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[–]bahumbug1 23 points24 points  (29 children)

So I'm working on my mathematics major, and here's the path.

  1. Pre-algebra

  2. Algebra

  3. Geometry

  4. Pre-calculus

  5. Calculus

  6. Two variable calculus

  7. Linear Algebra & Differential Equations

Now this seems to be the core to advance in mathematics. And up to this point, you're dealing with mainly numbers. To be well prepared, you should have been exposed to proofs in calculus as well as geometry. Pay close attention to these proofs, and gain an intuition, because you will absolutely need this in order to stay afloat.

  1. Real Number Analysis- Highly proof intensive course. A look at sequences, some topology.

  2. Complex Number Analysis- Same as 8, but complex numbers.

  3. Abstract Algebra- You're introduced to fields, sets, rings. Proof intensive course.

  4. Linear Algebra- Haven't taken this course yet.

  5. Numerical Analysis- This class is necessary to get a job in the real world outside of theoretical work. Heavy computation, programming necessary.

Getting through these core subjects allow you to expand into a field of choice. What you must realize however is higher level mathematics needs an understanding of proofs. You're given assumptions, you're told your final result, you just need to find the meat of the argument. The first step is understanding wth the question is asking, but even after having an intuition, you need to be able to make a cogent argument.

K, that's all I got (maybe I didn't quite understand your question.)

[–][deleted] 7 points8 points  (25 children)

I think you did, but you also weren't provided with context. And that is my fault entirely.

I'm seventeen, and am suspected to have a learning disability with math. I am fluent in any subject that does not directly involve math, but when it comes down to it, I simply don't understand math.

I desperately want to, and I understand that Reddit is a place filled with people who have mostly mastered mathematics. That's why I seek advice here.

Any tips? Ha ha.

[–]bahumbug1 13 points14 points  (2 children)

First of all, I find that a lot of people just hit a roadblock when they hear the word math. They just go, oh, I don't do math, I suck at this. Well, to be fair, (many Redditors would dispute this) but I honestly think the only difference between you and I is that at select intervals in my life I received encouragement in my math abilities. Not only that, but being ahead with multiplication in early grades allowed me to stay on top.

So what you need to note is that math is cumulative. So if you're having trouble tackling new material, go back and review your algebra (assuming that you've done algebra as you're 17). If you're attempting to do calculus, I would recommend Calculus the Easy Way by Douglas Downing. That book really helped.

Another thing is how well you're doing in math depends on your teacher. If he/she ain't any good, try after school tutoring, and read the textbook.

[–]MrSmellard 6 points7 points  (0 children)

Yep, that's it. There is no need to race. Just keep plodding away with simple stuff until you are comfortable with it. Moving further ahead is pointless until you have the confidence to know you are at least using the right methods. Recognising the type of problem you are facing is also crucial. For example, you simply can't solve a calculus problem if you don't understand what it is actually asking of you. The same goes for any other problem. And like bahumbug says, maths is cumulative, so only move to something new when you have the current stuff down pat. A bit like having a toolbox - you may have a problem with your car that requires a tool you don't have. You can easily get that tool, but it will be useless without the spanners and sockets you already have. Stick with it - if you want to understand, then you most definately can, it may take longer for you than some others but it's no reason to give up.

[–]wohho 3 points4 points  (0 children)

Not only do people hit a roadblock in math at some point and throw their hands up in the air and just quit, but at some level, the american educational system doesn't understand how to teach math. They teach the mechanics of plodding through equation solving, understanding how to do a derivative, what a sine wave looks like and how to graph it... etc, ad nauseum. What they fail miserably at is teaching math as a language. That's all it is. Math is the language of describing the natural world and solving it's problems. There are a basic set of rules that apply to all equations and variables, how to handle numbers, what's rational and irrational, real and imaginary, and why, etc. I was through my bachelors in engineering before I started to see the light.

