[QUOTE=ThisIsTheOne;44486597]It sounds like you're only talking about algebraic number theory. Of course a lot of it is interconnected, but Number theory is more interesting than that. Things like the Prime Number Theorem and Dirichlet L-series (Riemann Zeta function is one example) all involve lots of complex analysis and are really cool. Then there are really interesting results about the growth rates of arithmetic functions and their averages, and lots of cool facts like Bertrand's postulate and Dirichlet's theorem.[/QUOTE]
That's slightly more interesting. The Riemann zeta function is kind of neat but I don't think it's something I'd ever work on still.
[QUOTE=ThisIsTheOne;44486597]I did think like that but sometimes now it can start to feel a little dry if it's too abstract.[/QUOTE]
I think abstractness is still a lot of fun as long as it's well-motivated (and just because it's abstract doesn't mean it can't be). Dryness is mostly poor motivation.
Need to teach myself Calculus this summer since I've fallen way behind on math in my course, and I've found a decent set of books to do so. Can anyone recommend a decent book for math at a lover level than calculus? I've had it before, but I just want a quick book to read and work with to make sure I can handle all the basics first.
[QUOTE=kirderf;44569198]Need to teach myself Calculus this summer since I've fallen way behind on math in my course, and I've found a decent set of books to do so. Can anyone recommend a decent book for math at a lover level than calculus? I've had it before, but I just want a quick book to read and work with to make sure I can handle all the basics first.[/QUOTE]
I'm not really sure. Google told me [URL="http://www.amazon.com/Precalculus-Mathematics-Nutshell-Geometry-Trigonometry/dp/1592441300"]this[/URL] is good. Most of the of the people here probably didn't do much self study of pre-calc (I may be wrong), and most likely just used whatever text happened to be in their school curriculum.
got some math investigation about cylinders, square based prisms and their surface area and volume
question asks to find h in terms of r for the cylinder, and H in terms of a for the prism
h being height, r being radius, H being height and a being the base edge
[QUOTE=GentlemanLexi;44570739]got some math investigation about cylinders, square based prisms and their surface area and volume
question asks to find h in terms of r for the cylinder, and H in terms of a for the prism
h being height, r being radius, H being height and a being the base edge[/QUOTE]
Can you specify what exactly you are given for the cylinder? Do you know it's volume or surface area? If they just tell you it's a cylinder you can't do much.
[QUOTE=Falubii;44570941]Can you specify what exactly you are given for the cylinder? Do you know it's volume or surface area? If they just tell you it's a cylinder you can't do much.[/QUOTE]
we aren't given anything for the cylinder
the question states:
"use question 1 to find h in terms of r for the cylinder and H in terms of a for the prism"
question 1 was write down the algebraic expressions for the volume and surface area of each container
[QUOTE=GentlemanLexi;44570959]we aren't given anything for the cylinder
the question states:
"use question 1 to find h in terms of r for the cylinder and H in terms of a for the prism"
question 1 was write down the algebraic expressions for the volume and surface area of each container[/QUOTE]
If the volume and surface area are not fixed I cannot give you an explicit relationship between the radius and height.
[QUOTE=Falubii;44571066]If the volume and surface area are not fixed I cannot give you an explicit relationship between the radius and height.[/QUOTE]
Are you sure? This is grade 10 math standard, there's no way this is impossible or anything. Algebraically maybe?
I could be missing something obvious. Maybe somebody else will pick it up.
[QUOTE=GentlemanLexi;44571264]Are you sure? This is grade 10 math standard, there's no way this is impossible or anything. Algebraically maybe?[/QUOTE]
It might be helpful to post your answer for question 1.
The way I see it is this, though:
They're asking you to find the height of a cylinder in terms of its radius. There can't be any such relationship, because you can make a cylinder of any height for a given radius.
They might be asking you to find the height in terms of the radius and the surface area or volume, but I really don't know.
