Why is math considered beautiful?

[happyhiker]

I had a horrible overall experience in math. Growing up, I was expected to learn the material on my own and didn't really have any support with the subject at home. In school, I managed to pull off above average grades in my math classes (following countless hours of work). Following summer break, I would return to school without any knowledge of what we learned the previous academic year.

I will enter college next fall and have about 8 months to review. My fear of math has reached a point where it's almost paralyzing.

Here are my questions for you math geniuses out there:Why do you love math? What is the best way to review? On average, how long do you think it would take an average person to review math (algebra-calculus)?

 

[Simon Bridge]

Why do you love math?
I don't - a large chunk of my skillset involves avoiding math ...

What is the best way to review?
Find someone who knows a bit less than you and help them.
Find a context that you enjoy - presumably you need the math for something that doesn't scare you?

On average, how long do you think it would take an average person to review math (algebra-calculus)?
I have a course I teach for adults who need to review HS math with statistics and calculus. It is a 1 semester course, but people can go at their own speeds - about half have ovecome math fear in the first few weeks.

I used to teach remedial math and physics to pre-med students on an accelerated program, that was a whole year but it was physics as well.

I did a 10 min speech for Toastmasters on basic toolset math which took 10mins. A bit under a quarter of the audience got it... but no exercises you see.

 

[galoisjr]

There is a very easy way. Work through examples. If you cannot figure something out, then ask a question.

 

[jedishrfu]

there is also the khan's academy videos on the web that provide 10 min discussions on various math subjects:

http://www.khanacademy.org/

He covers a lot of HS math topics that could help you strengthen your learning of areas that were problematic.

One strategy would be to start with algebra and get good enough to teach others then move onto geometry... preparing yourself for calculus in college. calculus isn't that hard once you learn the basics of linear functions. calculus brings together your HS math giving you new tools to solve a larger range of problems.

 

[Jamma]

Firstly, i am really sorry to tell you that there is no reason for me to love math. It is just from on my own, in my mind and in my heart. it belong to your personality. if you do not like it, even you try your best, you can not be good at math.
About the way to review, you should review at the beginning. if you do not understand the basic, you can not go further. i think it does not take much time if you concentrate on.

I don't agree with this- many people say they don't like maths, but I don't see how that could be true if they knew some of the beauties of the subject that I know. I think the problem isn't that they are bad at maths or that they don't like it, it's that they haven't seen good maths- they've just been told how to complete tedious tasks.

 

[e.bar.goum]

Practice practice practice. It's the only way, I'm afraid.

Jamma - I agree. I'm going to bring out an analogy a mathematitian friend told me - learning maths in high school is like learning an instrument by only every playing scales, again and again. What's more, you don't even get to *hear* a song, so naturally, you only think of music in terms of scales. No wonder people "hate maths"!

Then, when you get to university, you are (sometimes very suddenly) playing music. Just "chopsticks" and "hot cross buns" at first, but it's music. Eventually, you can play a symphony. That's where the beauty comes in. But to be able to play in a symphony, you've got to practice.

 

[Jamma]

That's a wonderful analogy- I'll use that myself, thanks!

 

[Harrisonized]

Why do you love math?

It's interesting. Much of math is beautiful in its simplicity and it's generality. It's like a giant puzzle/game, except the results are useful.

What is the best way to review?

Learn the concepts.

First, learn what's going on. When you have a problem to solve, learn and apply the procedure for how to solve the problem. Go over the procedure and the derivations. This part is usually slightly boring, since you are following in someone's footsteps. However, this part also gives a lot of insight. Alternatively, you can attempt to solve the problem yourself, but it is not in the best interest of your time to do so, since you're still in algebra/calculus. (Later on though, it's very helpful to attempt problems by yourself without first looking at the general procedures.)

After solving the problem, start breaking down the problem. Figure out why each step is used. If it's not apparent after working one problem, work another one. Try to pick a problem that's very similar, but not exactly the same. Sometimes, it even helps if you just replace all the numbers with variables.