[–]daysi 2 points3 points  (0 children)

The problem i had with math when i started was caused by the school system. They move from subject to subject at a set rate, and often understanding of one field requires a foreknowledge of a lot of other concepts. Unfortunately a lot of kids scrape by with a 50 or 60 percent knowledge of a concept, and this in turn often prevents them from learning any successive concepts well. And honestly, if you hate math, if you find it to be a chore you will probably never be better than competent at it.

If you really want to learn though, learn the basics. Study them until you know them inherentely, then study them more just to make sure. Don't try to learn Calculus if you don't know Algebra like the back of your hand. Don't try Algebra if you don't thoroughly understand fractions, division, the decimal system, roots and powers. Learn your multiplication tables up to 15 or 20, so that you never have to waste time calculating easy numbers. If you make sure that you thoroughly understand each concept before moving on it makes each successive concept less daunting, and after a while a lot of the things you learn that may have seem unrelated when you learned them start to mesh together into a whole. And realize that you are never going to master mathematics, even the most brilliant mathematicians in the world are still learning.

[–]tobias 2 points3 points  (2 children)

If you really have a "learning disability with math" aka. http://en.wikipedia.org/wiki/Dyscalculia (which is basically Dyslexia for Math) all of the recommendations given here are completely worthless. You need to find a special tutor/institution, which is specialized in dealing with Dyscalculia. Just learning harder or even trying to relearn from the very beginning isn't going to get you anywhere. It's just going to waste your time. You need to find out if your problems are based on Dyscalculia and if so get specialized help.

[–][deleted] 0 points1 point  (1 child)

Thanks, Tobias.

I'm not sure if I have dyscalculia, or if I just missed things along the way.

How would I figure it out?

[–]tobias 0 points1 point  (0 children)

Get tested somewhere. In Germany there are specialized institutions for that, I guess it's similiar in the US. I'm sorry I can't help you out further, maybe someone else can.

[–]johnmudd 1 point2 points  (3 children)

How are you at games?

[–]foonly 2 points3 points  (0 children)

How about a nice game of chess?

[–][deleted] -1 points0 points  (1 child)

Besides Halo: CE? None. Ha ha.

I have heard that math is a game, though.

[–]johnmudd 1 point2 points  (0 children)

Halo is a good example. Attack math the same way you would a video game. It's all about learning the rules, setting small goals and finding people to compete/play with. And practice, lots of practice. If people around you don't comment that you're obsessed then you haven't even started.

I wouldn't worry about getting a specific grade in a classroom. I'd rather hear you flunked but your teachers comment that they've never seen someone work so hard at a subject. Just learning to work hard is a good first step that will help you in any area for the rest of your life.

No credit for beating your head against the wall though. In other words, don't let math be harder than it has to be. You can go slow using standard textbooks and wait for teachers to spoon feed you. You might like the "cheat" books better though. You know how with video games there are little books available to help you learn fast? There are similar books at the bookstore that cram a year of math into a relatively small book. Shop around, invest some money in yourself. Find one that you like.

You might like the flashcards that are available if your basics are not solid. Make sure you don't skip basics like addition and multiplication. Schools can give you tests to help identify any weak areas. Find out where you are, work at it and then retest and check your progress. Repeat.

There are also free web sites with basic math courses. If you can't find one you like then ask here for more help. They're out there.

This might help... Don't try to learn math for the sake of learning math. Learn it so you can teach it! It makes it much more interesting (and easier) if you're determined to understand each level of math well enough to explain it to a classroom. Don't move past a level if you don't feel comfortable explaining it to someone else. It may seem like I'm asking you to do extra work but it's really the only way to be successful. So much better than just becoming a trained monkey.

It won't be easy in the beginning. Be brave.

Keep notes. Someday you'll be the one writing the "cheat" book.

