>>7020951 Oh i just forgot what that was called. >>7020954 They are simple from a pure math perspective and i know them because i study math but i also study physics and you don't learn most of these outside of math
>>7021031 Why do people think CS majors don't do math? Maybe at your shitty institution they just program fizzbuzz for 4 years or whatever but at most schools CS students are usually required to excel at mathematics.
>>7021058 >Never heard of computability theory >Never heard of algorithm design >Never heard of group theoretic word problems >Never heard of Turing machines I'm not even a CS fag and I pity your idiocy.
>>7021110 I'm not the person you've been corresponding with, but you are highly underestimating the math required for those topics. Unlike your shitty university, my university host outstanding mathematicians which studies fields in recursion theory, etc. It is apparent you go a shit university, because I can go ahead and eliminate that you do not attend schools such as Berkeley, Chicago, Cornell, Michigan, etc. These universities offer courses in mathematical logic, and if you ever took a few graduate courses in recursion theory, reverse math and so forth then you'd realize your 'muh undergrad rigor in analysis etc., etc.' will seem like child's play.
I mean it's fine to not attend a university as such, but you have a narrow world view, and it isn't your fault your math department is outside the top 10/doesn't teach courses beyond the vanilla standard.
Even if you did attend such a university, then you won't be taken seriously in the field. I certainly wouldn't.
>>7021378 What in that post made you think I was edgy? I'm just an artist with a somewhat sciency day job who browses 4chan in quiet times and enjoys reading these threads. If anyone's trying to be edgy here it looks like it's you.
>>7021435 >Yeah, no. Even at Berkeley and Cornell, the undergraduate CS courses are pathetic.
I'm not a CS major. I'm a math major that took math courses in recursion theory. I'm pretty sure they were more rigorous than the CS counterparts, but they cover the same topics in terms of computability. So, no, those courses are not 'pathetic'.
>>7021378 >Why would a scientist need to prove there are infinitely many primes? It's high school math. Every self respecting scientist can do math. If you can't proof it, you shouldn't call yourself a scientist.
>>7020939 I'm an hybrid between theoretical physics and engineer. Is it bad if I can't really come up with a way by myself to formally prove things like 4, 5 or 14? I'm pretty sure I could understand the concepts in half an hour at most but it's just not things I've never had to think about.
It's 6th grade elementary school math at best and really should be done by the 3rd grade.
>>7021458 >Is it bad if I can't really come up with a way by myself to formally prove things like 4, 5
Yes because they are so trivial and straight forward you should be able to do them.
for 4 see >>7021027 for 5, assume √2=p/q with GCD(p,q)=1. Can you tell if p and/or q is even? Do you see the contradiction? for 14, just show [0,1] is uncountable. Assume f(n) can count them all and let d(n) be the nth digit of f(n). Can you find a new number in [0,1] that was missed for all n?
1. Just remember the equation and fix it to ax^2+bx+c=0. 2. Mark the integral with "I" and find I^2 as double integral. 3. Drav a square and divide it with 4 secants. 4. Antithesis, there are finitely many primes. Multiply them all and add one, none of them divides the number, so it has dividers that doesn't belong to that group. 5. Antithesis, square root of two is rational p/q. square the equation, multiply by q^2 and look if the sides are divisible by 2. 6. For x^n use definition and binomial equation. For sin(x) use trigonometrial identities and the limit of sin(x)/x=1. 7. Draw a picture buy Newtons method also has many drawbacks.
>>7021792 2 is really really really really easy. You could absolutely do it you just have to know the trick. Look up "Gaussian Integral" on youtube and you'll probably be able to find a video showing how to solve that integral.
>>7021792 >I can do these except for 2, 11 and 12 >I'm going to school for engineering
Gaussians are fucking important in engineering Euler identity is really fucking important in engineering Minimizing error with least squares (point to solution "plane"/space) is fucking important in real life engineering
>>7021849 Abstract algebra is pretty autistic and useless. I mean it's okay to know how to use the most important results from algebra to apply them in other fields of math, but doing algebra as an end in itself is wasted time, almost on par with philosophy.
