Search results

  1. Sy123

    Philosophy of Mathematics and Metamathematics

    The philosophy of mathematics asks questions about the foundations of mathematics, validity of certain truths in mathematics, it's assumptions, implications, the correspondence of mathematics and reality and so on. One primary question to ask is whether mathematics is a subject that refers...
  2. Sy123

    HSC 2016 MX2 Marathon ADVANCED (archive)

    Post questions within the scope of Mathematics Extension 2 that are in general Q16 and beyond, focusing on problem solving and neat results within the reach of elementary mathematics.
  3. Sy123

    Poems

    Post good poems here for reflection! All human beings are members of one frame, Since all, at first, from the same essence came. When time afflicts a limb with pain The other limbs at rest cannot remain. If thou feel not for other’s misery A human being is no name for thee. - Saadia Shirazi
  4. Sy123

    Sy123's BOS Minecraft Server

    This is the official thread for the current BOS Minecraft server. To join the server you need to have bought Minecraft and have it installed for the latest version (1.8). The IP of the server is: 119.252.191.106:26757 The server is whitelisted, if you want to be whitelisted, then either...
  5. Sy123

    UWS ATAR Cutoff

    A friend of mine told me that your ATAR goes away after 2 years and universities use your GPA/WAM instead as an "atar" cutoff I'm specifically talking about UWS Medicine, as a GWS student I only need 93.5, my atar is 98.4 If I continue 2015 at USYD Engineering and do well in UMAT, will UWS...
  6. Sy123

    Uniform Probabilities and Borel paradox

    I thought this was an interesting post: http://alexanderpruss.blogspot.com.au/2013/07/uniform-probabilities-and-borel-paradox.html More on Borel paradox: http://en.wikipedia.org/wiki/Borel%E2%80%93Kolmogorov_paradox
  7. Sy123

    Limits and Infinity

    \\ $Comment on the following statement$ \\ \lim_{x \to \infty} x = \infty
  8. Sy123

    Double Induction?

    So I was thinking of whether the following inductive statements are logically valid: Say we have 2 statements, S_1 and S_2 \\ $For the base case,$ \ S_1 \ $is true, assuming$ \ S_1 \ $is true for the general case, then if$ \ S_2 \ $is true, then the inductive step for$ \ S_1 \ $is true$ \\...
  9. Sy123

    HSC 2015 MX2 Integration Marathon (archive)

    Here post integrals for helping 2015 students with integration! Do not post a question until the last one is answered Do not post in the other thread because that is locked ------------- \int_0^{\pi /6} \sin^4 x \cos^3 x \ dx
  10. Sy123

    Life

    yeah I'm not going to waste my post: ----------------------------------- There is no meaning of life on atheism, I think this is clear to anyone who really considers the question properly. If you say, "the meaning of life is happiness" or "the meaning of life is to stay alive and...
  11. Sy123

    Investigation of a certain function

    So, just for fun I wanted to investigate the properties of this function: f(x) = \int_0^{\frac{\pi}{2}} \frac{\sin (xt)}{\sin t} \ $d$t , \ $and$ \ x \in \mathbb{R} Right now I know: \\ $Define$ \ I(N) = \int_0^{\frac{\pi}{2}} \frac{\sin ((2N)t)}{\sin t} \ $d$t , \ N \in \mathbb{N} \\...
  12. Sy123

    Poll: Difficulty of 2013 vs 2014 paper

    Pick whether you found the 2014 paper harder or easier (separated into categories so we can observe bias) EDIT: Why won't it let me make a poll? I selected the option when making the thread
  13. Sy123

    Properties of a special Digit/Sum function

    Hello all, I decided to investigate a function that I thought of: f(n) = \begin{cases}$Sum of digits$ \ \ $if$ \ n \ $is prime$ \\ $Sum of prime factors$ \ \ $if$ \ n \ $is composite$ \end{cases} i.e. n=14 14 -> 9 -> 6 -> 5 Then I decided to iterate f(n), and as expected, if...
  14. Sy123

    Programming Limitations and Project Euler

    Hello all, I am posting this here because it has something to do with mathematics, but mostly programming, however the programming forums are mostly dead. This is regarding Problem 14 of Project Euler I decided to try and compute everything to see if I can brute force out the answer I...
  15. Sy123

    Linear independence

    \\ $If$ \ \vec{v}_1 , \vec{v}_2 , \vec{v}_3 \ \text{are linear independent} \\ \\ $and$ \ \ a\vec{v}_1 + b\vec{v}_2 + c\vec{v}_3 = x\vec{u}_1 + y\vec{u}_2 + z\vec{v}_3 \\ \\ $then this implies$ \ \vec{u}_1 , \vec{u}_2 , \vec{u}_3 \ \text{is linear indepdendent} Is this true? I am very strongly...
  16. Sy123

    Addition of Position Vectors of Reg. Tetrahedron - Spherical Geometry/Vectors

    I recently came across a STEP question involving vectors in 3D Space, and a tetrahedron bound by a Sphere. If we consider the points on the sphere which are the vertices of the regular tetrahedron P_1, P_2, P_3, P_4 And consider the position vectors \mathbf{p_1 , p_2, p_3, p_4} from O...
  17. Sy123

    nth derivative is itself

    Are there any elementary functions with its 3rd, 4th etc derivative is itself? (i.e. f''''=f) If so how would we find these functions? (except for f(x) = 0)
  18. Sy123

    2nd year transfer to Adv Maths USYD from Engineering USYD

    According to: http://sydney.edu.au/science/cstudent/ug/forms/transfer.shtml If I do a BEng in USYD, while doing the appropriate Adv Maths units (MATH1901 and etc), will I be able to internally transfer to 2nd year BSc (Adv Maths). Or would I need to start it again? Thank you
  19. Sy123

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

    A recent Numberphile video had "proven" this result and during their proof they seem to run off the axiom that S = 1 - 1 + 1- 1 + 1 - 1 + \dots = \frac{1}{2} And they said that this is the case since if we stop at an integer N it will be either 1 or 0 depending on the parity of N, so...
  20. Sy123

    USYD - Masters in Engineering (Chemical and Bio-molecular)

    Hello, I am considering doing a Bachelor of Science (Advanced Mathematics) for 3 years before undertaking a Masters in Engineering for another 1.5 years. According to the USYD Masters of Engineering site, I can do a Bachelor of Science degree before doing a Masters in Engineering provided...
Top