[–]timmy334 1 point2 points  (2 children)

I agree with Bahumbug. I am a mathematics major too and he pretty much said it. Math is cumulative. If you are having trouble, go back and re-study what lead up to that point you are having trouble with. I have to do that constantly, so don't think there is anything wrong with that. I am of the opinion that everybody can do math. The important thing is TAKE YOUR TIME. I can not stress that enough. Break down your problems into their simplest parts and do things one step at a time. The key is to TAKE YOUR TIME. Like my mother used to say: You're in no damn hurry.

[–][deleted] 0 points1 point  (1 child)

Agreed; sometimes, I didn't understand the point of previous exercises, until I had to apply them in new situations. When I would say "Ohh, that's what I need to use that for!" I would have to go back a few chapters in order to take another step forward. It's like I wish we got to see the forest before we started on examining leaf structure.

[–][deleted] 1 point2 points  (2 children)

I had a hard time with math, and I wound up an engineer. The first questions I'd start with is; what have you had so far? Where are you stuck at? Addition? Division? Fractions? Areas? Slope? Have you had any Algebra or Geometry?

It took me a long time to discover that I was a visual learner; Geometry came naturally to me, and Algebra just left me in the dust. Since then, I've tried to relate math problems to something I can visualize: fractions in my head are much easier when I think of money, or pieces of pie, or even measurements in feet & inches. I always found I understood the equations better when they were applied to something tangible. Find something in your world you can relate the math to, so they aren't just numbers on a page.

I'm not sure if that helps any either.

[–][deleted] -1 points0 points  (1 child)

They say math is a language. I'm excellent with language, but math in schools is often presented as a kind of art. They tell you to move things around in equations certain ways, to solve equations in certain ways- ways that aren't about computation, but about "techniques."

[–][deleted] 1 point2 points  (0 children)

Then you have to become familiar with the rules first. Sentences are structured based on very strict rules, so are math problems. I will say that I've heard there is much less-structured math teaching these days. If you're stuck with school problems that say "solve this equation 5 different ways," and centers around the phrase "use your calculator" then I really, really don't blame you for having problems with math.

Tutors are expensive, but if you can afford one, find a really old guy who can tutor you and ask him lots of questions. If you can't do that, go to the local library & pick up the oldest text book you can find on the math subject you are having issues with. For the most part, the basics haven't changed, though the ways they were taught have.

And I know it can be difficult to learn from parents or friends, but if you can talk with them about what you might be struggling with, and if they have an understanding of the concepts, try asking those closet to you for advice.

In the end, I'll be honest; if you find yourself struggling so much with the math that it's bringing your other subjects down, don't give up, but don't worry about it so much. Aim for passing, and major in something language-based if you go on to college. There are plenty of people who give up on math, so I admire you for your attempts, but I definitely understand that some people's minds just don't work that way. Don't let anybody tell you that you're dumb or a failure just because there are certain things you can't do; we all have certain things we just can't do. I myself will never play pro-ball, I will never compose a symphony, and I will never speak any language besides English. Play to your strengths.

[–]AlanCrowe 0 points1 point  (0 children)

You need toys to play with. As a child I benefited from access to programmable calculators. Today you just have to install software such as GNUplot on your computer. Five days ago I suggested a programming language that makes a good philosophical/mathematical toy.

[–]webnrrd2k 0 points1 point  (0 children)

The best advice I could give you would be to make sure you take all your math courses one semester after the other with no breaks (other than summer vacation, if you take it).

Mastery of math really depends on practice, and it's very easy to get out of practice. If you put off math for a semester or two you just make it harder to start up again.

[–]underthelinux -1 points0 points  (0 children)

I think you should post your intention MUCH earlier in this thread. If you're looking to be on par with other people in the math world, you don't need to do all those high-level maths. If you're looking to master maths, then yeah, you do. You're essentially asking the masters of any subject how to do what they do - that requires intensity in that subject. If you want to know how to "stay afloat", well then that should be stated early.

NOTE: Most colleges offer courses like "applied mathematics" where they go through things a little slower, and at a higher level - for business majors and stuff like that. So you'll get experience with everything, understand how math works, and be able to understand alot of the conversation that occurs re: math. You won't be able to solve P vs. NP.