[QUOTE=Krinkels;44571628]It might be helpful to post your answer for question 1.
The way I see it is this, though:
They're asking you to find the height of a cylinder in terms of its radius. There can't be any such relationship, because you can make a cylinder of any height for a given radius.
They might be asking you to find the height in terms of the radius and the surface area or volume, but I really don't know.[/QUOTE]
My answers were A = (2πhr) + (2πr²) to find surface area, and V = πr²h for volume for cylinder.
Why don't you take a picture or scan the page or something. Just to make sure we're not misinterpreting the question.
I think I'm too much a mathematician to be a physicist anymore. Watching Zwiebach multiply and divide by ds and dt all over his string theory text just hurts me deep inside.
[QUOTE=JohnnyMo1;44579364]I think I'm too much a mathematician to be a physicist anymore. Watching Zwiebach multiply and divide by ds and dt all over his string theory text just hurts me deep inside.[/QUOTE]
Then just picture them as deltas and then take the limit to 0 :v:
[url]http://theproofistrivial.com/[/url]
Way more fun than it should be.
[QUOTE=JohnnyMo1;44644040][url]http://theproofistrivial.com/[/url]
Way more fun than it should be.[/QUOTE]
I love pages like these, that are simply just filled with a small piece of text.
More quotes from uni profs (collected from multiple friends)-
[b]R, Diffusion in Solids-[/b]
"You said FCC structures are the most fun to draw? Cool, OK, I don't judge... Some people go out on saturday nights, and some people stay at home and draw FCC structures."
"This thing's always true, except on the test"
[b]S, Quantum Mechanics-[/b]
Student: "I didn't understand the explanation." "Neither did I! But you have it worse than me, you actually have to take the exam."
"Schrodinger is the hero of this story"
"You don't have to be a rocket scientist for this, only a physicist"
"Now we'll do some advanced cheating..."
(Realising he made a mistake)-"Oh! You're right. I recommend that I be fired immediately!"
"You said you're disappointed in me? You'll be disappointed in your grade!"
"If you become a scientist, you have to maintain the proper ethics, don't copy your articles! Not if you're engineers, though. For them, copying is a way of life!"
[b]A, Quantum Mechanics[/b]
"This is the Cauchy–Schwarz inequality, you learned this in 7th grade!"
"Complex numbers are nice and all, but you can't go to the store with complex numbers"
"The connection between the letter and its meaning is important, at least emotionally"
"This is a completely kosher Hilbert space"
"You know what they say, you can't understand Shakespeare if you don't speak any english"
[b]I, Material Thermodynamics[/b]
"That process is imaginary in my imagination"
[b]G, Thermal Statistics-[/b]
"It's 8:49 AM! Why are you asking such a complicated question?"
"Negative temperature sounds very exotic but it's cheating, it's a total scam!
"I'll continue to massage this expression"
"Take this material in the lab, put it in water, and you'll have little pieces of shit floating around"
"This isn't on pen and paper, it's nature!"
"The advantage of this method is that it's very simple. The disadvantage is that's completely false"
[b]E, Thermal Statistics-[/b]
"Here, in the realm of thermodynamics, everything is fake!"
"We'll take a small volume. And when I say small, I don't really mean small"
"You should never underestimate the pleasure of hearing something you already know"
[b]Z, Calculus-[/b]
"Infinity divided by infinity equals one? Who said that? You? Get out, bang your head against the wall, and when you go back inside I wanna see blood"
[b]Y, Analytical Chemistry-[/b]
"Any idiot with a spoon can make crystal meth. You study chemistry to invent stuff that does the same shit, only legally"
[b]E, Organic Chemistry-[/b]
"I solved the first part, do the rest at home. It'll only take about a hundred years or so"
"Did everyone copy this disgusting thing?"