>>7021908 >coming up with novel unifying theories encompassing the entirety of several scientific fields vs >solve some basic 2nd year undergrad level problems that are so trivial they wouldn't even be on a math exam outside of maybe babbys first proofs class
>>7021951 You say that, but all we hear is: >No it's because I feel like I was born in the 1800s and enjoy massively inconveniencing myself. Also, fear of social interaction? Seriously? The bank tellers probably think "oh, there's that massive douche who hits on us when he comes in every week" whenever they see you.
>>7021956 I understand thats a difficult concept for you to understand given your personal experience, but I encourage you to broaden your horizons and entertain the idea that some people who post here are, in fact, normal functioning members of society.
>>7021298 Anon, some of these guys are so dysfunctional outside of a few specific classrooms that it's very important to them to feel superior to everyone who ignored them it high school. Pretending 4chan matters helps them suffer through. Let them have it.
>Science & Math >can't post here if you don't into maths
3rd smartest board...
I'm a fairly successful lawyer, meaning I've had as much if not more (and more difficult) higher education and certification exams than 95% of the posters on this board. I can't into maths for the life of me. The last math class I took was calc 2 in freshman year of undergrad.
But I'm on this board and theres nothing you can do to stop me. I can discuss and enjoy abstract physics, astrophysics, and astronomy with no higher understanding of math because muh theories do not equate to muh data research
>>7022044 >I'm a fairly successful lawyer, meaning I've had as much if not more (and more difficult) higher education and certification exams than 95% of the posters on this board. I can't into maths for the life of me. The last math class I took was calc 2 in freshman year of undergrad. HAHAHAHAHAHAHAHAHAHAHAHAHAHHAAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHA Some of my best friends are lawyer but you sir are so full of yourself
What do you guys think? Is sci legit or is it just a lot of fronting mostly? Honestly, Im in my second year at a good university, math major. I am no expert and I def not compare to what people on sci claim is the norm. for example from this list as of now, I could only do 1 3 4 5 6 8 10 12 and maybe some easy problems with 13? Any legit response?
>>7022088 Yeah, /sci/ and 4chan in general is mostly dickwaving, trolling and trying to fuck with people.
If you take people seriously when they say stuff like "enjoy being a low iq beta pleb who has a small 7 inch peen and will never amount to anything in life. I bet you can't even squat 3x your bodyweight.", you have bigger problems than proofs.
>>7022108 Okay, but why would a first engineer know that? what course? Im at McGill and know lots of intelligent engineers, I doubt any of them would know what that even means. Im sure there just dumb compared to you, who clearly solved poincares conjecture at age 11 and followed up with a quick proof of P=NP before the end of middle school
Can't do 7 or 9 because I don't give a shit about differential equations.
The only proof I know for pythagorean's theorem is the visual one, but I guess that's good enough. Actually, I suppose I could proof it using sin and cos after defining them by their taylor series, but I feel like that is cheating.
This thread confirms why you guys are future Elliott Rogers, and rage at stupid shit that no one cares. This HURRR DURRR MUH FIELD IS BETTA THAN YOOOURS, is retardation, not autism. You guys fight over things someone else has solved, and claim it as your. This is fraud behavior, not intelligence. Any monkey can learn these proofs, but can you solve existing problems with no solutions? Also if you're in America, good luck getting funding its going to get deeper budget cuts. Ted Cruz is the chair of the science, space, and whatever the other thing is called.
>>7022088 You should REALLY be able to do 11 and 14. The former is basic calculus, and the latter is one of the more famous proofs out there, not to mention that diagonal arguments apply in a lot of other situations in other ways.
2 is famous so you should learn it - it's a really cool proof and quite short. It's an exercise in Rudin (with hints given)
I think for 13 the image is only implying that you should be able to do basic ones, obviously there can be vary hard induction proofs.
>>7022150 I know you're just some punk kid who think he's hot shit. Well you're not, you are taking someone work as your own, and then saying others are stupid, because you learn how to copy someone answer. Newsflash engineers in general don't have great math rigor. Some maybe able to do ODE, or higher, but in the industry you're mainly doing at best third semester calc. Your bosses will not trust you to do your own work, because of human error. So you need a computer to do it for you. By the way this younger is dumber than their parents. There are a lot of studies on this subject. Even in tier 1 universities, the kids have poor rigor in their subjects.