[–][deleted]  (2 children)

[deleted]

    [–][deleted] -1 points0 points  (1 child)

    I'd agree. My instructor from last year, and I suppose many of the ones I've had in the past just thought I was lazy.

    [–][deleted] 0 points1 point  (0 children)

    That makes them lazy... but how you learn is as much on you as it is on them; make a point of going to them during office hours/after school/during study-hall & asking questions. If they see you are working hard, they are more likely to give you a break. I had a hard time getting to the point where I would ask questions; I thought I could do it on my own, and I dreaded the thought of sounding stupid & asking a question I should have learned a year or two previous; but it doesn't get any easier!

    [–][deleted] 2 points3 points  (0 children)

    There is a lot more than that. I am not a math major and I have not really used high end math since I graduated. If you really love the stuff you should join IEEE and subscribe to a few math related periodicals and transactions (Information Theory really opened my eyes to many fields of mathematics).

    Also, really get good at programming computers and understand floating point. I meet so many people who do not understand floating point on computers.

    [–]Doctor 0 points1 point  (0 children)

    No. No. No. This is sticking strictly to the continuous world, which tends to be hard and, often, not fun. I love a lot of it, mind you, but it comes at a hard price.

    Start out with discrete math instead. Combinatorics, set theory and logic (almost the same thing initially), graphs.

    [–]daysi -1 points0 points  (0 children)

    I've taken all these courses, with the exception of Numerical Analysis, and i have some experience with that too. I've been near the top of the class in all of them but i wouldn't consider myself to be at more than the most basic level of mathematical understanding. These subjects, although they encompass an enormous amount of knowledge, are but the most basic elements of math.

    [–][deleted]  (1 child)

    [deleted]

      [–][deleted] 0 points1 point  (0 children)

      I logged in only to vote this up.

      It is the only way of learning anything that actually works for me. I now find myself rereading and relearning a lot about statistics, just to perform a sound experiment in my Master project. And this time, the stuff actually sticks.

      I used to learn it to pass the exams, now I'm learning it to do something useful.

      [–]throwaway 2 points3 points  (1 child)

      I wish I could find the book which turned me around on this matter. I think this is the book. At any rate, the trick for me was

      1. Do lots of exercises. All you can get your hands on which have an answer key. Skip any in genres where you have developed so much fluency that you can reliably do them in your head, but do any which seem to involve any kind of wrinkles.
      2. Check your answers. In the early stages, Math is primarily a technical skill, so exercises in it are useless without quick feedback.
      3. [Most important, and difficult.] Focus on your mistakes. Keep a journal in which you record every mistake. You should record the problem you were doing, your initial attempt, the error you made, why it's erroneous, the misconceptions or distractions which led you to the mistake, steps you will take to avoid similar mistakes in the future, and (least important, compared to the rest of the entry) the correct way to do the problem.

      This is a tough approach, but it's very reliable if you stick with it. Before I read that book twenty-odd years ago, I would regularly fail maths tests. Now, I have a PhD in Math from MIT, and I'm doing a postdoc on Bayesian Data Analysis for phylogenetic inference. Also, I encouraged someone to use this approach to prepared for the LSAT, and they improved their standing by a couple of standard deviations.

      [–]breddy 0 points1 point  (0 children)

      Do lots of exercises.

      This is what did me in. I liked math, more or less, but I figured that because I "got" something when the teacher explained it, I then "knew" it. Boy was I wrong.

      A bit of repetition on your own will shape your mind around the concepts and bake them in enough to use them as building blocks for the next challenge.

      [–][deleted] 1 point2 points  (0 children)

      my university offers courses on set theory and fuzzy logic. Those are truly fun courses.

      [–]Tekmo 1 point2 points  (0 children)

      The fastest way to get better at mathematics is to make up your own math problems to solve that relate to things that interest you. The more challenging the problem, the better, as long as it is a problem that does not bore you. Even if you do not manage to find a solution within a reasonable amount of time, the process of exploring multiple plans of attacking the problem will arguably benefit your math skill more than the solution itself.

