## Math is so hard!

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- chaosakita
- Leliel
**Age:**25**Posts:**721**Joined:**Nov 17, 2009**Gender:**Female

### Math is so hard!

So I just got done with my Calculus (AB) and AP Physics (B) exams. What a disaster! For the first one, I got kicked out of the class at the beginning of this semester because I literally got a 50 in the class. As for Physics, which is basically just more math, I can't say I'm doing much better. Why does math have to be so hard? At least I don't really have to do any more math until August or so.

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- chaosakita
- Leliel
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- Seepage Murid
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physics is a branch of science that uses math, so it is a science. Why Ornette is saying that calculus is not math I have no idea.

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- chaosakita
- Leliel
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Also, physics is a lot of fun imo and if you understand the concepts, the maths should follow,

**but**I didn't ever take calc-based physics and I had an excellent high school physics teacher. Your mileage may vary.

EDIT: Ah, see? Knowing an equation and knowing how to algebraically transform it to solve for other variables is about as far as you need to go in high school physics. Knowing where to plug values in is a matter of conceptual understanding of physics, not of maths.

- Ornette
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Physics isn't a branch of math, it uses a lot of straightforward math, but both that math and Calculus are based on a very small subset of the bigger picture. It works ONLY with metric fields (meaning the involved points follow a set of rules: see below) and ONLY with Real and Complex numbers.

First years in college, some people may take a class that could be called "Modern Math" or "Intro to Abstract Math" or something along the lines of that, which will cover sets, combinatorics, discrete math, number theory, etc. None of those will involve much actual arithmetic computations (whereas Calculus, differentiation and integration, linear algebra, etc all mostly involve computation), there's a bit in combinatorics I guess. Each of these things have entire fields dedicated to them. It's mostly all abstract, meaning you're probably never work with actual numbers.

When I got my bachelors in math, I did the abstract route with sets. Pretty much a dozen or so classes dedicated to different kinds of sets, like Groups, Rings, Fields, Metric Spaces, Topographies. Sets themselves are pretty interesting, it's a fundamental way of defining the basic principles, even the principles of Calculus (or sometimes called Analysis). Those other things I mentioned are sets paired together with a function, the function maps an element in the set to another element in the set, with a couple of properties such as communitivity and transitivity. With just these definitions, you can prove an immense amount of properties of sets, groups, etc. without knowing anything about them, what's in them, how many of whatever are actually in them. Metric Spaces (topology, fractals) are sets with a function that has a few extra properties, essentially that they're continuous distance functions.

The other fields that I mention are all equally as rich and interesting. Number Theory is great, the nature of primes, why numbers have the emergent properties they do, etc. In all, the only available classes that are offered in the Math department (at CMU at least) are 3 kinds of calculus, for engineers and non-engineers, differential equations, and 2 classes for calculus verification (like removing the limits out of the definitions of differentiation and integration).

When I said "real math", I was sort of being a little facetious. But people who actually go into fields of math probably won't consider calculus "math" anymore than "statistics" (which also isn't "math").

- chaosakita
- Leliel
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Calculus-based physics seems better in some ways. It's way easier to understand kinematics with calculus, and you can understand circular motion better as well. Also, understanding how sound waves are actually shaped requires you to know how to do solids of revolution.

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- Mr. Tines
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I've done math tuition at various times over the years for highschoolers, and what I've seen is that the general standards of teaching are terrible for maths and sciences. Given that the pay and conditions are poor compared with what you can get in industry if you are any good, it's clear only the people with marginal skills in their subject end up in teaching -- and very few of those have skill in teaching in the abstract. Without mastery of the topic -- which is a prerequisite for truly being able to teach anything -- and without the knack of communicating that mastery, lessons become exercises in transferring course notes from one piece of paper to another.

It's not that the basics are intrinsically hard, more that they are rarely explained lucidly; and in the mass-production classroom, dealing with each individual's conceptual sticking points just doesn't happen.

It's not that the basics are intrinsically hard, more that they are rarely explained lucidly; and in the mass-production classroom, dealing with each individual's conceptual sticking points just doesn't happen.

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- chaosakita
- Leliel
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Mr. Tines wrote:I've done math tuition at various times over the years for highschoolers, and what I've seen is that the general standards of teaching are terrible for maths and sciences. Given that the pay and conditions are poor compared with what you can get in industry if you are any good, it's clear only the people with marginal skills in their subject end up in teaching -- and very few of those have skill in teaching in the abstract. Without mastery of the topic -- which is a prerequisite for truly being able to teach anything -- and without the knack of communicating that mastery, lessons become exercises in transferring course notes from one piece of paper to another.

It's not that the basics are intrinsically hard, more that they are rarely explained lucidly; and in the mass-production classroom, dealing with each individual's conceptual sticking points just doesn't happen.

I think math instruction for anything other than calculus was pretty pointless. If you can read the book, bother to study a little, and pay attention when doing your tests, you can get a good grade. I didn't bother to do the last two things. And uh, I don't think most high school students are doing calculus.

My teachers were pretty competent - one was an engineer and the other was a part-time (community) college professor. It was all my fault though. I hit a roadblock and I couldn't bother to climb over it. But even so, despite not having done significant math work for the last two months, I feel confident that I passed my Calculus test to the point where some decent colleges would consider it an appropriate substitute for one of their math classes.

