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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Yesterday at 3:18 PM
Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.

WOOT early bird pricing is in effect, don’t miss out! If you took MathWOOT Level 2 last year, no worries, it is all new problems this year! Our Worldwide Online Olympiad Training program is for high school level competitors. AoPS designed these courses to help our top students get the deep focus they need to succeed in their specific competition goals. Check out the details at this link for all our WOOT programs in math, computer science, chemistry, and physics.

Looking for summer camps in math and language arts? Be sure to check out the video-based summer camps offered at the Virtual Campus that are 2- to 4-weeks in duration. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!

Be sure to mark your calendars for the following events:
[list][*]April 3rd (Webinar), 4pm PT/7:00pm ET, Learning with AoPS: Perspectives from a Parent, Math Camp Instructor, and University Professor
[*]April 8th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS State Discussion
April 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
[*]April 10th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MathILy and MathILy-Er Math Jam: Multibackwards Numbers
[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
Our full course list for upcoming classes is below:
All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.

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0 replies
jlacosta
Yesterday at 3:18 PM
0 replies
Basis vectors type question
RenheMiResembleRice   1
N 23 minutes ago by RenheMiResembleRice
Source: Yurou Ju, Tuo Guan
Solve the following attached with explanation.
1 reply
RenheMiResembleRice
2 hours ago
RenheMiResembleRice
23 minutes ago
Strange limit
Snoop76   5
N an hour ago by Alphaamss
Find: $\lim_{n \to \infty} n\cdot\sum_{k=1}^n \frac 1 {k(n-k)!}$
5 replies
1 viewing
Snoop76
Mar 29, 2025
Alphaamss
an hour ago
Equivalent definition for C^1 functions
Ciobi_   1
N 3 hours ago by KAME06
Source: Romania NMO 2025 11.3
Prove that, for a function $f \colon \mathbb{R} \to \mathbb{R}$, the following $2$ statements are equivalent:
a) $f$ is differentiable, with continuous first derivative.
b) For any $a\in\mathbb{R}$ and for any two sequences $(x_n)_{n\geq 1},(y_n)_{n\geq 1}$, convergent to $a$, such that $x_n \neq y_n$ for any positive integer $n$, the sequence $\left(\frac{f(x_n)-f(y_n)}{x_n-y_n}\right)_{n\geq 1}$ is convergent.
1 reply
Ciobi_
Yesterday at 1:54 PM
KAME06
3 hours ago
Range of solutions to the log equation
obihs   1
N 4 hours ago by rchokler
Source: Own
Let $n$ be a positive integer, and consider the equation:
$$(\log x)^n - x + 1 = 0\quad\cdots(\heartsuit)$$Answer the following questions. You may assume that $2.7<e<2.72$ is known.

$(1)\quad$ Determine the number of real solutions of equation $(\heartsuit)$ for each $n$.

$(2)\quad$ For $n\ge 3$ , let $r_n$ be the segond largest real solution of $(\heartsuit)$.

$(\i)\quad$ Find $\alpha$ such that $\lim_{n\to\infty} r_n =\alpha.$

$(\i\i)\quad$ Find $\lfloor\beta\rfloor$, where $\beta$ is defined as

$$\lim_{n\to\infty}n(r_n-\alpha)=\beta.$$
1 reply
obihs
Tuesday at 6:18 PM
rchokler
4 hours ago
No more topics!
AB=BA if A-nilpotent
KevinDB17   1
N Mar 30, 2025 by RobertRogo
Let A,B 2 complex n*n matrices such that AB+I=A+B+BA
If A is nilpotent prove that AB=BA
1 reply
KevinDB17
Mar 30, 2025
RobertRogo
Mar 30, 2025
AB=BA if A-nilpotent
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KevinDB17
1 post
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Let A,B 2 complex n*n matrices such that AB+I=A+B+BA
If A is nilpotent prove that AB=BA
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RobertRogo
41 posts
#2 • 2 Y
Y by Filipjack, Ciobi_
The new number of Gazeta Matematica just appeared a few days ago........ : )(( could you guys just give it a few weeks at least, before you start posting active problems? : )(
This post has been edited 1 time. Last edited by RobertRogo, Mar 30, 2025, 9:51 AM
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