Getting back to College

Taking a math prep for college sometime next month.  However, I have rusted in some areas and want to do some reviewing.  What would the anons here suggest?

algebra, trig (specifically common angles for sine and cosine, and be aware that trig identities exist), and you're pretty ready.  don't know what you've already done or if you're doing calculus.

Thanks for the advice and I have taken first year college calculus when I was a high school senior (although I sucked at it and got a D).  So does it make a difference if I have already taken Calculus?

doesn't really change much, since i'm guessing you'll be taking calculus over again, and algebra and familiarity with trig are the only real requirements as far as i remember.

college math is where you start to finally move away from the arithmetic and manipulative aspects and get more into theorems and proofs.  calculus usually feels like an extension of algebra with new things called derivatives and integrals that popped out of nowhere, but if you do anything else like number theory or abstract algebra or analysis, it'll be a different direction most people don't have any experience with from highschool, so you can't really brush up on it, it'll be new.

the only specific things i can remember wishing i had kept practiced in in my first year were factoring polynomials, dividing polynomials by other polynomials (which i only rarely needed and it was reviewed in the class quickly), and i sucked at remembering angles and their trig values.

>>3
Please adopt a more positive attitude.  Once you embrace the Calculus, you'll find that it's a new level of mathematical thinking.  I consider it a "more natural" way of thinking about calculating things, especially in the real world.  I know I'm going to offend some of the Calculus Purists, but using algebra and the concept of infinitesimals and limits, you break through the restrictions of algebra and enter a new realm of finding the metrics of all kinds of new objects.  As long as you can sufficiently describe a curve with a function, then you can find rather precise characteristics of that curve -- its length, the area or volume it encloses, it's "curviness", etc.

The Calculus is a fucking better way of doing math.  Algebra is sufficient for most people, but to truly understand math and to go beyond, you have to become one with Leibniz and Newton.

There are some fairly good workbooks out there for naturally prodding algebraic thinkers into the Calculus.  I don't recall any of their titles, so you'll have to search for them yourself.  College texts on the Calculus can be fairly over-assuming and I find them dis-serving of helping students make the transition.  Spend an hour in a good (i.e. nerdy) bookstore and find one of those gems in all the rough stones.  Thirty bucks and 1 month later, you'll love me so much for my advice you'll demand to have my children.

>>5
Why can't you make more posts like this and less like every other post?

>>6
Because I'm not your personal savior.  My personality as expressed in the 4chanverse is highly aggressive, uses more wisdom and intuition than intellect and deduction, and draws out the beast within in order to determine a larger truth seldom accessible in public discourse.  I'm a dirty river that you have to pan a lot for the nuggets of gold I contain.  If that's too much labor for you, then GTFO.  :^)

You might understand better what I'm doing if you'd read up on what Soren Kierkegaard did as a young man to develop his prodigious mental capacities.  I can't claim to be as bright as he was, but some of his methods are models for Western thought amongst men who claim to be learned.

>>3
Having seen the material before always helps, so it should be a little easier the second time around.

Definitely know your trig and algebra (especially polynomials).

>>5
I don't quite see it as a "new way of thinking".  I see it more as an extension of algebra that merges it with analytic geometry.  Of course, these are just subjective interpretations.

>>6
Lurk Moar.  He doesn't become psychotic unless the R or G words are mentioned.

>>8
I don't really need to lurk more, I've been his active opponent in the majority of threads.

>>9
Don't let our secret out!  Now, kiss me, you mad fool!

>>10
/hotsex

>>7

Suddenly, I find it a lot easier to tolerate you.

OP here.  Thanks for all the advice.  Wish me luck on my prep next month

>>5

Quoted for fucking truth.  I still remember the first time Calculus "clicked" for me.  It was almost like a damn religious experience, and I felt like I suddenly saw so much deeper into mathematics.  I could look back on all the math I had learned before, and I saw how it all fell into place, it was beautiful.

Goddamnit, I love math.

>>14

Indeed.

>>14

True.

>>14
>>15
>>16
i don't get when people talk like this about math.  nothing ever 'clicked' for me, i just understood it, and it wasn't any more or less beautiful than anythin else.  it's just the necessary results of the way the universe and our assumptions are structured.

>>17

No, you're just wrong there.

>>17

I'm guessing your everyday life isn't very interesting if you're not looking for the specifics of any structures you take implicitly for granted...

>>19
who said i didn't?  i just said it's not any more beautiful than anything else.  i'm usually at the top of my classes, i usually think deeper into subjects than most of my peers and have a better intuitive grasp of things, i like learning connections between various things, across subjects or just to find out why something behaves as it does.  i've learned a lot of math now, and i just don't share that feeling i've heard about for years.  i've had professors talk about "it is just beautiful when you can see these intricacies!" and kids light up and get genuinely excited at the mention of the words "measure theory".  it doesn't do anything for me.  at times i've found it interesting, but i've never found it more beautiful than other things.  how can you?  how can you say "this is beautiful!" as though things beside it were less so.  i think it's just intellectual masturbation.

I've just begun Calculus and would like an example of how everything is going to fall in place and hit me as beautiful.

>>21

Me too

>>20
>>i think it's just intellectual masturbation

Ah, you're a high achiever, but apparently not a smart one. Congratulations, you're commonplace in this world.

>>21
>>22

wait it out, man. wait it out. once you get past doing integral after integral of trig functions and start to look at the interesting stuff like de moivre, you can arrive at shit like euler

>>24

What?
That's just one particularly interesting result, there's nothing unfying or fundamental about it.

>>25

"and hit me as beautiful"

why not just go ahead and give your suggestion of what is unifying and fundamental? the distributive property? that's pretty fundamental. addition?

>>26

Studying general metric and topological spaces is one I'd suggest.

The result he's referring to is only really a suprise depending on the way you define the exponential and trigonometric functions and derive their properties.
It's a pretty obvious fact when you do it a certain way.


General topological spaces tie in calculus and geometry and algebra and a whole host of other things in a really beautiful way.

Newsflash: Beauty is subjective.

>>23
smart =/= good aesthetic sense

I didn't find calculus to be particularly beautiful either.  I do recognize it as a critical step in human development.

GR struck me as particularly elegant, though that's somewhat related to what >>27 was suggesting.