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k a March Highlights and 2025 AoPS Online Class Information

jlacosta 0

Mar 2, 2025

March is the month for State MATHCOUNTS competitions! Kudos to everyone who participated in their local chapter competitions and best of luck to all going to State! Join us on March 11th for a Math Jam devoted to our favorite Chapter competition problems! Are you interested in training for MATHCOUNTS? Be sure to check out our AMC 8/MATHCOUNTS Basics and Advanced courses.

Are you ready to level up with Olympiad training? Registration is open with early bird pricing available for our WOOT programs: MathWOOT (Levels 1 and 2), CodeWOOT, PhysicsWOOT, and ChemWOOT. What is WOOT? WOOT stands for Worldwide Online Olympiad Training and is a 7-month high school math Olympiad preparation and testing program that brings together many of the best students from around the world to learn Olympiad problem solving skills. Classes begin in September!

Do you have plans this summer? There are so many options to fit your schedule and goals whether attending a summer camp or taking online classes, it can be a great break from the routine of the school year. Check out our summer courses at AoPS Online, or if you want a math or language arts class that doesn’t have homework, but is an enriching summer experience, our AoPS Virtual Campus summer camps may be just the ticket! We are expanding our locations for our AoPS Academies across the country with 15 locations so far and new campuses opening in Saratoga CA, Johns Creek GA, and the Upper West Side NY. Check out this page for summer camp information.

Be sure to mark your calendars for the following events:
[list][*]March 5th (Wednesday), 4:30pm PT/7:30pm ET, HCSSiM Math Jam 2025. Amber Verser, Assistant Director of the Hampshire College Summer Studies in Mathematics, will host an information session about HCSSiM, a summer program for high school students.
[*]March 6th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar on Math Competitions from elementary through high school. Join us for an enlightening session that demystifies the world of math competitions and helps you make informed decisions about your contest journey.
[*]March 11th (Tuesday), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS Chapter Discussion MATH JAM. AoPS instructors will discuss some of their favorite problems from the MATHCOUNTS Chapter Competition. All are welcome!
[*]March 13th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar about Summer Camps at the Virtual Campus. Transform your summer into an unforgettable learning adventure! From elementary through high school, we offer dynamic summer camps featuring topics in mathematics, language arts, and competition preparation - all designed to fit your schedule and ignite your passion for learning.[/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

Mar 2, 2025

0 replies

k Happy Pi Day!

greenplanet2050 5

N 5 hours ago by Yihangzh

Happy Pi Day! $3.141592653589793238462643383279 50288419716939937510 5820974944 5923078164062862089986280348253421170679$

:D :D :D :D

5 replies

greenplanet2050

Today at 12:10 AM

Yihangzh

5 hours ago

Linear algebra

Dynic 2

N Today at 3:32 PM by loup blanc

Let A and B be two square matrices with the same size. Prove that if AB is an invertible matrix, then A and B are also invertible matrices

2 replies

Dynic

Today at 2:48 PM

loup blanc

Today at 3:32 PM

3-dimensional matrix system

loup blanc 0

Today at 1:04 PM

Let $A=\begin{pmatrix}1&1&0\\0&1&1\\0&0&1\end{pmatrix}$ .
i) Find the matrices $B\in M_3(\mathbb{R})$ s.t. $A^TA=B^TB,AA^T=BB^T$ .
ii) Show that each solution of i) is in $M_3(K)$ , where $K=\mathbb{Q}[\sin^2(\dfrac{2}{3}\arctan(3\sqrt{3}))]$ .
iii) Solve i) when $B\in M_3(\mathbb{C})$ .
EDIT. In iii) we again consider the transpose of $B$ and not its conjugate transpose.

0 replies

loup blanc

Today at 1:04 PM

0 replies

Very hard group theory problem

mathscrazy 3

N Today at 9:50 AM by quasar_lord

Source: STEMS 2025 Category C6

Let $G$ be a finite abelian group. There is a magic box $T$ . At any point, an element of $G$ may be added to the box and all elements belonging to the subgroup (of $G$ ) generated by the elements currently inside $T$ are moved from outside $T$ to inside (unless they are already inside). Initially $T$ contains only the group identity, $1_G$ . Alice and Bob take turns moving an element from outside $T$ to inside it. Alice moves first. Whoever cannot make a move loses. Find all $G$ for which Bob has a winning strategy.

3 replies

mathscrazy

Dec 29, 2024

quasar_lord

Today at 9:50 AM

limit of u(pi/45)

EthanWYX2009 0

Today at 7:08 AM

Source: 2025 Pi Day Challenge T5

Let $\omega$ be a positive real number. Divide the positive real axis into intervals $[0, \omega)$ , $[\omega, 2\omega)$ , $[2\omega, 3\omega)$ , $[3\omega, 4\omega)$ , $\ldots$ , and color them alternately black and white. Consider the function $u(x)$ satisfying the following differential equations:
$u''(x) + 9^2u(x) = 0, \quad \text{for } x \text{ in black intervals},$ $u''(x) + 63^2u(x) = 0, \quad \text{for } x \text{ in white intervals},$ with the initial conditions:
$u(0) = 1, \quad u'(0) = 1,$ and the continuity conditions:
$u(x) \text{ and } u'(x) \text{ are continuous functions}.$ Show that
$\lim_{\omega \to 0} u\left(\frac{\pi}{45}\right) = 0.$

0 replies

EthanWYX2009

Today at 7:08 AM

0 replies

Error in Special AIME Seminar A solution

fermat_sLastAMC 1

N Today at 4:22 AM by MathPerson12321

The text in the following image (of the solution for problem #3 of the practice AIME of 4134 Special AIME Seminar A) should state that the positions of A and B are plotted on the vertical and time is plotted on the horizontal.

