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    Number of ways in a 3D lattice

    Check out this video: https://www.khanacademy.org/math/recreational-math/puzzles/brain-teasers/v/3-d-path-counting-brain-teaser Look at trinomial functions for general case
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    Post-grad feeling the tiniest bit lost

    I had a 3.6 gpa and 3.9 math gpa... Some leadership experiences / TA. Post college won a 2 national tech competitions I guess one of my problems is how to focus my interests
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    Post-grad feeling the tiniest bit lost

    I finished my bachelors a 2-3 years back in mathematics and working a pretty good job in New York in the tech industry, but I am having trouble deciding what to do next! My options are either continue down this route and become a product manager, go more heavily into software engineering...
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    Starting out in pde

    what is the method of characteristics?
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    Starting out in pde

    Homework Statement Hey I'm trying to get a sense of this problem, just starting pde class: au_x+bu_y+cu=0 Homework Equations The Attempt at a Solution Dunno what to do with that last term
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    Set theory

    I don't understand this. I think equivalence classes are generalized equal signs for some property. So (1,1) I understand, but how so for (1,2)?
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    Set theory

    Homework Statement Homework Equations An equivalence relation on a set A, is for a,b,c in A if: a~a a~b => b~a a~b and b~c => a~c The Attempt at a Solution It seems uncomplicated, but I don't know how I would write down a proof. The book I'm using is Topics in Algebra, 1st Edition Herstein
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    Studying What to do about textbooks with solutions

    edit: whoops, the title should read, "what to do about textbooks with no solutions" So I'm trying to learn real analysis (using C.C. Pugh's book) and its going alright until I hit the exercises. There are no solutions! How am I supposed to know I proved something correctly? Is there a website...
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    Riemann Lebesgue Theorem

    Homework Statement We have a corollary that if f(x) is in the set of Riemann Integrable functions and g(x) is continuous, then g(f(x)) is also a riemann integrable function Show that if g(x) is piecewise continuous then this is not true Homework Equations Hint: take f to be a ruler...
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    Analysis problem

    oh, now its clearer. thanks
  11. I

    Analysis problem

    Homework Statement Given x > 0 and n \in N, prove that there is a unique y > 0 s.t. y^n = x exists and is unique Homework Equations Hint is given: consider y = 1. u.b. \{s \in R : s^n < x\} The Attempt at a Solution I'm not used to this style of proof (real analysis I), help would be...
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    Modular arith, number theory problem

    yea, mod is used to represent items in terms of base n. But I don't understand how that is going to change the number of roots in the problem
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    Modular arith, number theory problem

    Homework Statement Find the number of roots for the equation x^2+1=0 \mod n \: for \: n = 8,9,10,45 Homework Equations The Attempt at a Solution I have no idea where to start. Could someone help me understand?
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    How hard is number theory?

    I'm taking the class next semester, and I heard that number theory is usually a difficult subject. Is that true? If so, how should I approach it?
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    British Mensa IQ test upper limit

    Ha ha ha! This is imranq from the MEGA Society! I bet you can feel my overwhelming intellect already. And as you can see, even my own initials spell IQ. How I laugh at you mere mortals... On a more serious note, however, the Stanford-Binet scale (if I remember correctly) was not used to measure...
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    Nicest/most beautiful area/field in maths

    Actually in my university (which is somewhat well regarded), you can easily get a math major without taking number theory (but you may be forced to take something like partial differential equations).
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    Testing Sat subject tests : Math,physics practice papers ?

    Im already in college, and from the states
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    Mathematics careers

    Grad school seems to be a general route (for anything really since math majors have analytical skills to pursue medicine, law, MBA, etc.). However, if the economy were better, you could be working for investment banks (contrary to popular perception, they still exist) and make 300k+ to make even...
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    Reimann Zeta Function at 2

    Thanks a lot!
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    What is mass?

    I don't know much about the inherent nature of mass (or matter) but I do know that no "matter" what happens, we will constantly be explaining the meanings behind the meanings behind the meanings forever, (I mean, what is energy per say?). Instead, take a look at the different types of mass and...
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    The Princeton Guide to Mathematics

    So I went ahead and got it (without a response from PF!). Luckily, the book is amazing in depth and accessibility. It is hefty, a full 1000 pages and costs $99 (but I got it for $50 through a border's deal). I can see this becoming useful in explaining some of the conceptual stuff in future math...
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    Testing Sat subject tests : Math,physics practice papers ?

    For your information, you don't have to take both Math I and IIC since they are looked at separately and are counted equally in college admissions. Personally, I would recommend you take Math IIC since it is curved very well (you can get 8 wrong and still get an 800!), but it is harder than Math...
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    E to i(pi) = -1

    So we can rearrange the formula to look like: \[e^{i\pi} = i^2 \] and therefore \[i = e^{\frac{i\pi}{2}}\] \[\frac{\ln i}{i} = \frac{\pi}{2}\]
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    Nicest/most beautiful area/field in maths

    Like the study of primes, look up Terrence Tao
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    Reimann Zeta Function at 2

    That was fast and I understand it now, thanks! By the way, what is the Fourier series used for?
  26. I

    Reimann Zeta Function at 2

    So we were going over geometric series in my calc class (basic, I know), however I was intrigued by one point that the prof. made during lecture \frac{\pi^2}{6} = \sum^{\infty}_{n=1}\frac{1}{n^2} = \zeta (2) That's amazing (at least to me). Looking for the explanation for this, I found a...
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    Nicest/most beautiful area/field in maths

    Number theory fits your definition pretty well, but it requires a departure from the 'lower' mathematics mindsets
  28. I

    The Princeton Guide to Mathematics

    by Timothy Gowers. How is the book? I'm thinking of purchasing it for my undergrad math career, can anyone recommend it?
  29. I

    Fibonacci series and golden ratio

    Personally, I liked that \[\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\cdots}}}} = \dfrac{1}{1 + \dfrac{1}{1+\frac{1}{1+...}}} = \phi\] or the golden ratio. Also, note (since phi is defined by those recursive sequences) that \frac{1}{\phi} = \phi -1
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    Nested Radicals

    Thanks, now I get it. But is there a way to find out where the sequence converges? We do know that \sqrt{3} < \lim_{n\rightarrow\infty} f(1,n) < 2 . Where: f(a, b) = \begin{cases} \sqrt{a + f(a+1, b-1)} & b > 0 \0 & b = 0 \end{cases}
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