And look in China, where teaching is even more rigid - they don't have any problems with math. I think most people (like me) just don't want to expend effort and study, that's all.

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- TaintedHero
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chaosakita wrote:I think math instruction for anything other than calculus was pretty pointless. If you can read the book, bother to study a little, and pay attention when doing your tests, you can get a good grade. I didn't bother to do the last two things. And uh, I don't think most high school students are doing calculus.

I beg to differ, I know a good many people who are taking/have taken calculus in high school including me. Though I tended to be friends with other calc students and thus it may have seemed like there were a lot of calc students.

Studying and practice was the major thing when I took calculus and cal physics.

I also found the teachers to be very helpful, as I do a terrible job when it comes to learning and understanding from books. It depends on what kind of a learner you are. I am very visual and hands on, I like doing examples in class as well as seeing concepts and key points written out and copied.

Sadly after Calc 2 I decided I hate math and never wanted to do it in the future to such a degree as engineering, so I switched major.

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This might be helpful if only for filling the conceptual gaps.

http://www.youtube.com/watch?v=EX_is9LzFSY

http://www.youtube.com/watch?v=EX_is9LzFSY

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As for physics being like maths. The actual essence of physics in high school is the grasping of physical concepts. The math is just there so that you can use it to apply the physical concepts and derive the answer in a physical problem, proving your understanding of the concept. Often the matter is not how you do the math in the problem, but the correct application of the accurate physics law that really counts. Similar can be said for maths problem, but in maths it is the mathematical concepts that is the main challenge.

As for physics being like maths. The actual essence of physics in high school is the grasping of physical concepts. The math is just there so that you can use it to apply the physical concepts and derive the answer in a physical problem, proving your understanding of the concept. Often the matter is not how you do the math in the problem, but the correct application of the accurate physics law that really counts. Similar can be said for maths problem, but in maths it is the mathematical concepts that is the main challenge.

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**chaosakita**: I'm assuming you don't have a Math Learning Disability problem (I do, math was always HELL for me, even with Extended Time and other Resource Room assistance. Damn premature birth.), but just in case: http://www.ldonline.org/article/5896 and http://learningdisabilities.about.com/od/learningdisabilitybasics/p/ldbasicmath.htm

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I get what Ornette was saying. It's all problem solving algorithms until real analysis. Whether it's calc. 1, calc. 2, calc. 3, or diff. eq., there is always a discrete and usually clear

Conceptually it's just: limits (or things going to infinity in general), what "d" means (dividing zeros of equal magnitude), and integration/differentiation. The rest are plans.

There's actually a rather DEEEEP point in calculus, I think, about how you can bring something into being from a void if you just have the form of it; the whole idea that integration is just adding up zeros.

In physics, calculus is used mostly -- in addition to describing the behavior of processes -- to apply simple, linear values like momentum, force, potential to large-scale, "odd" bodies by "building" them up from zero or d_/d_. The relationships between the values themselves, surprisingly, are often just measures of each other's change, which is where the math comes in. Physical processes themselves can be thought of as change or pure difference. Electrical induction only appears in a changing magnetic field and force only "appears" with changing velocity. But in general, the difficulty of the actually derivatives/integrations in physics compared to the stuff you're tested on in math is extremely low (unless you are working with weird shapes that are hard to describe, but usually you can build everything from spheres, infinite planes, cylinders, etc.) There is also the aspect with "real stuff" that you can choose to approximate reasonably and ignore terms that go to zero quickly, thereby making your math

But yeah, real mathematicians have to come up with proofs from "thin air" and such and are probably closer to philosophers (at least in the Pythagorean sense) than physicists.

*plan*to take when encountering a certain problem type. In calc. 2, you just learn more techniques for doing calc. 1 stuff, so you start needing meta-plans to know which technique to use in the first place. Calc. 3 is just everything before but in glorious 3-D. Diff. eq., which I'm taking now, is pretty much a list of dozens of plans for solving all kinds of weird looking things, but they're just plans, so you don't*really*need to be taught them.Conceptually it's just: limits (or things going to infinity in general), what "d" means (dividing zeros of equal magnitude), and integration/differentiation. The rest are plans.

There's actually a rather DEEEEP point in calculus, I think, about how you can bring something into being from a void if you just have the form of it; the whole idea that integration is just adding up zeros.

In physics, calculus is used mostly -- in addition to describing the behavior of processes -- to apply simple, linear values like momentum, force, potential to large-scale, "odd" bodies by "building" them up from zero or d_/d_. The relationships between the values themselves, surprisingly, are often just measures of each other's change, which is where the math comes in. Physical processes themselves can be thought of as change or pure difference. Electrical induction only appears in a changing magnetic field and force only "appears" with changing velocity. But in general, the difficulty of the actually derivatives/integrations in physics compared to the stuff you're tested on in math is extremely low (unless you are working with weird shapes that are hard to describe, but usually you can build everything from spheres, infinite planes, cylinders, etc.) There is also the aspect with "real stuff" that you can choose to approximate reasonably and ignore terms that go to zero quickly, thereby making your math

*even*easier.But yeah, real mathematicians have to come up with proofs from "thin air" and such and are probably closer to philosophers (at least in the Pythagorean sense) than physicists.

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