exactly in the middle of the range (although it does at each end), but I'm having trouble articulating why not. There are more points to gain or lose in the Accessibility section, but does that translate to a greater weight being placed on Accessibility?

I would like to find a solution that "weights" Acc. 20% more than Cost.
I would like to understand why the proposed average does or does not do that.
I would like the solution to be as transparent as possible so that vendors can understand the results even if they are as challenged as I am. (Assume they will be, this is not about cost or access and the vendors are not business people.)

Can you help?

Basic math test as part of a job application?

klausman — Sat, 09 Mar 2013 15:13:29 -0800

Which employers still use a basic math test as part of the application process? I'm thinking of when I worked at Subway 20 years ago, and they asked three basic arithmetic problems on the application. Do businesses still ask applicants this kind of thing?

If so, which basic math skills are being assessed? Do you have any current examples?

Just so I'm clear, I am not thinking of examples like my friend who had to work some linear algebra and number theory problems for a job at Boeing. Just arithmetic skills: Adding fractions, percent literacy, decimals, proportions, area, etc.

Math/Physics Question: Stability of an abruptly stopped object

Popular Ethics — Tue, 05 Mar 2013 21:16:31 -0800

If you have an object with a given base length and a given CG height, how fast can it travel before you have to worry about it running over an obstacle and falling over? This is for a work problem. I have a cart of given length and CG height. I'm trying to specify a "safe speed" which will guarantee that, if the cart were to run over an obstacle, it would not topple.

My first pass at this problem went as follows: The potential energy required to rotate the CG over the front wheels is:
delta_height = sqrt(cg_height^2 + (base_length/2)^2) - cg_height)
that is, the radius from the front wheels to the CG, minus the original Cg height
Ep = delta_height * mass * g

The kinetic energy at a given speed is:
Ek = 1/2 * mass * speed^2

Assuming all of the kinetic energy is transferred into potential energy when the front wheels hit an obstacle I equate the two E values and solve for speed:

speed_max = sqrt( 2 * delta_height * g)

This gives me a very pretty low value for speed_max (slower than a slow walk, for a base_length/cg_height ratio of about 1.5) which seems unreasonable. Have I made a mistake? Are my assumptions too stringent?

How to study math

Hey Judas! — Tue, 05 Mar 2013 19:44:51 -0800

What is the best way to manage time while studying for upper-division undergraduate math classes that are proof-based/STEM classes in general? I entered college as a social science major and I ended up a pure mathematics major with a minor in computer science. I'm taking my first proof-based upper-division courses this semester and I'm having trouble staying afloat.

I have the bad habit of cramming. I will often neglect other classes and just study for one class for every free hour of the days leading up to an exam, then repeat the process all over again next week for another class. This has worked so far, but I just recently realized what a waste it is. I have absolutely no free time to do anything other than cram and do homework.

I spent all weekend studying for my real analysis class and I really started to understand, and even enjoy, the material. Going through my notes, I can't believe how amazing some of the stuff we've learned so far is. I also can't believe it took me so long to realize that my cramming is seriously detrimental, not only to my grades and knowledge, but to my enjoyment of the material. Now that the classes are challenging and interesting, I really want to learn instead of just do well on tests. It is such a waste of time and money to cram for exams rather than actually learn.

My only hangup is I have absolutely no idea how to transition from cramming/memorizing for tests to studying the correct way. My mindset has always been study for Monday classes on Sunday, Tuesday classes on Monday, etc.. I want to spend a set amount of time each day studying for each class. I also want to set aside time for hobbies, reading or studying other material. My spring break starts next Friday and I plan on catching up completely so I can finish the semester using this studying method.

I do not necessarily need advice on HOW to study for these types of classes (cross referencing proofs with other textbooks, doing extra problems and asking for clarification from profs/TAs works for me). I just need advice on how to implement the "study a little every day" method I always see suggested. Has anyone actually used this studying method and has it actually worked? Does anyone have any tips on how to manage my time to fit an hour for each class every day?

I would also specifically like to hear from math/STEM majors about your study schedule and study methods (be as specific as you want). I would appreciate hearing how someone in the same types of classes goes about studying. Thanks for any advice!

Can a transcendental number raised to an algebraic power be algebraic?

ch3cooh — Sat, 02 Mar 2013 06:33:30 -0800

Can a transcendental number such as pi, be raised to an irrational, but algebraic power resulting in an algebraic solution? Complex solutions would be acceptable. There might be a quick proof here, or there might not be. - Thanks for any help you can offer answering this! (And I promise that this isn't for a class or anything like that!)

Books about mathematics for the interested layman?

dfriedman — Mon, 25 Feb 2013 11:30:29 -0800

So, physicists like Brian Greene, Lisa Randall, Kip Thorne, and others have written books aimed at an interested lay audience. What are similar books written by mathematicians? I'm aware of Godel, Escher & Bach. And that's about it.

