/sqt/ - Stupid Question Thread

What is degree in "applied mathematics"? Isn't a physics degree a degree in applied math?

If you assume that there exists a set that contains all sets then you are tacitly assuming that there is no set that isn't cointained in that set.

You are basically asking that if 1+1=2 then can 1+1=3??????? xD hurrrrr

Is computer (hardware) engineering the best for delving into building circuits and everything that follows?
Considering electrical engineering, just not sure on the differences in course material.

Just want to be able to build my own rudimentary circuits and random machinery in my free time.

Best path to get into scientific computing / applied mathematics?

Former biochemistry major, did two years then dropped out because of personal reasons, now want to go back to school. During that time studied math and got into it.

Don't really sure what degree to go back for. CS / Math, Comp. Engineering, Applied Math.

What should I specialise in?

Could you rephrase the question?

If you introduce a gene drive to 100 individuals among a population of 10000 then how does it become ubiquitous among the population? Why isnt it bred out?

Meant to reply to

Ok, well if it conveys a benefit to the inclusive fitness of the organism, then it is highly likely to proliferate throughout the population, obviously.

However, you seem to be specifically inquiring as to how deleterious genes manage to spread through a population and become universal.

So, it is possible that a gene is antagonistically pleiotropic, in that it conveys some form of benefit to survival or reproductive success in younger – fertile – organisms, however causes harmful effects in later life.

Now, to address your main concern, entirely deleterious genes that convey no benefit may proliferate through the gene pool providing that they do not reduce reproductive success by more than 30%.

Essentially, the competitive edge that a higher than 50% chance of transmission provides deleterious genes, is only stable when the detriment to reproductive success is less than 30%.

Can a deleterious gene strongly linked to a beneficial one can remain and proliferate passively with the other ?

Yes, of course, it's rarely the case that gene X is solely responsible for a particular phenotypic effect.

Any given phenotypic effect is generally produced by more than one gene, and its manifestation is dependent on the environment in which it is situated.

Therefore, a potentially deleterious gene that contributes to the inclusive fitness of the organism in the presence of another beneficial gene may proliferate through the population, again providing that the harm to reproductive success is less than 30%.

What's a good minor to take with a physics major? I'm leaning towards Comp.Sci., but Math or extended Physics seem reasonable too.

I plan on continuing to Astrophysics afterwards.

Minors don't mean anything. Just take some graduate level classes.

I remember at my school a math minor with a physics degree was literally just taking Linear Algebra as an elective and boom math minor.

But ya, doesn't really mean much in the long run.

Not him, but does one have to do anything to take graduate level courses or just pass undergrad courses and take graduate courses as an elective?

For associativity of composition of functions what is the order you evaluate the functions in the below composition?

(f o g) o h

do you evaluate h first then (fog) due to left to right evaulation or do you evaluate (fog) then h?

say

h(x)=y
g(y)=x
f(z)=t

It isn't cleat to me if you evaulate h first or (fog) due to the parathensis.

im trying to learn linear algebra but i dont understand how Ab1 becomes [11, -1], same with Ab2 and Ab3
(also how do i latex on here)

Just matrix multiplication

o shit im retarded, thanks user

Will I be able to grasp stochastic calculus if the most advanced Calc course I've ever taken is AP Calculus BC?

niggers

Oh ok, sweet.

possibly. Depends how deep into the theory they get.
You need a primer on statistics too

What are the pros/cons of Civil Engineering?

>Inb4 it's not mechanical

Depends. You might have to contact the professor and ask for prerequisites.

Some classes legit require none.

Can someone address this question?

I believe you evaluate h then (fog)

Why are cosets defined the way they are? Or rather, why is the equivalence relation that generates them defined the way it is? My book defines them as:

Let H be a subgroup of G. Define x~y xy^-1 is in H, x and y in G.

The equivalence classes are then Hg = {x in G : x=hg, h in H}

For some reason this just isn't clicking for me. Am I missing something?

Composition is defined by
(p o q) x = p (q x)
So
((f o g) o h) x = (f o g) (h x) = f (g (h x))
(f o (g o h)) x = f ((g o h) x) = f (g (h x))

Why do discretized values so often involve fractions, specifically 1/2? Most obvious example is spin half-integers. For quark charges in thirds I can presume history of charge reason enough, but spin seems to have involved half-integers from the beginning.

cosets are a useful notion, mostly because you define them to eventually define the notion of a normal subgroup, where the cosets themselves form a group

though the better definition of a normal subgroup is one that can be a kernel, these two definition turn out to be equivalent though

way down the line if you study representation theory or some higher algebra you might see double cosets in something called a 'Hecke algebra'

>majored in Math with a minor in Comp Sci
>feel like I barely learned anything

Is this normal?

if everything keeps going the way it currently has, and assuming we get fusion power implemented in 30 or so years, how long does Veeky Forums think we have before we get immigration crisis' and society breaks down due to global warming?