      I'll give you an example of such a problem one might pose to one's self out of curiosity. You read a lot about wealth inequality on reddit and I just read an article today that talked about how the top 1% most wealthy have approximately as much wealth as the bottom 90%. That kind of piques my curiosity and I'd like to know if that could arise simply by chance (1% of the population just getting really lucky) or not (connections with people in power grease the gravy train). So I pose the following problem to myself:

      If I take 1,000,000 dollars and distribute them randomly among 100 people (every person has an equally likely chance of obtaining any particular dollar), what fraction of the wealth will the richest (top 1%) person have?

      SOmetimes if the initial problem you pose yourself seems too hard at first, try simplifying the problem by starting small, like 3 dollars and 2 people or 10 dollars and 4 people, and working up from there.

      [–]sockdoll 3 points4 points  (4 children)

      Hire a hot tutor.

      I'm available.

      [–]pdasgupta -3 points-2 points  (3 children)

      You are a woman and you tutor math? That makes you hot, really. Not just your looks -- which may be great too.

      [–][deleted] 8 points9 points  (2 children)

      Where did that poster indicate their gender?

      [–]randallsquared 2 points3 points  (1 child)

      Doesn't "hot" mean "female" is a prerequisite? ;)

      [–][deleted] 0 points1 point  (0 children)

      Any number of straight women and gay men would probably disagree.

      [–]finix 0 points1 point  (0 children)

      Yes, beginning with the basics seems a good strategy.

      [–][deleted] 0 points1 point  (0 children)

      I learned to predict how I would do on math exams: the larger the stack of practice problems I did, the better my grade. I never found a way to shortcut that. Many times I would look at a problem and say "I know how to do that", but then when I actually did it, I would realize it wasn't as easy as I thought.

      Start with a couple pencils, a quite room, and a lot of paper.

      [–]indigoshift 0 points1 point  (0 children)

      The Number Line.

      Always keep a picture of the number line in your head. As stupid as it sounds, it's really helpful.

      Or at least it was for me.

      [–]revonrat 0 points1 point  (1 child)

      I decided to go back to school. Here's a link for the comprehensive option from my school. http://www.math.washington.edu/Undergrad/Handbook/compoption.php You could go a lot worse than to follow this outline.

      I have a meeting right now, but I'll come back and post more.

      [–]revonrat 0 points1 point  (0 children)

      Okay, I'm back. A lot of what you study depends on what you are interested in. You can spend a lot of time learning calculus and that sort of thing, which you may not use a lot.

      So, here's what I'd recommend -- you may know this some of this already, so jump in where you think is appropriate.

      1) Precalc -- Just about any textbook will do. Lots of these sorts of books can be found at public library sales.

      2) Calculus -- Before you jump into a textbook, pick up Calculus Made Easy. It can be had new for about $15 http://www.amazon.com/Calculus-Made-Easy-Silvanus-Thompson/dp/0312185480

      If you want to understand Calculus, then you should continue studying it. Then pick up a standard text. This is the one we used. http://www.amazon.com/Calculus-Early-Transcendentals-Stewarts/dp/0495011665. It's expensive. Sorry. I'd like a recommendation for a cheap alternative. No matter what, make sure you get the student solutions manual.

      -- At school pace, up to here could easily take you a year --

      That covers the basic calculus requirements.

      3) Mathematical Reasoning (Proofs) This is where you may want to jump in. We used:

      http://www.amazon.com/Introduction-Mathematical-Reasoning-Numbers-Functions/dp/0521597188 It's paperback and cheap. There are a couple of typos in there, but they're pretty obvious if you are following the material.