After one or two problems, figure out which steps are used the most, or which steps are the most clever (or tricky), because these steps are the most important or most general. When a process or concept in math is used a lot, it is important, and if it is important, it is usually given a name. Learn the name. Then learn the definitions. Figure out why the concept or process is defined the way it is, what is included in the definition, what isn't included in the definition, and ultimately why the concept or process is important. If it's a concept, figure out why the name is appropriate. If it's a procedure, figure out what else you can use the procedure for.

After learning the above, go back and work another problem. More if you like to do them.

Finally, go back and learn how to derive things from scratch. This part is the most important. Don't use numbers; use variables. If no variables are involved, define some, and try to be as general as possible. Make sure what you're using is well defined. Whenever you see a problem in your own reasoning, try to correct it. (For example, you don't want to be dividing by 0, or multiplying by 0/0, etc.) If you run into trouble and you really can't figure it out, if you have the time, let the problem sit on your table and come back to it later. Maybe come back tomorrow to solve it. If you don't have time, look in a textbook or online for help.

I have to say I disagree with working on a lot of practice problems over and over. Practice problems are usually written by instructors with the goal of having a determined, easily computable solution. This can build confidence in a student, but it also teaches the student to just apply procedures like a machine. Also, many realistic problems do not have simple solutions, and many times, complicated solutions can lead to new insights.

Working many, many practice problems is the number one reason that many students forget everything after a final. Without deep understanding, there is very little chance that a student will remember even only after a year. It's nice to work practice problems to build confidence, but don't get so wrapped up in it that you forget what's important.

On average, how long do you think it would take an average person to review math (algebra-calculus)?

I would estimate an hour per concept. Under this model, how long you review is dependent on how many concepts you are reviewing.

 

[Hobin]

I don't agree with this- many people say they don't like maths, but I don't see how that could be true if they knew some of the beauties of the subject that I know. I think the problem isn't that they are bad at maths or that they don't like it, it's that they haven't seen good maths- they've just been told how to complete tedious tasks.

I disagree. I have seen many of the 'beauties' of math, and I still don't like the subject. I can understand that others do, of course, but, just like there are people who don't like paintings, I don't like art. I hope you didn't mean to say that everyone would like math if only they had seen the beauties of the subject, as this would show a lack of empathic capability.

 

[happyhiker]

I thank everyone for the helpful advice! I will put these tips into action.

 

[Sankaku]

I have seen many of the 'beauties' of math, and I still don't like the subject.

Wow. Does that mean you can tell us some of the inner secrets of Category Theory, then? Or perhaps just a little insight into Differential Geometry for us?

If you miss the irony above, it says: "No you haven't." If you say you don't like some music, then I believe you. If you say you don't like ALL music, then I don't.

 

[bael]

i think the equation for finding the volume of a cube is quite beautiful

 

[mal4mac]

I had a horrible overall experience in math. Growing up, I was expected to learn the material on my own and didn't really have any support with the subject at home. In school, I managed to pull off above average grades in my math classes (following countless hours of work). Following summer break, I would return to school without any knowledge of what we learned the previous academic year.

I will enter college next fall and have about 8 months to review. My fear of math has reached a point where it's almost paralyzing.

Here are my questions for you math geniuses out there:Why do you love math? What is the best way to review? On average, how long do you think it would take an average person to review math (algebra-calculus)?

Maybe you need to relax a little! Then the experience might not be so horrible... If you are getting above average grades then where is the problem?

I very much doubt you return with no knowledge of what you did the previous year - otherwise your grades would quickly nose-dive! Maybe you can't remember a few specifics, but getting up to speed with them will take a lot less time than learning them for the first time. Given all the stress and tension you're feeling perhaps eight months off would be the best thing. Your college chums will not be spending eight months reviewing maths before going to college - and the few months they do have will probably be spent lying on a beach (if they are sensible).