Explain the Riemann-Christoffel curvature tensor

jesman — Thu, 14 Feb 2013 09:04:08 -0800

Greetings Ask Metafilter: Can anyone suggest a book or article that provides a simple, yet comprehensive explanation of the Riemann-Christoffel curvature tensor? I've studied the explanation provided by Lillian Lieber in her book The Einstein Theory of Relativity, but for several reasons I am suspicious of the validity of her derivation, and her claim that the tensor can be used to distinguish between Euclidean and non-Euclidean space. Lieber gives the Rieman-Christoffel curvature as follows: {σρ,ε} {ετ,α}- ∂/(∂x_ρ ) {στ,α}+∂/(∂x_τ ) {σρ,α}-{στ,ε} {ερ,α} Lieber derives the curvature tensor from a covariant tensor of rank one that has undergone two different sequences of covariant differentiation. This supposedly produces two different versions of the second, partial, covariant derivative of a covariant tensor of rank one. The curvature tensor is produced when the first version of the covariant derivative is subtracted from the second version of the covariant derivative.

The first version of the covariant derivative is produced when a covariant tensor of rank one is covariantly differentiated with respect to x_τ and then that quantity is covariantly differentiated with respect to x_ρ.

The second version of the covariant derivative is produced when the same covariant tensor of rank one is covariantly differentiated with respect to x_ρ, and then that quantity is covariantly differentiated with respect to x_τ.

Interestingly, x_τ and x_ρ seem to be equivalent terms so the first version of the tensor seems to be equivalent to the second version of the tensor. This indicates that when the first version of the covariant derivative is subtracted from the second version of the covariant derivative the difference will be zero.

This undercuts the claim that the curvature tensor can be used to distinguish between Euclidean and non-Euclidean space, since the claim is that in Euclidean space the curvature tensor will be equal to zero and in non-Euclidean space the curvature tensor will not be equal to zero.

Fiction help: Name something a math genius could do to improve a bar.

Cool Papa Bell — Sat, 09 Feb 2013 15:32:31 -0800

Writing a script, need a few believable, throwaway lines for a character. A guy running a TGI.Friday's-like bar praises his bartender, a math genius, for giving him an idea that saves money and improves the business overall. An example of outside-of-the-box thinking that enforces that our math-genius-in-disguise really is a genius. Bonus points if the idea skirts the line of legality -- something funky with accounting, maybe? I'll give you an example. In the movie Phenomenon, John Travolta's character gives a bar owner a sketch showing a way he can restripe the building's parking lot to add extra spaces and make the lot safer at the same time.

How do I learn to be an effective tutor?

cognitio — Sun, 03 Feb 2013 18:01:18 -0800

If I know the material that I'm teaching well, but don't have any experience with tutoring or teaching, how do I learn the skills and techniques that will help me be an effective tutor? I've just graduated college with a degree in physics and I'm about to start tutoring a friend in a first year intro mechanics course. I'm also hoping to pick up some more tutoring positions in the near future to help me get through this weird post-graduation time.

I'm pretty confident in my understanding of the material that I'll be teaching, aside from needing to review the specific techniques that are being covered, but I'm nervous that I don't have the proper communication and pedagogical skills to really help someone else learn the material.

In my past experience helping people out with their coursework, I get stuck when I have explained the way that I understand the problem from the fundamentals, but it hasn't "clicked" with them yet. I can recognize when someone else has a different learning style than me, but I have a hard time translating my style of understanding into theirs.

For people who have experience tutoring: where do you learn these skills? Are there any references you could point me to or tips/techniques you can share?

For people who have had helpful or unhelpful tutors in the past: What makes a great tutor for you? What should I learn to avoid?

Clearly, this proves that I'm stupid

lucia_engel — Thu, 31 Jan 2013 20:35:00 -0800

I can't seem to wrap my mind around the language of higher level math. Definitions, theorems, and proofs make me fall asleep, but I really do want to understand. Do you know of any good resources that can help me out? Back in high school (Canadian) I was a math whiz. I had no trouble with any of the concepts, including calculus in Gr 12. I can "do the math" and am good at problem solving. However when I got to university and started taking Number Theories, Abstract Algebra, etc., my logic suddenly disappeared on seemingly simple concepts. I've obtained my degree in CS already, somehow memorizing or handwaving my way through on my assignments and exams, but now I actually need to understand higher math for my current job.

For example, these are excerpts from one of my textbooks (A Concrete Introduction to Higher Algebra by Lindsay Childs):

[on real numbers] "The real numbers form a complete Archimedean ordered field...Archimedean means that for every positive real number r there is a natural number n with n > r."
[division theorem] "Given nonnegative integers a > 0 and b, there exist integers q> 0 and r with 0 <= r < a such that b = aq +r

I thought I understood real numbers and division until I read these definitions and was also asked to prove them. First of all, my brain have difficulty just parsing out what's written; it's like a foreign language to me. Secondly I never know how to begin when proving things. I can somewhat follow along if there's an example in the textbook, but on my own I would be completely lost.

I'm not looking to take any classes in math or hire a tutor. Books or online resources would be good. At minimum I'm hoping to at least be able to read through a math textbook and actually understand the explanation.