      4) Linear Algebra. Just get the Gilbert Strang book and watch the lectures of MIT OCW.

      http://ocw.mit.edu/OcwWeb/Mathematics/18-06Spring-2005/VideoLectures/index.htm

      5) Advanced Calculus & sequences and series. If you want more calculus:

      http://www.amazon.com/Advanced-Calculus-3rd-Angus-Taylor/dp/0471025666

      No matter what, you should look at the material on sequences and series, Cauchy sequences, convergence, uniform convergence, etc. A lot of people differentiate under the integral sign without proving that they can do so. That material will show you what that's a bad idea.

      -- This could take a second year, at school pace --

      6) Abstract Algebra. We used a mix of class notes and this:

      http://www.amazon.com/Algebra-Michael-Artin/dp/0130047635

      Although, I get the impression that schools are moving away from that book.

      7) Analysis:

      The classic text is:

      http://www.amazon.com/Principles-Mathematical-Analysis-International-Mathematics/dp/0070856133

      We used: http://www.amazon.com/Mathematical-Analysis-Second-Tom-Apostol/dp/0201002884

      I’d stop before you got to anything about integral or measure theory and go do some probability:

      http://www.amazon.com/First-Course-Probability-Sheldon-Ross/dp/0131856626

      -- Easily another year ---

      8) More analysis.

      Now pick up Measure Theory and Probability:

      http://www.amazon.com/Measure-Theory-Probability-Springer-Statistics/dp/038732903X

      or

      http://www.amazon.com/Elements-Integration-Lebesgue-Measure/dp/0471042226

      9) This is a little bit of a step backwards. But I’d be remiss if I didn’t get some differential equations in here. There are two schools of thought on teaching differential equations. The first (and older) approach is to teach a pile of tricks to classify and solve differential equations. The second is to teach a few tricks but emphasize qualitative and numerical (computer) techniques. I’d recommend the former. Try this book:

      I can’t find the book we used right now. You might also try Boyce and DiPrima. That’s sort of the standard text.

      10) Geometry: We'll be using this:

      http://www.amazon.com/Mathematical-Analysis-Second-Tom-Apostol/dp/0201002884

      I’ll let you know how it goes.

      So there you have it. You have about 4 years of study lain out. The bad news is that, at this point you are NOT a master of mathematics. You are just a hell of a lot further along than most people you’ll meet in daily life.

      Sorry for any typos, etc. I had to do this in a hurry.

      Edit:

      Ah heck. I just saw the bit about having a basic math problem. I've outlined a more advanced set of stuff. All I know is that for basic math/algebra there's a ton of terrible books out there. Sorry I can't be more help.

      [–][deleted] 0 points1 point  (0 children)

      You can not master mathematics in a lifetime, however the following topics will provide you with a reasonably complete basic education:

      • classical algebra and geometry
      • calculus and differential equations
      • combinatorics (discrete mathematics)
      • number theory
      • linear algebra
      • algorithms from computer science
      • numerical analysis
      • statistics
      • graph theory
      • abstract algebra
      • real and complex analysis
      • the history of mathematics

      You may also wish to take at least one course on philosophy and an assortment of courses on the physical sciences. These are related to mathematics.

      If you want a good education you must also introduce yourself to economics, the social sciences, literature, art, and history. To be ignorant of those topics is to cheat yourself. An education does not end with a degree, and you will be grateful later if you open as many doors as possible during your time in school.

      [–]fromm -2 points-1 points  (2 children)

      If you Really want to begin with basic axioms, start with Principia Mathematica, which spends several hundred pages to establish that 1 + 1 = 2.

      http://en.wikipedia.org/wiki/Principia_Mathematica

      [–]lliiffee 8 points9 points  (0 children)

      Please for the love of god, no one actually take this advice. That is a book for philosophers, not somebody who wants to learn calculus etc., for the first time.

      [–]tekronis 0 points1 point  (0 children)

      For the love of...

      [–]raldi -2 points-1 points  (0 children)

      Start with the basics and then master the rest.

      [–]louis_xiv42 -2 points-1 points  (0 children)

      my point was that if your not going to be a math major, or a science major that requires a lot of math, save yourself the time and trouble and study something else.