>>7020939 I can't do one. I attended nigger tier schools, and never got any help, because teachers were in general not interested in helping. So i just gave up, before I even enter the race. Now its too late to learn all of these proofs and maths in general.
>>7022044 >I can discuss and enjoy abstract physics, astrophysics, and astronomy with no higher understanding of math
Nearly as well as a person with no conception of the English language can enjoy Keats or Blake. Yes, I'm sure you can parrot all sorts of neat theories you've heard discussed by qualified individuals, but don't presume to have any real understanding of any of the things you listed while discounting mathematics.
>>7022044 lel I know a lawyer and he said his undergrad in engr was way more difficult than anything he had to do in law school. i know this is pasta but just letting you lawfags know your shit is piss ez
>>7022088 I'm not a mathematician, I'm a chemist, I can do 1, 3,4,5,6,7,8,and 14. Probably one of my weakest points is proof by induction. I only know these answers because I've seen the answers from somewhere else. I would've never been able to come up with these myself . I don't understand all this elitism of being able to solve these.
>>7022200 >Nearly as well as a person with no conception of the English language can enjoy Keats or Blake by this logic we shouldn't even bother to learn how to read, because we won't understand reading as linguistic professors. To be fair, even the professional don't know what they're doing. Half the time, they don't understand what they're looking at.
>>7022208 >I don't understand all this elitism of being able to solve these. They went to college, and realized they're not hot shit and someone else is better than them at their field. They like to take credit for someone else work to make themselves feel better.
>>7022221 >These topics aren't anywhere close to being advanced
They're not suppose to be, but OP picture is just a circlejerk of Austimo asshats who don't know what real maths is in real life. This is for high school kids, but most high school kids aren't given proper math rigor. American schools don't teach diddly, nor do Britbongs. You're the one that's getting butthurt, because you are upset a lot of people can't do this, but are scientists. You are by definition Austimo general.
>>7022209 >by this logic we shouldn't even bother to learn how to read
That's a very poor and inaccurate interpretation of what I was trying to get across. We should all strive for understanding. That doesn't imply some sort of specialized expertise. Going back to the analogy; it would make little sense to claim you understand a poem, a sonnet, or whatever else, without having a decent grasp of basic grammar.
>>7022232 >We should all strive for understanding. That doesn't imply some sort of specialized expertise. That's exactly what you didn't say. You told other anon he can't understand it, because he has no training in the subject. He can understand it, to an extent. But you're being an absolutist on the matter.
>>7022242 Nowhere in my post did I say he can't understand it. I only implied that he didn't. That doesn't exclude him from being capable. And I'll stand beside what I said before. Being able to describe theories or put concepts in lay terms, no matter how well-meaning, cannot be mistaken for true understanding.
>>7022256 Sorry, I misread your post as he didn't understand it. You want him to understand the data, jargon, and ideas in an articulated matter. I know what you mean. Although I never major anything related in STEM, I do know what you're trying to say about theories being described in lay terms.
This is a pretty decent list, although some of these need to be scrapped because they should be known to every kid in high school with any interest in mathematics (for example 1 and 3).
Also, you definitely need to add the following:
>Know at least one proof of quadratic reciprocity. This is like the Pythagorean theorem for undergraduates, because there are a ton of proofs for this relatively simple but profound result. >Be able to prove the central limit theorem. This is one of the most important results in mathematics/statistics, with a remarkably simple proof. >Know the proofs to the fundamental theorems of algebra, calculus and arithmetic. You might have mentioned some of these in your OP, but they are all important, and should be trivial to prove, apart from maybe the algebra one.
>>7022271 >They have been doing just that for over 2000 years. This is very basic material from Euclid.
Just because modern schools within the last century decided to become daycares instead of educational facilities does not mean kids are incapable of learning the material they once learnt.
Education in the past was reserved for those who could afford it or tested into the schools. Today, everyone is just pass to the next level because the government wants to compete in the ranking system with other countries as dick measuring. Anyone can learn, but most people have no interest in math or science. If they do, they have been beaten down by school, and just want to move onto getting a job.
