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How can I explain math to someone who doesn't know math?

  1. Aug 9, 2009 #1

    So I am an undergraduate math major who goes to a state university, and often time I get into conversations like the following:

    My friend: "What are you taking this summer?"
    Me: "I'll be taking (abstract) linear algebra."

    Case 1:
    My friend: "Hmm... 'linear' and 'algebra'? That doesn't sound really hard! How is that different from college algebra?"
    Me: "Well..."

    Case 2:
    My friend: "Well... what's that?"
    Me: "Um... you know... it has to do with vector spaces and... stuff like 10-dimensional space and..."
    My friend: "Wait, 10-dimensional what?"

    (Of course, there's the third case where s/he looks at you strangely and ask why I want to do that, but I omit that case here since it's not important in this discussion.)

    The thing with this is that I am having a hard time explaining the things I do in my math classes to someone who only knows math like college algebra or calculus (at best). This is sad because I want to describe what I'm actually doing so that they don't think math is a mysterious subject that only some people can appreciate it (well, this might be true, but still...). And I also think it is a good skill for me to explain what I'm actually studying to someone who is not a math major. I had a friend who was a physics major who was really talented at this--he could explain physics to someone who only knows a little bit about classical mechanics. I want to be able to do the same with math as well.

    So, if you have any suggestion/comment, please let me know. Thanks.
  2. jcsd
  3. Aug 9, 2009 #2


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    Well you gotta move out of the terminology that you learn in the class. Think about what you're doing and try to simplify them to terms younger or less mathematically based people would understand. Eigensystems? That's just solving special systems of equations (and if you're talking to someone who has a calculus background, toss in "differential" equations instead). Matrix methods? Heck we knew them back in the normal algebra, we just take it up another level and learn more advanced methods including having complex matrices and all that goodness. Vector spaces? Easy! A "vector" that "we all know" is a 3-dimensional vector. Vector spaces are simply the precise mathematical definitions of these vectors and that the 3-dimensional vector could be 4,5, or 500 dimensions. It's fairly easy to think up nice examples of vector spaces that someone can understand (my personal favorite is the cartesian system for explaining). You obviously don't need to get too technical and don't have to be perfect in your explanation but taking a step back and just looking at what you learned isn't too hard.

    I think the biggest mistake is explaining it like you'd explain it to someone who's interested in taking the class. Personally, if someone asks what in the world electrodynamics is, I explain what the application is. I'd say "we learn techniques that let us calculate the electric field in or around a wire or atom or something that can be modeled close to it".
  4. Aug 9, 2009 #3
    ug...nothing is worse than when i'm reading an algebra book and they say "oh yeah I took algebra in high school." even people that know i've taken a lot of math will say it. do they think i've been studying math at school for years and am still at the same place they were in high school?

    i usually just tell them exactly what it is until they never want to ask me another question about math again. "Linear algebra is the study of vector spaces. You know, a vector space, an abelian group with scalar multiplication defined. Well, it all starts with these things called sets..."

    Five minutes of that will usually suffice.
  5. Aug 9, 2009 #4
    I find it much more effective to discuss the applications of a particular subject/discipline rather than the content. Yeah, Linear Algebra is about vector spaces, linear transformations, eigenvectors, linear independence, spanning bases, and invertibility, but when you explian that Linear Algebra is the math behind computer generated imagery (a la Jurassic Park, Lord of the Rings, any Sci-Fi flick in the last 10 years...) listeners tend to be more receptive.

    I do not have recommendations for each discipline (Set Theory being a difficult one I suspect) but putting some thought into what does one do with the math I think gives it more accessibility to the public.

    Part of the social stigma attached to Mathematics (especially in the USA) is that math majors are mostly wierd and the classes are arcane. Trying to promote the utility of the subject goes a long way to dispelling the ubiquitous "Oh... I kind of mostly sucked at Math" type responses people give when you explain what you do.