Given your hard work at school, and above average grades, you should (with a bit more hard work!) be quite capable of keeping up an above average performance in college, without spending the next eight months "doing scales".

Rather than going through (what for you is ) the pain of a full technical review why not read a few biographies of mathematicians who actually enjoyed the subject without suffering all the angst you are feeling - start with A Mathematician's Apology by G. H. Hardy.

 

[Lavabug]

I had a horrible overall experience in math. Growing up, I was expected to learn the material on my own and didn't really have any support with the subject at home. In school, I managed to pull off above average grades in my math classes (following countless hours of work). Following summer break, I would return to school without any knowledge of what we learned the previous academic year.

I will enter college next fall and have about 8 months to review. My fear of math has reached a point where it's almost paralyzing.

Here are my questions for you math geniuses out there:Why do you love math? What is the best way to review? On average, how long do you think it would take an average person to review math (algebra-calculus)?

I'm not a math genius by any stretch of imagination, I too had difficulties with math in high school. I generally did not grasp concepts (perhaps not entirely my fault) and ended up learning to compute things furiously in order to pass with average marks. I disliked it generally, but I had a feeling there was some aspect in math that I would like, but had not yet discovered.

Then when I reached university (after not doing any math for 3 years) I actually came to understand calculus a lot better than back in high school and started to enjoy it. I struggled with linear algebra a bit, but progressively my interest in math increased. In my 2nd year (after much hard work), I made some of the highest marks in my math courses, something I never thought I'd achieve in high school.

Along my journey, Khan Academy helped immensely as did Paul's online math notes. There are many excellent online resources. Best advice I can give: concepts come first, followed immediately by thorough, exhaustive practice. Leave no stone unturned. Take as much time as you need on your math courses, hire a tutor to speed up the learning process if necessary. All the hours you put into them will be well-spent. The more bits that become second nature to you, the more confident you will feel in many future courses in math and any quantitative subjects.

What to review: try to find where you are lacking currently and work on that.

Algebraic manipulation, graph plotting, analytic geometry.
Functions, series, limits & continuity, differentiation/integration.
Matrix algebra: determinants, solving systems of equations, line/plane intersections. Complex numbers: basics.

If you can do all that before college, you will be very prepared. Head over to Khan Academy and work through the relevant playlists, that's probably the best way to start.

 

[deRham]

My fear of math has reached a point where it's almost paralyzing.

For right now, you should focus on attaining small goals in school, rather than trying for an insane turn-around. And you need to be ready to reward yourself for milestones you reach yourself (regardless of another's recognition).

So do it this way - when you need to learn a concept, really fiddle with it. Ask a lot of questions - why does this work, why does that work, and what's the intuition behind it? Often, students who don't consider themselves good at the subject will just try to get by plugging and chugging as much as possible. This is ultimately a problem, because their confidence keeps declining, as does their grasp on what's going on. Every time you have a small "aha!" moment, your confidence in your abilities will rise.

and I still don't like the subject.

Like someone else said, I don't see how you can dislike a subject as a whole when it has so many different aspects. Also, "not liking a subject" is itself a vague thing - does it mean you don't like doing it or you don't like hearing about it or that you don't like that it exists?

 

[deRham]

Much of math is beautiful

Perhaps some people are puzzled by this. Well, let me ask them: can you find a piece of writing beautiful? I think this is one of the closest ways to explain. The thing about writing is that it does not claim to be reality, yet it can express elements of what one may call reality. It can get one to feel and be in touch with something that relates to things they have felt, and things they could feel.

Mathematics does this in a way too. Whether it idealizes reality or not, in a way our experience of reality is in our minds, which leaves room for imagination to describe not only reality, but various offshoots which our minds can come up with.

In some ways, this is also why a painting can be beautiful - why not abolish paintings and just take photographs? Because we like to recreate/create. Writing does so through one medium, painting does through another, and mathematics does so through the study of axioms, formal theories, structures, etc. All of these are potentially fascinating ways of looking at something or the other.