>>7022268 No, no, it's perfectly fine. I understand the need for things like that, and it isn't inherently a bad thing. It's simply that when I see somebody claiming knowledge of physics (or any other STEM field) based purely on superficial facts or explanations, I die a little inside.
>>7022290 I'm trying to learn it as a physicist would learn physics. The thing is, my fucking attention span prevents me. But I can understand your feeling toward a passionate subject being bastardized. I try my best to read the literature. But I can't do a proof to save my life. Was never given proofs in my life, just do this problem and output the return.
>>7022324 Most STEM kids do AP calculus or at least rub it out the summer before their first semester. Otherwise you're stuck during your 1st year without being able to take any relevant courses since they all require it.
>>7022344 This board isn't for hobbyists who can sip wine and listen to Mozart and "appreciate" the advancements of scientists, it's for people who aspire to do science. You don't know jack shit about physics. Lurk, but don't post.
>>7022371 Actually, this board is for people like me.
I can post whenever I want, and you can't stop me. Does that bobble your knobbies?
If and when I decide to post, it's clearly in a context where I can add to the conversation. Most often, it's about theoretical space travel or existential concepts too abstract for math. Also known as science is just for academics, you toolbox.
If I did decide to post in an inappropriate context where I cleary don't know what in talking about, that's called trolling and is pretty rare (and obvious) on this board. Trolls get called out and ridiculed. Kinda like your post, pleb
>>7022394 >>7022394 >>7022394 >Most often, it's about theoretical space travel or existential concepts too abstract for math So you're the ones making all the stupid threads. Please just stop making threads. Please.
The only one of those that is really serious is Computability Theory. That said, Computability is really legit shit and it's a really big deal in mathematical foundations and other parts of mathematics. Here are some lecture notes detailing the introductory material. http://www.personal.psu.edu/t20/notes/fom.pdf
Computability also leads to the development of a bunch of other hardcore badass "computable" versions of normal math stuff.
Some other big topics that CSfags get into are Category Theory, Type Theory, and Homotopy Type Theory.
That said, most CS students do not take these courses and instead choose to stick to more practical courses.
>>7022415 >That said, most CS students do not take these courses and instead choose to stick to more practical courses. Because they want to make money some dough, instead of advancing the field. Also most cannot hack higher level maths.
>>7022484 Oddly that's a system I envision a few years ago. I never seen this picture before, but kids are amazingly resilient and eager to learn. They can learn higher level maths at a young age. The concept of limits can be taught to third graders. Teaching them proofs will help their analytical skills. But you need to add in linguistic, history, geography, political science(legitimatize, not clapistan style). The math is correct, but kids need more than STEM subjects.
>>7022593 >I'm not mad. I smoked weed age 14 to 20, retard.
>I stopped now
Now that the neuronal development has ended and your brain has fully matured, you've quit smoking and you think that will change anything. LEL. Damage was already done, kid. You've fucked up your brain when it was growing maturing. You've probably shaved 20+ IQ points with weed.
>but I was always top of the class in math.
kek'd hard. top of the class in some shithole full of other potheads and morons.
>>7022271 >They have been doing just that for over 2000 years. This is very basic material from Euclid. I agree for 1,3,4,5,10,12 and 13. But you can't expect kids 10-11yo solving diff. eq. and integrals while understanding the theory behind them. And no, they didn't do that 2000 years ago, since analysis wasn't a thing until the 17th century. Hence>>7022238
>>7022651 A math teacher is to a mathematician as a gym teacher is to Michael Phelps. You get paid to regurgitate material selected from a book and to answer stupid questions, you aren't paid to think.
>>7022637 Let P(ℕ) be the power set of ℕ. Define f:P(ℕ)↠R as follows. For an element s∈P(ℕ), order the numbers in s by size so s(n) is the nth largest number. Create a decimal 0.2_2_2_2.... where the nth blank is filled by s(n) in binary. If s is finite, end with all 2s. Clearly this is an injection of an uncountable set into R.
>>7022648 So, say that you give me a (infinite) list of numbers in [0,1] indexed by the naturals. Represent them as decimal expansions that do not end in an infinite number of nines.
