Math Nerds Answer Math Questions

Option 1 at minimum, with Option 3 being the preferred one. Option 2 on its own is a no-go.

Quick question: on a scale of 1-10 how hard are physics and calculus to learn?

In doing some research, the degree I want to get at Michigan State after my time in the Army requires physics and calculus.

For both physics and calculus, it depends heavily on your mathematical background and at what level you want to learn them.

Honestly, I'm not TOO bad at math, it's just teachers and their "show your work!" mentality don't like my own internal jury-rigged-but-same-answer math style, lol.

Honestly I just want to pass my requisites for my microbiology degree with flying colors. I just need a rough estimate on the difficulty, so I know how much time I'll need to allocate those classes.

The "'show your work!' mentality" is because the purpose of mathematical writing is to communicate precise meaning. If you use nonstandard notion without explaining what it means, or if you leave out key steps, then readers have to guess at your reasoning. The "answer" to a mathematical problem isn't the number (or whatever) at the end, but the whole chain of reasoning — a complete proof must give enough information to allow anyone with the necessary background to verify the correctness of the reasoning. It's the same reason why scientists make lab reports and keep detailed records of experiments, rather than just stating their conclusions.

Anyway, like I said, there's no way to give a good estimate of the difficulty without more information. What sort of physics do you want to learn? (Basic Newtonian mechanics is pretty straightforward, quantum gauge theory much less so, and a whole lot in the middle.) At what level do you want to learn calculus — do you want to deeply understand the underlying theory and what's really going on mathematically, or do you just want to get enough familiarity with some standard procedures to be able to compute some simple examples? Is single-variable calculus enough, or do you need to know how to do calculus in more than one dimension (which is more like differential geometry)? I don't know enough about microbiology to have any idea how much mathematics is required for a typical degree.

I feel like a lot of math I had trouble with as a kid as just....come to me over time. How good do you have to be at math to understand C++? Because the program I'm trying to get into requires learning that.

C++ itself doesn't require any mathematics beyond elementary arithmetic, though like all programming languages, the same sort of structured, precise reasoning as in mathematics helps you write code. However, many common programming tasks require some mathematics, and writing algorithms often requires a more careful, systematic understanding of certain mathematical concepts and procedures than computing by hand — it's more like writing proofs in some ways. (Obligatory link to the Curry-Howard correspondence.)

Sounds good enough :)

1+2+3+4+...=-1/12

Can any math nerds out there explain in why you're allowed to treat a series that alternates between 0 and 1 as being equal to 1/2 as an actual number that you're allowed to perform further calculations with?

edited 27th Dec '14 12:22:29 PM by NateTheGreat

The so-called "proof" in that video involves several steps that are logically invalid and results in complete nonsense if you apply the same argument to many other sequences.

What's actually going on is this: There's a famous function ζ, the Riemann zeta function, that's very important in number theory due to its connections with the distribution of prime numbers. Two relevant properties of the Riemann zeta function:

• For all real numbers s > 1, ζ(s) = 1^-s + 2^-s + 3^-s + 4^-s + ...
• ζ(–1) = –1/12.

Now, the series 1^-s + 2^-s + 3^-s + 4^-s + ... only converges for s > 1, so it doesn't even make sense to evaluate it for s ≤ 1. (There's a more general formula for ζ(s) that holds for all complex numbers s.) But if you formally substitute s = –1, then you get the infinite series 1 + 2 + 3 + 4 + ...; this series is still divergent and doesn't have a value, but the zeta function it arises from can be evaluated at s = –1 to get a value of –1/12.

This is an example of zeta function regularization. To summarize, 1 + 2 + 3 + 4 + ... is a divergent series (i.e., doesn't have a value), but applying a certain regularization process to this series results in –1/12. Although this regularization process agrees with ordinary summation for convergent series, it is not summation.

edited 27th Dec '14 10:17:32 PM by Enthryn

Thank goodness someone else thinks it's complete hokum. There's a big difference between a series sum that converges and a series sum that oscillates. You can't treat their results as the same "kind" of number.

The way I would put it is, series that converge have a numerical value. Series that fail to converge (by either oscillating or having unbounded partial sums) don't have a value, and can only be "treated formally".

To make this precise, we can think of series "formally" as formal power series (e.g., 1 + 2 + 3 + 4 + ... is formally identified with 1t⁰ + 2t¹ + 3t² + 4t³ + ...), and consider the "evaluate at 1" map defined on polynomials, which extends by continuity to convergent series, but doesn't extend to divergent series.

edited 28th Dec '14 1:24:16 PM by Enthryn

Basic Algebra question:

Multiplying and simplifying binomials, are there situations where the variables don't become squared or cubed?

Ex:

(2 + 5x)(11 + 12x)

Multiply the front numbers and the back numbers. 2 * 11, 2 *12x, 5x * 11, 5x * 12x.

I solved this and got: 22 + 24x + 55x + 60x^2.

Then combined like terms: 22 + 79x^2 + 60x^2.

Done? Nope. The answer sheet's telling me that 24x and 55x don't combine into a square. The answer is actually: 22 + 79x + 60x^2.

I assume the sheet's just wrong and I'll have to tell someone about it, but maybe I'm wrong and the sum of those terms isn't squared.