YES. It just means you have some self awareness. The only way to temper this feeling is to constantly learn.

Spin half-integers is due to the fact that this is the `natural' way to label eigenvalues of the Casimir of su(2). If you want, you could rescale these eigenvalues to find different integers, but then the rest of the physics community would look at you funny. So basically, it is no different than the quark charge thing; one starts with one convention and in order to stick with it, ends up with fractions elsewhere.

Yes.

No wait- No.

This is what I was looking for.

((f o g) o h) x = (f o g) (h x) = f (g (h x))

So, no matter if you do

(f o g) o h or f o (g o h), you will always evaluate it the same by doing h first, followed by g followed by f.

Correct?

so f o g o h could be evaluated without the parenthesis

say you want a job at novartis, should you go the molecular biology path or the biochemistry one?

correct

I really need help with this 'obvious' thing. I cant find this domain. Can someone help me and tell me HOW is this domain found?

Also, is there a general case formula for figuring out logarithms? Like, not by going to the power of 1, than if not to the power of two, than if not to the power of 3 etc till I get there, but a general case method to figure out to what power the base is, if it is equal to a 6 digits number for example.

log is only defined for numbers greater than zero. 2 is obviously greater than zero. When is (1-y) greater than zero? Whenever y < 1

I'm not sure what you mean in the second half. You want to, say, compute the value of log base 7 of 400 or something?
You can do it via Taylor series if you need a precise answer but the fastest way is to just try and estimate it in your head

you're finding the inverse of y, and so you now have x as a function of y (x=-log(1-y)/log2).

so the domain is all possible values of y you can put into the function -log(1-y)/log2

the only place y shows up is in the log(1-y) and this is defined for 1-y > 0 since log is defined only for positive numbers

and so 1> y

>obviously
lmao

the domain of log is (0,infinity)
when you have log(1-y), the domain becomes all of the places where 1-y is in (0,infinity)
in other words, where 1-y is greater than 0

thank you, it all makes sense when you say that logarithm must be greater than zero

Can also anyone help me with |x-1|

whenever you see |f(x)|

Thanks user. This helped quite a bit.

I still dont understand

I understand that |x-1|

never mind, I think I got it, I think I misunderstood thing called subtraction of squares......

|x-1| < 3 if and only if -3 < x - 1 < 3 if and only if -2 < x < 4

What is the cardinality of the set containing all propositions undecidable in ZFC? By a proposition I mean a well founded statement in the language of ZFC and by undecidable I mean undecidable.
I don't have the best understanding of the concept, but I was thinking about it and was wondering if such a set was even well founded. Like could you possibly run into a situation where you'd have to introduce the concept of a class because the set of such propositions is 'too large', violating the axiom of regularity?

Are there any rules about functors between n-categories and m-categories where n doesn't equal m?
like, is it okay to say that there is a functor from Set to Cat?

thank you again, I wish I could thank you somehow in person, this example really helped me out

The set of propositions is countable what do you mean too large?
For the question I would guess the answer is also countable but I have no idea how to prove it.

Nvm. If the set of such propositions was finite you would get a complete recursively axiomatizable description of Peano arithmetic, contradicting Gödel's incompleteness.

What is the "geometrical" meaning or interpretation of the curl and divergence of a vector in R^3?

Like, what does it mean that the curl of E (electric field vector) is zero?

I checked out of biology quite a while ago, bit I do not advise a molecular biology degree. They are a dime a dozen these days, so you will probably be a more competitive applicant with a biochem degree

What would one study to prepare to get a physics degree?
Assume we're starting at middle school and working from scratch because I went to a hippie highschool where we were taught we didn't have to learn or produce to be special.

Taking my first, non-business calculus class this fall. I am average at math but want to be great at it. I went to a middle and high school in one of the worst school districts in the southern United States for math and I am fucked from that. I think my problem lies in the fact that I never really had a good education of algebra and because of that couldn't really build from there. Is Khan Academy the best place to learn that or is there a textbook that will allow me to learn more?

What does it mean when it asks "Find the smallest possible value x^2 + bx + c and of ax^2 + bx + c, for a>0" How would I find it, by what means?

