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 Aug 10 comment Studying for the Putnam Exam 'the role of talent is vastly overestimated in mathematics' There's this thing called deliberate practice, and this book called The Cambridge Handbook of Expertise and Expert Performance (I very highly recommend this book). It says many things which sound like 'doing deliberate practice 4-5 hours/day for many years makes a mathematician' and 'hard work (deliberate practice) makes an expert, not innate talent'. Btw deliberate practice is hard work but not all hard work is deliberate practice. I just wanted to tell you because you seem very interested in it. Jul 28 comment why can not define G := Group((1),(3,2));; you could always try asking on stackoverflow.com Jul 20 comment How to self study Linear Algebra I love this book so much Elementary Linear Algebra. Jul 3 comment Is memorization a good skill to learn or master mathematics? courses are a joke Jun 15 comment A bounded sequence It looks like you've already answered your own question in the quoted part of your question. Assuming that the quoted part of your question is TZakrevskiy's answer, which specific part of TZakrevskiy's answer are you unsatisfied with? Try to spend some time thinking hard about TZakrevskiy's answer and whether it makes sense or not. I don't know analysis so I can't help you any further Jun 15 comment A bounded sequence What article are you referring to? Jun 14 comment poisson distribution of chocolate @user48495 "We know that the MGF of a multinomial distribution is: $M(t_1, t_2,...t_k-1) = (p_1*e^t_1 + .... + p_k+1*e^t_k+1 + p_k)^n$ hence, the MGF of $X_2$, $X_3$, .... $X_k-1$ is $M(0, t_2,...t_k-1) = (p_1 + .... + p_k+1*e^t_k+1 + p_k)^n$" -adapted from rad at actuarialoutpost.com/actuarial_discussion_forum/archive/… Jun 10 comment My sister absolutely refuses to learn math @IttayWeiss You're right. Jun 10 comment My sister absolutely refuses to learn math I didn't learn much in math classes in elementary. I found math easy but it simply didn't make sense to skip classes and self-study more advanced math. Math in school isn't fun for normal students (students who don't get high scores in math). In fact, we can make psychological arguments that education in school filled to the brink with negative feedback. Math in school only becomes fun if you understand how awesome math is in the 'adult world' Jun 10 comment My sister absolutely refuses to learn math "When I became motivated, which was when I encountered university level mathematics through a book I found" I really want children to be surrounded by university level books. It's important for children to at least know that so many things are explained in those books. When I was young I didn't even know that I could find explanations to things in university books. People just don't give 10-year-olds university books, but this is a wrong attitude. Exposing a child to to university books could motivate him/her to love learning very intensely. Jun 10 comment What subject teaches derivation of trigonometric identities? should I delete my question? Jun 10 comment My sister absolutely refuses to learn math I did spend hours upon hours reading childrens science books, but only much later I realised that I could find answers to these simple things from college books. In fact, if a child has the prerequisite knowledge for a college book, the college book 'reduces' to a 'thick childrens science book'. If a child doesn't have the prerequisite knowledge, then either get a book without the prerequisite, or since she has an expert (i.e. you) around, the expert should explain what she is curious about in simple terms. Jun 10 comment My sister absolutely refuses to learn math It's kind of unrelated but when I was a kid I was curious about why the grass is green. It was only much later when I realised that the answer I was looking for was in Quantum Mechanics. When I asked my elder sister, obviously she didn't tell me to read Quantum Mechanics, since I was probably about 10 years old. However, I really was curious, and I would definitely have been willing to spend hours upon hours learning Quantum Mechanics to understand why grass is green. Jun 10 comment My sister absolutely refuses to learn math In my opinion, you shouldn't focus on making your sister get a good grade in math. Rather, you should focus on cultivating her to become an extraordinary expert. That way, things like 'getting a good grade in math' would be automatically accomplished in her free time. I really find it to be such a waste to care about grades. Good grades in math in school are silly: she should not be wasting her talent memorizing silly things that the education authorities came up with, rather she should focus on long-term development of expert ability. Refer to syllabus.byu.edu/uploads/h52kB4gCLyQP.pdf Jun 10 comment My sister absolutely refuses to learn math instead of teaching her math, try having math conversations with her. Talk about interesting things which are math related. If you want a better idea of what I'm talking about, see youtube.com/watch?feature=player_embedded&v=Bgaw9qe7DEE#! . Also, if she isn't interested in math, try talking to her about other things like physics or biology. The important thing is that she should hopefully develop a love for learning. Once she loves learning, you should 'push' her to read books by telling her 'Hey, these books on Quantum Mechanics explain why grass is green so please read it' etc Jun 10 comment A recursive formula for $a_n$ = $\int_0^{\pi/2} \sin^{2n}(x)dx$, namely $a_n = \frac{2n-1}{2n} a_{n-1}$ I meant $\frac {\cos^3 x}{3} +\cos x +C$ Jun 10 comment Find an orthogonal matrix $Q$ so that the matrix $QAQ^{-1}$ is diagonal. Side note: The eigenvector for eigenvalue 3 is (1,1,1) Jun 1 comment How do I enter the equation $y=\sin\frac{2\pi }{3}x$ into Wolfram Alpha? You should use chat for questions like this. chat.stackexchange.com/rooms/36/mathematics May 31 comment Are these solutions of $2 = x^{x^{x^{\:\cdot^{\:\cdot^{\:\cdot}}}}}$ correct? Note that interpreting it as $$x^2=2$$ demonstrates a problem-solving technique for 'infinite things'. You can use it for other problems involving infinite things which converge. See the solution for problem 4 in this question as an example: math.stackexchange.com/questions/407047/… May 31 comment What was the first bit of mathematics that made you realize that math is beautiful? (For children's book) Let's take an example: 5*5=25. The reason you find it so easy is because you have used it so many times in your life. You don't actually have to 'actively remember' things. Another example is 4+5=9, one 'real way' of finding out that 4+5=9 is by drawing 4 circles and 5 circles, then counting how many total circles there are. We're just so used to addition and multiplication that they have become second nature. An analogy is that when we come across new math in our life, it requires effort to learn it, but after lots of using that math it becomes second nature.