    There is a book (about which you may already be aware) by James Stein called "How Math Explains the World." I have not read it personally, but I have been told that it does a good job of showing how Mathematics impacts day-to-day life.

    If people are genuinely asking about content, I'd stress the transformation/relation/rate-of-change/predictability/solution angle of whatever it is you are discussing. Simple concepts and examples go a long way.

    Trying to dodge the question or disuading discussion of Mathematics only makes it harder for future students to be engaged. Most students (especially at the remedial level) have an "I dare you to make me learn Math" attitude. - mostly engendered by the warped perception of the discipline by a predominantly ignorant public (that is ignorant of mathematics, not ignorant in general, although that wouldn't help either).

    I hope this is helpful.

  6. Aug 10, 2009 #5


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    I believe that if you're ignorant of the beauty of mathematics by the late highschool level and beyond, then you will never truly appreciate the discipline no matter how it is described to you.

    If they develop this attitude very early on, at least they would have learnt how to count and not get ripped off by every second clerk they encounter.
    But honestly, only a select few ever continue to study mathematics to a very high level, and most likely these people didn't need their parents, teachers or friends to tell them they must do it. It is their choice.
  7. Aug 10, 2009 #6


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    I guess I'm the exception that disproves the rule :biggrin:
  8. Aug 10, 2009 #7
    Thanks for sharing your ideas. Personally I want to try out reading the books about mathematics that are written for non-math people (like the one Elucidus suggested). I just personally think being able to explain difficult stuff (like math) to someone who knows nothing about this subject would be fun and perhaps useful, since it would take quite a bit of communication skills.

    By the way, the easiest subject that I can actually explain to people seems to be number theory, since it's all about numbers and everybody knows numbers:smile: I had a few friends who actually thought it interesting when you add each digit of an integer and if the sum is divisible by 3, then the integer itself is divisible by 3 (divisibility rule). I wonder if there are other subjects in math that are easy to explain.

    I was fine with math when I was in high school, but I never really thought about majoring in it; I was just taking it because I was interested in learning chemistry, and I needed math to study chemistry--math was merely a tool for me. That kind of changed when I took the third quarter of calculus (sequence and series) and linear algebra in college. I think there's something about high school math (or K-12 math) that just make people think math is a dull and arcane subject.
  9. Aug 10, 2009 #8
    Some books written for the layreader that I've run across off the top of my head are:

    Strength in Numbers by Sherman K. Stein (Wiley 1999)

    The Numbers Game by Michael Blastland and Andrew Dilnot (Gotham 2008)

    Innumeracy John Allen Paulos (Hill and Wang 1988 and 2001)

    Math Doesn't Suck by Danicka McKellar (Plume 2008)

    I've read the first three and think they're very well written and excellent reads. I have not read the fourth and only mention it because it is written by a woman mathemtician (and actress) for high-school girls. I have no feedback about the quality of its content though.

  10. Aug 10, 2009 #9
    Just pick out the most colorful, geometric examples of each subject. Get the basic ideas down in terms they'll understand.

    Abstract algebra. "Algebra" is just the word for math in symbols. Abstract algebra is like high school algebra, except you're not necessarily working with real numbers (they might be matrices or functions or something even more interesting). In abstract algebra, you start off with a few basic rules, such as how addition and multiplication works over these objects, and see what you can prove without any other assumptions about them.

    Linear algebra. The study of linear functions. Linear functions play nicely with addition and scaling (multiplication), governed by two simple rules: f(x + y) = f(x) + f(y) and f(ax) = a f(x). The big important space we're working with is called R^n where R^1 is the real line, R^2 is two-dimentional space, R^3 is three-dimentional space, and R^4 and above is hard to visualize, but described easily in the math. Important topics include classifying linear operators and finding their matrix representations.

    You're never going to be able to fully get your point across unless the person you're talking to has some background. Even with a student who has all the necessary prereqs, it's not always clear to them what's going on until they understand the introductory material. Math is just too cool for comprehension.
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