Consider the nth digit of the nth number on the list. We can define a new number whose nth digit is unequal to the nth digit of the nth number on your list (and doesn't have a 9 in its decimal expansion). Is that number on your list?
So yeah, if you're just sitting there, "counting reals," you'll never be able to exhaust all of them (since you can't exhaust [0,1]).
>>7022688 Who actually uses >muh degerenacy. Stop being a grandpa and have a little bit of fun in your life. For someone that's on a science board you sure seem to ignore the science done showing that marijuana is not harmful to your brain with moderate use.
>>7022642 I guarantee you with 100% certainty there is an autistic math board out there you could join.
This is a fucking math AND science board. That includes all the shit you don't like. Biology, geology, psychology are all included by the rules of this board--not by your own personal ideals. Get over it bro.
>>7021555 9. So, let's look at a general 1st order equation. These are of the form y' + p(t) * y = q(t), and we want to find an equation y(t) that satisfies this equation.. We're looking to reduce this to a function we can simply integrate. So keep in mind the product rule, d(f(x) * g(x)) = f(x) * g'(x) + g(x) * f'(x), we want to reduce the left side of the equation to this. If you look, the left side of the equation already has y' on one term and y on another, so y can act as our g. Therefore, our p is currently f = 1 and f' = p. This is impossible in and of itself, but we can multiply both by a common factor to make these two equations true. Remember that the derivative of the exponential function, exp(x) is itself. Further, by the chain rule, the derivative of exp(u(x)) is u'(x) * exp(u(x)). If we take p to be our u'(x), and P(t) is the definite integral of p(t), then we have exp(P(t)) is p(t) * exp(P(t)). It should be clear now that multiplying the two equations I pointed out earlier (f = 1 and f' = p) by exp(P(t)), we get f = exp(P(t)) and f' = p(t) * exp(P(t)). Multiplying the entire equation by this function, now called our integrating factor, will give us exp(P(t)) * y' + p(t) * exp(P(t)) * y = exp(P(t)) * q(t). The left side can be reduced to exp(P(t)) * y' + (exp(P(t)))' * y, which can be reduced by the product rule to (y * exp(P(t)))'. So now we have (exp(P(t)) * y)' = exp(P(t)) * q(t). Now we can simply integrate to get exp(P(t)) * y = Int(exp(P(t)) * q(t)). Divide by your integrating factor, exp(P(t)) to get your solution.
tldr, multiply by exp(Int(p(t))) (integrating factor), left side reduces to (Int(p(t)) * y)'. Integrate both sides and divide by integrating factor.
>>702155510. I specifically want to discuss, very informally, why the geometric series converges or diverges for certain numbers. So remember that the geometric series is the infinite series over n of r^n. The sum, when it converges, is 1 \ (1 – r). This series only converges for |r| < 1, and diverges for everything else.
So let's look at where it converges first, when r is a fraction. r being less than one, multiplying by itself multiple times will result in a smaller number. As n approaches infinity, r^n approaches 0. So the terms of the series eventually begin to contribute nothing to the overall sum. Therefore, the sum does not increase without bound and the sum converges.
Now let's consider why the sum doesn't converge at r = 1. This is obvious from the convergence formula since the denominator is 1 – r. When r is one, of course you have a division by zero. Look at the sum, though. One to any power is one. Now you are adding together an infinite number of ones. This, of course, leads to a sum that grows without bounds.
This is precisely why the series diverges for any r > 1. Any r > 1 to any power greater than 1 is a larger number than r itself. Again, your sum will grow without bounds, and the sum diverges.
The derivation of 1 \ (1 – r) is left as an exercise.
>>7022229 >OP picture is just a circlejerk of Austimo asshats who don't know what real maths is in real life The picture is literally a collection of legitimate mathematical principles anyone studying real math (or any technical material) should understand, presented as would be seen in any fairly rigorous mathematical setting.
>a lot of people can't do this, but are scientists Aside from the abstract proofs given (4, 5, 14), every competent scientist and engineer will be able to do this. Even then, anyone in a technical field should at least understand the statement being proved in 4, 5, and 14.
You are functionally retarded and cannot handle people on an anonymous image board telling you this.