I was writing a program and I found the need to take a number and break it up into its factors such that pq = c where c is constant, and |p - q| is as small as possible for any configuration of p and q where p and q are natural numbers. Using some algebra I found that some number k such that pk - q/k = 0 should be k = sqrt(q/p). From this I came up with an algorithm to take that square root, round it down to the nearest natural number, and then check for the nearest configuration of p and q. I expected there to be deviation above and below the rounded square root for the value of k, but it always seems that k is greater than the rounded square root. I'm wondering if this is true for any value of c, from my testing it seems to be as all numbers up to 2 million are with k being found above the rounded square root. Is there an obvious answer that I'm not seeing or is it more complicated that that?

Not only can you find super cheap (not necessarily that old) textbooks online, you can also access many of these books as free pdfs (just google free x-subject PDF).

Khan is great, especially for brushing up / relearning the basics but I've found Paul's online math notes to be indispensable when going through the calculus sequence. He even has comprehensive cheat sheets for algebra and trig so you can quickly see where you stand with requisite material before pursuing calculus as well as a reference for down the road.

Honestly if I were you i would make sure my understanding of algebra (especially Cartesian coordinate stuff) and trig is air tight before you take your calculus class. If you're wanting to do this quickly with a textbook, perhaps an user can recommend a good pre-calculus book, or you can always search google.

thanks user. I'm not really BAD at math at all. I am able to handle exponential and logarithmic stuff well but collapse with trig. I just really want to succeed in the class. I think without doing some prep I could finish with a mid B but I want to push that to an A and continue to succeed in upper level maths.

How do we eliminate vestigial structures from our genes?
shit seems like a waste of energy

Actually, it's always found below the rounded square root, my bad.

selective breeding or bringing back evolutionary pressure.

As the other user said, the most important thing going into Calculus is to make sure you're very comfortable with all the algebra/trig that you did before it.

If you want to brush up on these concepts, Khan Academy is good, but I highly recommend also using a book. Reading through the material at your own pace and doing lots of exercises is the best way to learn math, Khan Academy is good if you need another perspective because you don't understand something.

One book which I've heard is good is Basic Mathematics by Serge Lang. I haven't read it myself, so I can vouch for it, but looking at the table of contents, it certainly seems to contain everything you would want to know going into a Calculus Course (except possibly chapter 17).

Immortality when?

i would like to study computer science, mathematics and physics and hopefully get phds in all 3. would it be best to triple major (i know i will get flak for asking that) or just go one by one. which should i study first

after you die.

You should study not falling for memes first.

When we go full retard and multiply by dx while solving a differential equation, the prof always goes "lol I hope there are no mathematicians watching", but doesn't explain why we can do that. I'd like to know what I have to study in order to understand when and why we can do that. Is it analysis? Calculus?

I'd go for math first so the others will be easier (for example, you will already know almost all the necessary math for physics and computer science after getting your math degree, you may even get credit for the courses you've already taken, like analysis or linear algebra, though I guess it depends on the country).

Thank you.

By 'too large' I mean you would violate the axiom of regularity.
'Too large' is a shitty description

I'm trying to learn organic chem from scratch.. the q was to draw the chemical and come up with a shorter name.
I don't have the solutions manual.. how did I do?

> so f o g o h could be evaluated without the parenthesis
Parentheses don't matter for associative operations. The definition of associativity is
(a @ b) @ c = a @ (b @ c)
With more than 3 operands, this rule can be applied repeatedly to move the parentheses around arbitrarily (generalized associative law). The order of the operands never changes.

> What does it mean when it asks "Find the smallest possible value x^2 + bx + c and of ax^2 + bx + c, for a>0" How would I find it, by what means?
Any equation of the form y=ax^2+bx+c is a parabola. The curve has the same shape as y=x^2, but may be scaled and translated. Roughly, a determines the scale, b the horizontal (x) translation, c the vertical (y) translation.

If a is positive, the parabola has a minimum in the middle (trough shape), going to +infinity as x goes to -infinity or +infinity.

The parabola y=(x+k)"2 is identical to y=x^2 except that it's shifted left by k. y=(x+k)^2 can be expanded to y=x^2+2kx+k^2. If you set k to b/2, then you get y=x^2+bx+b^2/4. This is the same as y=x^2+bx+c apart from a vertical translation of b^2/4-c. Significantly, both curves have their minima at the same value of x, i.e. at x=-b/2.

If you substitute x=-b/2 into y=x^2+bx+c, you get y=c-b^2/4, which is the minimum value the function can have.