[b]A, Linear Algebra-[/b]
"Pay attention! This is what you do when M is bigger than 0. You do the same thing when M is smaller than 0, only completely differently"
"This matrix is full of zeros, just like the class in front of me"
"A few weeks ago I got really drunk at (pub) when my daughter called, asking me to pick her up." "And you drove there?" "Absolutely! I couldn't walk in that condition."
The double integral is trivial but I don't know what general principle they're talking about. Any ideas?
[t]http://puu.sh/8Eilu.jpg[/t]
Edit: just realized I called the integral trivial and the took it as a derivative. This is what happens when you've been studying for 6 hours. Still, given the answer is 1/40, I don't know what general principle they're talking about.
I really don't know what I'm talking about here, but it might be this:
Let f and g be polynomials in x and y respectively.
Then ∫∫f*g dxdy = (∫fdx)*(∫gdy)
Imagine there are limits of integration on those integral signs there.
It's just such an overly vague question. I guess they could be talking about commutativity and Fubini's Theorem.
[QUOTE=Falubii;44757876]I guess they could be talking about commutativity and Fubini's Theorem.[/QUOTE]
That's kind of obvious though, isn't it? Seems silly to ask a question about it.
I hate those obvious questions that are actually so easy they throw you off completely...
I don't think it's really obvious though, because it's [I]so goddamn vague[/I]
So I'm trying to do some fancy parametric graphing of curves by integrating (x'(t), y'(t)) = (cos(s(t)), sin(s(t)) where s(t) is the definite integral of a piecewise function representing the change in the angle the curve is currently traveling along
And using simple, non-piecewise definition of s(t) I managed to graph a circle and something like a gang sign in Wolfram Alpha, finally working out an example with the piecewise put in as this:
[code]Parametric plot x(t) = int(cos(int(Piecewise[{{-1, 0<=r<1}, {-r, 1<=r<2}}],r,0,s)),s,0,t), y(t) = int(sin(int(Piecewise[{{-1, 0<=r<1}, {-r, 1<=r<2}}],r,0,s)),s,0,t)[/code]
And now WA manages to correctly interpret the input, but not graph it or anything so I guess I hit a limit for what it can do
I think the only thing I can do now is get Mathematica...
Messed up on my differential equations final and ended up with a C for the semester. At least I understand Laplace Transforms if that counts for anything.
ive finally gotten enough of the required bullshit for my software degree out of the way (like electrical engineering stuff, econ stuff, professional stuff) to really start on my math minor.
i'm taking discrete mathematics, statistics, probability, and algebra 1, and probably a class called "topics in geometry" because it sounds interesting
and after that i still have a good 3 more courses to choose from, woo
I assume algebra 1 is abstract algebra?
I'd say topic in geometry sounds fun if it's like an intro to differential geometry, but as a math minor I doubt it.
the minor has nothing to do with the courses, I just take fewer courses from the selection they offer.
its one of the only geometry courses offered, apparently a bird course but still interesting. I like historical math so I think it'll be cool
I'm preparing myself for my first year of engineering physics. The math part of the first year will consist of two analysis courses (both single and multi-variable) and a linear algebra course. What is the best things I can do in order to prepare for the university-level math? I've taken an "introductory course to real analysis" before, if that matters.
Have a good understanding of epsilon-delta proofs? I don't know if you really need "preparation", i.e. any preparation just coincides with a part of the course itself. So preparing would just be spoiling the course I think :v:
In my case, the courses started really from the bottom. You could (in principle) walk in with the knowledge of just basic arithmetic and no idea what a matrix is and you would have no holes in your knowledge in either analysis or linear algebra. It would be tough because some concepts you have to get comfortable with, like epsilon-delta proofs and the idea of an abstract vector space. I struggled a lot with those when I heard of them for the first time.
In retrospect, one thing that could help with both analysis and linear algebra is imho some basic set theory (morphisms, relations, ...), at least the theoretical parts.
Just look at the first chapters of the courses you'll take and maybe delve deeper into things that seem difficult or that you are not familiar with.
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