The Seven Bridges of Königsberg in 200 Words or Less

kristi — Tue, 29 Jan 2013 11:26:25 -0800

Can you recommend short, easy-to-understand math writing I can read before bed? I would love to find short, clear, engaging explanations of mathematical concepts that I can read before bed.

1-4 pages would be great. I would especially love books filled with these, but individual articles would be great too.

Ideally, each piece would
- explain the idea clearly and simply enough for a teenager to understand
- describe how the mathematician developed it
- talk about how it's involved in everyday life

Some of the segments of A Brief History of Mathematics come close to this. (However, I'm looking for the printed word, here, not podcasts or videos.)

Puzzlers could be okay, but I'm really looking for descriptions and explanations, not mathematical puzzles that will keep me up all night.

I am completely open to reading children's books.

Thanks!

Fallacies and Errors in Inferential Statistics

Scientist — Sat, 26 Jan 2013 00:17:38 -0800

I have recently been introduced to the concept of pseudoreplication as a mistake that people often make when using inferential statistics to evaluate treatment outcomes. My field (evolutionary and conservation biology) makes heavy use of inferential statistics, including techniques that are vulnerable to pseudoreplication, yet nowhere in my formal education have I been taught about how poor experimental design and lack of statistical rigor can lead to fallacies like this. My personal statistical proficiency is poor, but I am working to remedy that. To that end, could folks help me by identifying and ideally explaining whatever other potential pitfalls you can think of, and explaining how they can be avoided through careful experimental design and data-analysis?

What does a mathematician do all day?

Lownotes — Thu, 24 Jan 2013 18:52:56 -0800

I'm wondering, after breakfast, and a shower, and a commute, and coffee - what is next? I'm working on an article that will detail the work of a famous mathematician, and it occurred to me that I have no idea what mathematicians do all day. I'd like to add that to the article.

What is the typical day like for a mathematician? I'm not talking about a job description, but the humdrum, daily grind sort of stuff you won't learn about from a typical Google search.

I'm sure there are many variations on the typical work week, and I would like some insight into that. Please, no assumptions and speculation, I'd rather hear real, first-person accounts or get pointed in the right direction.

Thanks!

How do I figure out how to divvy out these projects?

pwb503 — Tue, 22 Jan 2013 16:16:06 -0800

I have roughly 20 people who each need a project. I have 27 projects and don't want anyone to share a project. I let the people pick their top five projects and rank them so I know who wants what. What is the best (easiest...) way for me to fairly figure out who should get what project so that the most people get their top choice, or at least one of their top choices? This isn't some homework problem, I promise. I am teaching a class and have 20 poster topics I want my students to do and I gave them 27 options, and now I don't know what to do with all these "vote" sheets they handed back to me...

The heck is a modular form?

Zerowensboring — Fri, 18 Jan 2013 10:47:01 -0800

For a work assignment, I need to come by a conceptual understanding of modular forms that's light on jargon and, ahem, actual math. If such a thing is possible.

Teach myself Math virtually for the first time.

Krazor — Tue, 15 Jan 2013 10:05:32 -0800

I'm a 21 year old college senior liberal arts major who has managed to slide by in school (and life) without ever really learning math beyond a middle school/very early high school level. For no reason in particular, I've decided that I want to get serious about bettering myself in the math department. How can I teach myself the academic math skills I missed out on? Throughout my academic career, math has always been a serious hang up for me. Even at the times when I at least vaguely grasped the concepts, it was my worst subject. I was a straight A student through high school, with the exception of math, in which I maintained a C average with some difficulty.

For reasons that don't bear explanation, I have managed to pass (barely) mathematics and physics classes with virtually no comprehension beyond a middle school level. My most recent math class, for example, was my Freshman "Intro to Math" course for liberal arts majors. It is far and away the most simple math course my university offers. I passed with a D-, and thought it an absolute miracle.

When I think about all of the years I wasted doing so poorly, knowing I never made even the slightest effort to improve, it makes me sick at heart. I want to learn mathematics. How can I? Internet and book-learning are options. Tutoring is not. Assume that I will be learning about these concepts more or less for the first time.

Here's what I do know:

These are all clear as day, and I can solve any number problem put before me:

Addition
Subtraction
Multiplication
Division
Very basic algebra

Here's what I don't know, but want to:
Algebra
Pre/Calculus
Physics
Percentages
Fractions- Fractions were where the shit really started to hit the fan in my education. Maybe sixth grade?
Probability- Draw a card/pick balls and replace/don't replace
Combinations- If you have X number of condiments, Y kind of meats, and Z types of fries, how many different meals can you have. That sort of thing
sin/cos/tan/logs
Geometry
Proofs
Functions
Trigonometry
Compound interest
General Economics math
Order of Operations
Permutations

I don't want to just punch things into a calculator. I want to understand how they work. I basically need a ground up math education. With time and patience can I teach myself? If so, please help me with the how! Thank you for your attention. I appreciate your responses in advance!