For the case where y=ax^2+bx+c, factor out a to give y=a(x^2+bx/a+c/a) = a(x^2+b'x+c') where b'=b/a and c'=c/a. So the minimum is at x=-b'/2 = -b/2a, and the value is a*(c'-b'^2/4) = a*(c/a-b^2/4a^2) = c-b^2/4a.

A good rule of thumb in math is to do things only if you can prove you can do them.

I'm at my wit's end

Can you mount a keyed shaft (that will be rotating continuously) in a normal ball bearing?

Pls respond

The portion of the shaft resting on the bearing won't be keyed, of course (since it wouldn't fit, see: round peg in square hole)

Analysis

This gets stuck on "Running..." in Mathematica

x2 := x1 + Cos[a]
y2 := y1 + Sin[a]
Px := ((x1*x2 - y1*x2)*(x3 - x4) - (x1 - x2)*(x3*y4 - y3*x4))/((x1 -
x2)*(y3 - y4) - (y1 - y2)*(x3 - x4))
Py := ((x1*x2 - y1*x2)*(y3 - y4) - (y1 - y2)*(x3*y4 - y3*x4))/((x1 -
x2)*(y3 - y4) - (y1 - y2)*(x3 - x4))
Integrate[ArcTan[z / Sqrt[(Px - x1)^2 + (Py - y1)^2]], a]

Am I fucked? Does it look solvable at all?

All right. Do you happen to know what are the prerequisites to reading baby Rudin? Like knowledge of measure theory or set theory?

I've never actually studied it but I would imagine some basic set theory and some experience with proofs is a necessity.

thanks

i am not looking for money or a job. only looking for knowledge

Baby Rudin doesn't have any strictly formal prerequisites in the sense that it defines everything it needs from scratch.

However you should at least have a strong calculus course's experience (e.g. Apostol or Spivak).
Just use another book though Rudin is garbage as a learning tool

I've had calculus courses up to calc II. I have seen too much memery on the internet about rudin to know whether it's good or not, but hey, the book was free, and I saw some lectures recommended on stackoverflow to go with it.

You can still supplement with books that give in depth explanations. Try Abbot's Understanding Analysis (or some similar title).

I tried to get into Mathematical Analysis only to find out most of what I was reading didn't make much sense to me.

I am trying to build from the ground up a foundation that will help me understand all of this stuff so I decided to pick Spivak Calculus.

The first chapter talks about real numbers, mathematical induction, recursion, etc, and then a bunch of problems are presented.

I am ashamed to say that I am having a hard time to understand all of these concepts, ''proofs'' and mathematical language. And couldn't figure out how to solve any of the problems because my brain is just looking for a ''general'' method or a series of steps to solve them. Being completely honest, Ive never been taught this type of Math before.

So how do I make myself less dumb? When do these things ''click'' in ones brain?

Going from babby math to rigorous math is quite difficult, and can take a lot of time. It's something that is recognized to be traumatic.

I mean I took some calc courses back in college. That covered Derivatives, integrals, etc... But everything they teach me there was just so methodical. It was ''Use this equation to get the answer''.

This stuff is just so different from that.

I felt the same thing when I picked up spivak's calculus, I didn't see the motivation behind presenting those rules about numbers. I was like "yeah, I already know that 5+2=2+5, why are you telling me this?". I also felt that the things I had to prove were too basic and I wasn't sure whether I was "cheating" or not. Also, I just wanted to go to the more calculus-y chapters in general.
I haven't finished that book, but I have started uni since, and I think I can give you some help. I think you should write out which one of the 12 properties are you using at each step like this:

Problem 1/ii - prove that x^2-y^2=(x-y)(x+y)
Step 1: use P9 (if a, b and c are any numbers, then a*(b+c)=a*b+a*c). Let a=(x-y):
(x-y)(x+y)=a(x+y)=ax+ay=(x-y)x+(x-y)y
Step 2: use P9 again, twice:
(x-y)x+(x-y)y=xx-yx+xy-yy
Step 3: use P1 (associative law for addition) to add some parentheses:
xx-yx+xy-yy=xx+(-yx+xy)-yy
Step 4: use P5 (the associative law for multiplication) to turn xy into yx:
xx+(-yx+xy)-yy=xx+(-yx+yx)-yy
Step 5: use P3 (existence of additive inverse):
xx+(-yx+yx)-yy=xx+0-yy
Step 6: use P1 to add parentheses:
xx+0-yy=(xx+0)-yy
Step 7: use P2 (existence of an additive identity) to remove that fucking zero:
(xx+0)-yy=xx-yy=x^2-y^2 - changing xx to x^2 and yy to y^2 is just a question of notation, you don't need to invoke any laws to do that