Does it make sense to say that 24x + 55x is the same thing as 79x^2? Remember, x isn't just a meaningless mark on the page — it denotes an actual number, and if you don't know anything about which number x is, you can only deduce that two expressions involving x are equal if they're equal no matter which number x happens to be. For example, is it true that 24*2 + 55*2 denotes the same number as 79*2^2? (Seeing what happens if an unknown quantity happens to be a particular number is a good first step to test the validity of claims and to find errors in algebraic manipulations.)

You can also think about physical interpretations of addition and multiplication: If you have a rectangle with side lengths 24 and x, and another rectangle with side lengths 55 and x, what is the total area of the two rectangles? (Area of rectangles is a useful geometric interpretation of multiplication of positive real numbers.)

Keep in mind that numbers don't magically "become squared or cubed" — in mathematics, every step or claim can (and should) be justified by precise reasoning. The key property of addition and multiplication that describes how these operations interact is the fact that multiplication distributes over addition: if r, s, and t are any numbers, then rs + rt is equal to r(s + t), and rt + st is equal to (r + s)t. (Actually, since multiplication is commutative (meaning that rs = sr for any numbers r and s), it's redundant to state distributivity both "on the left" and "on the right", since either one implies the other.)

You can visualize the distributive property for positive real numbers by cutting a rectangle with side lengths r + s and t into two rectangles, one with side lengths r and t, the other with side lengths s and t. (The close relationship between algebra and geometry is a theme that permeates much of modern mathematics.)

edited 5th Jan '15 9:16:19 AM by Enthryn

Find all real solutions of the equation. Check your solutions in the original equation.

121t^4 + 119t^2 − 2 = 0

I'm really lost on what to do. I feel like I'm supposed to take the square root of the whole thing and work from there.

Hint: Does that resemble some other kind of equation you know how to solve?

I'm not looking for the answer for free I'm just really having a hard time and stressing out about this. I just kind of need to go through some of these step by step so I can get the hang of it

I think it's supposed to end up a quadratic equation but the usual layout is aX^2 + bX + c. Square root of X^2 is X of course so that'd fix 119*X^2, but I can't remember how that works with powers greater than 2.

alright spent some more time on it.

got it to

11t^2 + root119t − root2 = 0

I believe I'm supposed to move the root 2 to the 0 side and then work from there

alright i think i've got it.

no. no I don't. Or webassign's being stupid again.

edited 27th Jan '15 7:03:11 PM by Joesolo

As an exponential power square root is half (1/2) so that's why sqrt(t²) = t. Which also makes sqrt(t⁴) = t^4/2 = t².

However you can't say that sqrt(A + B + C) = sqrt(A) + sqrt(B) + sqrt(C). So that's not going to work.

What you'll want to do is pretend that x² is some other variable such as z. Then you get 121z² + 119z + 2 = 0 which is nice and quadratic. Use the quadratic formula to find z (which is actually x²).

edited 28th Jan '15 12:26:57 AM by Luthen

121(t²)² + 119(t²) − 2 = 0

t² = ?

(don't solve for t, solve for t²)

Slight correction:
sqrt(t²) = |t|

So the measurement of a human tooth is 2 centimeters on a 5 foot human. If that human was scaled to 75 feet, how big would their teeth now be?

I want to do this myself but have no idea how, whether by multiplying 2 x 5 or whatever, or converting the feet into centimeters and going from there.

Basically I want to see if the tooth of a 75 foot human is actually 5 feet high, or larger.

Edit: Okay after crunching numbers, a tooth is 2cm, and the average human is 182cm. So if a human became 2,286cm, the tooth would scale upwards...somehow. I forget how to solve for this now. Do you add 1 cm for every 182 or something?

edited 9th Feb '15 11:47:20 PM by Aespai

Your problem assumes that all parts of a human would scale with height; that is, if the human's height doubles, then every other length would double as well. Scaling is a multiplying process. You can express this as

Tn/Hn = Tl/Hl

where Tn = length of normal tooth, Hn = height of normal human, Tl = length of large tooth, Hl = length of large human. Plugin the numbers that you know and solve for the last one.

Also note that you don't need to measure different things in the same units, as long as the units have the same dimensions.

In this case, you're scaling up body length, and asking for tooth length.

So how much bigger is 75 than 5? Divide 75 by 5 to get the scale.

Note that if you use the equation shown in the post above, and treat the units as things you multiply by (which is what they really are), the units actually cancel out, as long as they're the same for the same object (e.g. same unit used for both teeth). Both sides of the equation have the units [in/ft].

edited 14th Feb '15 4:51:49 AM by GlennMagusHarvey

Thanks for both! With those i should be able to solve scaling small to large much easier!

(You actually helped me way easier than my local college professor did, wtf, saying the tooth should have come out 80.085 centimeters)

edited 15th Feb '15 1:11:46 AM by Aespai

Also, if you know geometry, you can also try to think of them as similar triangles, fyi.

Does anyone know of any other free, reputable general math/basic algebra websites, or anything including those two? I've got tigeralgebra, Algebra dot Help, and algebasics.

edited 21st Feb '15 10:17:44 PM by FOFD