General Help in Discrete Math/Geometry and Physics

[dekoi]

Would anyone have any advice for a Grade 12 student taking the above courses? I have no trouble understanding concepts,yet when it comes to new questions (especially in discrete), i feel lost. Does anyone know of any methods which would fix this problem -- during tests as an example? I do a variety of review questions , and have had high grades in previous courses.

Thanks ahead of time.

 

[Diane_]

Well, since no one else has answered, let me take a stab at it.

First off, I find it odd that you're taking physics without having taken geometry. An awful lot of physics depends on geometry, and I can believe it would be confusing to try them both at the same time.

Generally speaking, though, I have found that students frequently have trouble in elementary physics because they have a hard time knowing how to get started, with a follow-up that they often don't carry through. This may translate through to the discrete math portion of things.

Chances are that, through most of your academic career, you've dealt with problems where you either already knew the answer or had a pretty good idea what it would look like. If I ask you "what's 7^2", well, you already know that. If I ask you for 7^3, you may not have it off the top of your head, but you know 7^2 and you know where to go from that.

With physics, it's different. You may look at a question and have no idea what the answer will be, or even what it will look like. Although you deal with accelerations all the time in daily life, it's still a relatively new concept, so when you're asked to find one, it feels a little alien.

The only real cure for this, I'm afraid, is experience, but there are some things you can do. First off, take a look at the answers to other questions here. Notice how often the answer begins with something like "make a diagram" or "what forces are acting". The first step in understanding physics is to get a good picture in your head of what is really going on, and what of that matters. Sketching things is an excellent first step in that direction. Add in arrows to indicate forces, pointing in roughly the right direction - the well-known "free-body diagram". Add in velocities, positions, anything else you can find. It's worth your time to write down all of the quantities you know using the standard symbols. The symbols themselves are just conventional - there is no magic in calling acceleration "a", for instance. However, there is equally no magic in the word "book", but if you choose to spell it "qpmfx", no one will know what you're talking about and you'll probably end up confusing yourself. If you understand and use the conventional notations consistently, you'll find things clearing up relatively quickly.

Beyond that, don't worry if you're doing all of this without any good idea why you're doing it. This is what I meant about not carrying through. A lot of students seem unwilling to start a problem without knowing exactly where it's going. The first steps I mentioned above will frequently teach you what the next step is. Get it down on paper, the look for relationships among the quantities.

Something that I've found helpful is to forget the math from time to time (which is sacrilege for a math major like me - don't tell my thesis advisor) and concentrate on the physics of the situation. If the problem given is a "real" problem, then it must be the case that there is only one solution. I try to figure out why there's only one. This is something of a legacy of one of my college professors, who used to give tests in which he would give you a situation and ask only if you had enough information to solve the problem and, if not, what else you needed to know. For instance, you are given the initial position, final position, and acceleration of an object. Is that enough to tell you how long it took to travel between the two? The answer, of course, is no - even assuming constant acceleration, it also depends on the velocity of the object. If you vary, for instance, the initial velocity, you will vary how long it takes to go from one place to another. This restriction is part of the universe at large, not just an arbitrary rule. Asking yourself that question about the problems you encounter is a good way to start working out the relationships between quantities like position, velocity, and acceleration in your head - and relationships like that are (IMHO) the key to physics.

Lastly, keep in mind that physics, like mathematics, is something like a language. There is information to be coded and relayed to others. As in a language, it takes awhile to learn the rules and the conventions. Some things will come easily, some will be hard, and there's no predicting what will be what for you. Just remember that thousands of people have done it, and you can, too. Just don't give up.

I have no idea if that will help, but I hope so. Good luck!

 

[dekoi]

That will surely help. You have been a great help.

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Another question: If I get extremely nervous during a test, is there some sort of method for me to calm down? I know i understand the question and am able to find the answer, yet my apprehension overcomes my reason. Any ideas?


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When memorizing a Theorem or a Property, is it a good idea to repeat? I sometimes find it difficult to remember vast amounts of information.

 

[Parth Dave]

I think its more important to understand a theory or concept rather than memorize it. If you fully understand it you will never forget it.

 

[dekoi]

Great.

Although i always understood it that way, i never actually practised this understanding of concepts.

Dave: I also live in Toronto. I go to school in Richmond Hill. :)

 

[Diane_]

As regards getting nervous on tests, I wish I did have a solution. It's not something I've ever had trouble with. I love puzzles - which may explain my major - and a test is really nothing more than a series of puzzles. If I like the professor, then I can view it playfully. If I don't like the professor, then I'll be - uhh - "darned" if (s)he's going to beat me at something. Perhaps that point of view will help.

About memorizing Theorems and so on, I only agree partly with Parth. It is, of course, better to understand something than to memorize it. In the early stages of any subject, though, there is an indispensable minimum of memorization - vocabulary, symbols, and other arbitrary things. In a subject like geometry, it's especially crucial, since many later developments depend on the specifics of the definitions. This crops up in physics as well - I had a student ask me once how I could be certain there were no positive electrons. That goes back to definition. (Note to quibblers: Don't tell me about positrons. Those are anti-electrons, not electrons.)

I do find repetition to be a valuable tool in memorization, but I find it more valuable to work with the definitions. For instance, in learning the definition of "parallel" as relates to lines, it was very useful to learn about "skew" lines. It helped to firm up the definition of parallel for me, particularly why the phrase "in the plane" was important.

I quite agree that there is a lot of information to learn. That's why you want to commit as little as you can get away with to memory. The more you understand, the less you have to memorize. When I was in high school, for instance, I was forever mixing up the rules of exponents: the difference between (x^a)*(x^b) and (x^a)^b, for instance. When I finally sat down and learned to derive the rules from the basics, it ceased to be a problem. I still mix them up today, but whenever I'm unsure, it takes me maybe five seconds to derive either of them, which gives me both of them. Fortunately, I've learned to do that in my head - it could be embarassing teaching algebra if I had to take a break in the middle of a lecture. :)

 

[shereen]

find number of ways in which 9 different bals can be put to 5 boxes, four of them contain two balls each and fifth only one.

can anybody help me wid dis?