What is 2017: Definition and 169 Discussions

2017 (MMXVII) was a common year starting on Sunday of the Gregorian calendar, the 2017th year of the Common Era (CE) and Anno Domini (AD) designations, the 17th year of the 3rd millennium, the 17th year of the 21st century, and the 8th year of the 2010s decade.
2017 was designated as International Year of Sustainable Tourism for Development by the United Nations General Assembly.

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  1. M

    Programs SULI DOE Acceptance Thread Summer 2017

    Since I don't see a thread for this already, I'm making one. This thread is to post updates in your application process, notably acceptances or waitlists. I applied to SULI at Argonne; they first opened applications up for staff/group review Jan. 26th, and I got an offer in the HEP division...
  2. Ackbach

    MHB Can you prove the power series expansion for (1-2x-x^2) has a specific pattern?

    Here is this week's POTW: ----- Consider the power series expansion \[\frac{1}{1-2x-x^2} = \sum_{n=0}^\infty a_n x^n.\] Prove that, for each integer $n\geq 0$, there is an integer $m$ such that \[a_n^2 + a_{n+1}^2 = a_m .\] ----- Remember to read the...
  3. Euge

    MHB Is a finite group of homeomorphisms with no fixed points able to act properly discontinuously on a Hausdorff space?

    Here is this week's POTW: ----- Suppose $\Gamma$ is a finite group of homeomorphisms of a Hausdorff space $M$ such that every non-identity element of $\Gamma$ is fixed point free. Show that $\Gamma$ acts on $M$ properly discontinuously. ----- Remember to read the...
  4. anemone

    MHB Solution to POTW #251: Find the value of a+b | MathHelpBoards

    Here is this week's POTW: ----- Suppose that for two real numbers $a$ and $b$ the following equality is true: $(a+\sqrt{a^2+1})(b+\sqrt{b^2+1})=1$. Find the value of $a+b$. ----- Remember to read the...
  5. anemone

    MHB Find the Value of a Polynomial with Given Constraints - POTW #250 Jan 17th, 2017

    Here is this week's POTW: ----- Let $P$ be a polynomial such that $P(x)=a_0+a_1x+\cdots+a_nx^n$ where $a_0,\,a_1,\cdots$ are non-negative integer. Given that $P(1)=4$ and $P(5)=152$, find $P(6)$. ----- Remember to read the...
  6. Ackbach

    MHB Can a nonnegative polynomial be expressed as a sum of squares of polynomials?

    Here is this week's POTW: ----- Let $p(x)$ be a polynomial that is nonnegative for all real $x$. Prove that for some $k$, there are polynomials $f_1(x),\dots,f_k(x$) such that \[p(x) = \sum_{j=1}^k (f_j(x))^2.\] ----- Remember to read the...
  7. Ackbach

    MHB How to Find Polynomials for a Piecewise Function?

    Here is this week's POTW: ----- Find polynomials $f(x), \: g(x),$ and $h(x),$ if they exist, such that for all $x,$ \[ |f(x)|-|g(x)|+h(x) = \begin{cases} -1 & \mbox{if $x<-1$} \\ 3x+2 & \mbox{if $-1 \leq x \leq 0$} \\ -2x+2 & \mbox{if $x>0$.}...
  8. Euge

    MHB Is an analytic map with a certain condition injective?

    Here is this week's POTW: ----- Consider an analytic map $f : \Bbb D \to \Bbb C$ such that $f(z) = \sum\limits_{n = 0}^\infty a_n z^n$ for all $z\in \Bbb D$. Prove that $f$ is injective, provided $$\sum_{n = 2}^\infty n\lvert a_n\rvert < \lvert a_1\rvert.$$ ----- Remember to read the...
  9. anemone

    MHB Probability of Player One Winning in N-Sided Die Game | POTW #249 Jan 7th, 2017

    Here is this week's POTW: ----- Two people take turns rolling an N-sided die. The object of the game is to roll a higher number than the previous roll. Failure to roll a higher number results in losing the game. Assuming player one rolls first, find the probability that player one wins the...
  10. Euge

    MHB Can a homeomorphism of the closed unit disk map $S^1$ onto $S^1$?

    Happy New Year, MHB! Since the year has just started I figured I'd start with a light problem which I'm sure several of you can solve. ----- Prove that a homeomorphism of the closed unit disk onto itself must map $S^1$ onto $S^1$. -----Remember to read the...
  11. Ackbach

    MHB Problem of the Week # 247 - Jan 02, 2017

    Here is this week's POTW, the first of the (prime) new year! ----- Prove that, for any integers $a, b, c$, there exists a positive integer $n$ such that $\sqrt{n^3+an^2+bn+c}$ is not an integer. ----- Remember to read the...
  12. anemone

    MHB Solving POTW #248: Prove |a1+2a2+...+na_n|<1 for g(x) with |g(x)|<|sin x|

    Here is this week New Year's POTW::) ----- Let $g(x)=a_1\sin x+a_2\sin 2x+\cdots+a_n\sin nx$, where $a_1,\,a_2,\,\cdots,\,a_n$ are real numbers. Suppose that $|g(x)|<|\sin x|$ for all real $x$. Prove $|a_1+2a_2+\cdots+na_n|<1$. ----- Remember to read the...
  13. S

    Other Which STEM field could be the most employable in 2017?

    Hi everyone! I thought I would pose this question to all of you on PF. Which STEM field do you think could be the most employable in the US and Canada in 2017, based on the following: (1) Past demand in the US and Canada circa 2015 and 2016. (2) Current demand in the US and Canada as of today...
  14. giokrutoi

    2017 times a is a natural number

    Homework Statement find 2017 times A Homework EquationsThe Attempt at a Solution the sum of last members denominator.is 2017 multiplied by 1008 the member before it is 2015 multiplied by 1008 before it 2015 times 1007 2013 times 1007 2013 times 2016 how can i move futher
  15. R

    What are the best Christmas Decoration Ideas for 2017

    Hi, I want some suggestion about christmas decorations, Because I`ll guest a party with my family & friends, So, I need some help. Cheers, Rebeca
  16. gleem

    What is Energy? Join the Flame Challenge 2017 and Explain it to 11 Year Olds!

    In 2012 actor Alan Alda started a competition in which scientists are asked to explain by whatever means a designated phenomenon or concept to 11 year olds. The explanations are judged by students whose schools are participating in the competition worldwide some 26,000 students so far. This...
  17. Borg

    Stargazing U.S. Solar Eclipse of Aug. 21, 2017

    I've been waiting for this for a long time and it's just a little more than a year away now. This will be the opportunity of a lifetime for people in the U.S. The 2017 solar eclipse will be visible across the width of the entire U.S! The points of Greatest Eclipse and Greatest Duration are...
  18. Ivan Seeking

    Stargazing Aug 21st, 2017, a total solar eclipse will cross the US

    And goes directly through Oregon. Woohoo! http://eclipse.gsfc.nasa.gov/SEgoogle/SEgoogle2001/SE2017Aug21Tgoogle.html
  19. apeiron

    News When will the world reach peak fossil fuel production?

    Steve Mohr of Australia's Newcastle University has modeled the Earth's fossil fuel reserves and come up with this massive study (warning: 13mb). PROJECTION OF WORLD FOSSIL FUEL PRODUCTION WITH SUPPLY AND DEMAND INTERACTIONS...
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