>>7022344 >I can know plenty of advanced physics and astrophysics without ever picking up a calculator. Absolutely true, because calculators and machines lack the creativity and ingenuity required to do the math required to develop and understand anything beyond high school physics. And so do you.
>>7022127 Your are a massive faggot and probably 29yo and learning FOIL at the local juco. ME/AE/Civil/ChemE all take a course called Statistics & Probability for Engineers. At a large school each department might teacher their own, and at a small school they will shares a course. EE people take two classes, a probability course and then a random process course. Stop shit posting and go practice First-Outside-Inside-Last.
UCLA Mechanical Engineering 174. Probability and Its Applications to Risk, Reliability, and Quality Control Introduction to probability theory; random variables, distributions, functions of random variables, models of failure of components, reliability, redundancy, complex systems, stress-strength models, fault tree analysis, statistical quality control by variables and by attributes, acceptance sampling.
C175A. Probability and Stochastic Processes in Dynamical Systems Probability spaces, random variables, stochastic sequences and processes, expectation, conditional expectation, Gauss/Markov sequences, and minimum variance estimator (Kalman filter) with applications.
UCLA Electrical Engineering
131A. Probability and Statistics Introduction to basic concepts of probability, including random variables and vectors, distributions and densities, moments, characteristic functions, and limit theorems. Applications to communication, control, and signal processing. Introduction to computer simulation and generation of random events.
131B. Introduction to Stochastic Processes Introduction to concepts of stochastic processes, emphasizing continuous- and discrete-time stationary processes, correlation function and spectral density, linear transformation, and mean-square estimation. Applications to communication, control, and signal processing. Introduction to computer simulation and analysis of stochastic processes.
The stuff posted by OP and the other questions later on are all first year stuff and some are set at 16-18 yos. However everyone should be allowed to take part in a discussion about /sci/ however I do feel that if we had entrance requires for this board we'd get less pseudointellectualism shit like >but what if time was a cake Basically if you can't do this shit the only questions you shouldn't be allowed to create threads.
>>7022614 I didn't give a reason to stop smoking weed. You're making false assumptions. I still use drugs, I only do mdma and lsd (every few months). Studying civil engineering atm, I pas all my analysis classes cuz I'm fucking good at math. Studying vector analysis atm. Proved Greens theorem by myself without opening my book/using internet.
It is possible to use drugs w/o fucking up your intelligence. My exams end in 10 days, then I go dancing with these two hot chicks. I will probably take drugs because it makes dancing so much fun. You jelly?
>Can't do any of this >STILL make more money than you dick stroking autists fucking stemfags, why are you all so smug when most of you won't achieve anything? >inb4 muh safe and insignificant research article is an achievement
>>7023686 What the fuck is MV calc? Multivariate? It's certainly not standardized so you will never be able to find an accredited university that accepts it as calc 3 credit, basically your only options are to start out in calc 3 and diff eq, or be a lazy piece of shit and take calc 1 and/or calc 2 over again.
There is some merit to retaking that sequence if you're at a top tier university, like seriously Harvard it's not even worth it at UCLA that's not top 5-10 worldwide, otherwise calc 1 is a complete waste of time and calc 2 is as well unless you didn't learn it that well in high school and need more practice.
>>7023686 Assuming you got college credit or tested out of vector calc:
ODEs, Proofs, and Matrix Algebra in the fall followed by Linear Algebra/Vector Spaces, (Complex Variables or Topology or Differential Geometry of Curves and Surfaces), and PDEs in the spring. Then brace your ass for 2 semesters each of Real Analysis and Abstract Algebra the follow year.
Different schools name their courses differently. The problem is whether he did it as a joint community college class and can get credit for it or needs to convince the math department/adviser/chair he knows it and can skip it for something else.
>>7023857 UCLA student here. We get rated in the top ten occasionally, but that's mostly for grad school. We also have "honors" courses in the math department, which pull some of their homework problems from the Ivy league and even graduate level courses of other schools. They can be pretty damn tough. Lots of students who go through the honors sequences sign up for grad courses, too.
>>7023861 What the hell is "Matrix Algebra" and "Proofs"? Certainly you don't have entire courses dedicated to those topics.
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