Where should I post these kinds of errors in the future?

1 reply

fermat_sLastAMC

Today at 3:44 AM

MathPerson12321

Today at 4:22 AM

Integration Bee Kaizo

Calcul8er 42

N Today at 12:57 AM by awzhang10

Hey integration fans. I decided to collate some of my favourite and most evil integrals I've written into one big integration bee problem set. I've been entering integration bees since 2017 and I've been really getting hands on with the writing side of things over the last couple of years. I hope you'll enjoy!

42 replies

Calcul8er

Mar 2, 2025

awzhang10

Today at 12:57 AM

Contest collection PDFs don't work when LaTeX is embedded within BBCode

Equinox8 5

N Yesterday at 11:26 PM by jlacosta

This could very well be reported before, however a quick search did not find anything.

While embedding LaTeX commands within BBCode (like this: [i]text $\dfrac{1}{2}$ text[/i]) typically displays as intended within a forum, trying to render a contest collection using these commands breaks the PDF renderer.

5 replies

Equinox8

Feb 26, 2025

jlacosta

Yesterday at 11:26 PM

k 2023 IMO

ostriches88 4

N Yesterday at 11:23 PM by jlacosta

As outlined in this (locked) post, the forum/blog creation message is out of date. It has been over a year since that post, and it still has not changed. I don't know if this got lost somewhere in the "passing this along" chain or if it was determined to be irrelevant, but it seems like a relatively simple fix ;)

4 replies

ostriches88

Mar 10, 2025

jlacosta

Yesterday at 11:23 PM

maximum value

Tip_pay 3

N Yesterday at 9:37 PM by alexheinis

Find the value $x\in [0,4]$ at which the function $f(x)=\int_{0}^{\sqrt{x}}\ln \frac{e}{1+t^2}dt$ takes its maximum value

3 replies

Tip_pay

Yesterday at 8:48 PM

alexheinis

Yesterday at 9:37 PM

Spheres and a point source of light

mofidy 3

N Yesterday at 9:22 PM by kiyoras_2001

How many spheres are needed to shield a point source of light?
Unfortunately, I didn't find a suitable solution for it on the page below:
https://artofproblemsolving.com/community/c4h1469498p8521602
Here too, two different solutions are given:
https://math.stackexchange.com/questions/2791186

3 replies

mofidy

Mar 11, 2025

kiyoras_2001

Yesterday at 9:22 PM

Real Analysis

rljmano 4

N Yesterday at 4:38 PM by alexheinis

In [0 1], {f(t)}*{f’(t)-1} =0 and f is continuously differentiable. How do we conclude that either f is identically zero or f’(t) is identically 1 in [0 1]?

4 replies

rljmano

Yesterday at 6:32 AM

alexheinis

Yesterday at 4:38 PM

find the isomorphism

nguyenalex 14

N Yesterday at 1:49 PM by Royrik123456

I have the following exercise:

Let $E$ be an algebraic extension of $K$ , and let $F$ be an algebraic closure of $K$ containing $E$ . Prove that if $\sigma : E \to F$ is an embedding such that $\sigma(c) = c$ for all $c \in K$ , then $\sigma$ extends to an automorphism of $F$ .

My attempt:

Theorem (*): Suppose that $E$ is an algebraic extension of the field $K$ , $F$ is an algebraically closed field, and $\sigma: K \to F$ is an embedding. Then, there exists an embedding $\tau: E \to F$ that extends $\sigma$ . Moreover, if $E$ is an algebraic closure of $K$ and $F$ is an algebraic extension of $\sigma(K)$ , then $\tau$ is an isomorphism.

Back to our main problem:

Since $K \subset E$ and $F$ is an algebraic extension of $K$ , it follows that $F$ is an algebraic extension of $E$ . Assume that there exists an embedding $\sigma : E \to F$ such that $\sigma(c) = c$ for all $c \in K$ . By Theorem (*), there exists an embedding $\tau : F \to F$ that extends $\sigma$ . Since $F$ is algebraically closed, $\tau(F)$ is also an algebraically closed field.

Furthermore, because $\sigma(c) = c$ for all $c \in K$ and $\tau$ is an extension of $\sigma$ , we have
$K = \sigma(K) \subset K \subset \sigma(E) \subset \tau(F) \subset F.$
This implies that $F$ is an algebraic extension of $\tau(F)$ . We conclude that $F = \tau(F)$ , meaning that $\tau$ is an automorphism. (Finished!!)

Let choose $F = A$ be the field of algebraic numbers, $K=\mathbb{Q}$ . Consider the embedding $\sigma: \mathbb{Q}(\sqrt{2}) \to \mathbb{Q}(\sqrt{2}) \subset A$ defined by
$a + b\sqrt{2} \mapsto a - b\sqrt{2}.$ Then, according to the exercise above, $\sigma$ extends to an isomorphism
$\bar{\sigma}: A \to A.$ How should we interpret $\bar{\sigma}$ ?

14 replies

nguyenalex

Mar 12, 2025

Royrik123456

Yesterday at 1:49 PM

find the convex sets satisfied

nguyenalex 2

N Yesterday at 9:54 AM by ILOVEMYFAMILY

In $\mathbb{R}^2$ , let $B = \{(x, y) \mid x \geq 0\}$ . Find all convex sets $C$ such that

$\mathcal{E}(B \cup C) = B \cup C.$

2 replies

nguyenalex

Yesterday at 8:57 AM

ILOVEMYFAMILY

Yesterday at 9:54 AM

Happy Pi Day!

G H J

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greenplanet2050

1281 posts

greenplanet2050

#1 h Today at 12:10 AM

Y by

Happy Pi Day! $3.141592653589793238462643383279 50288419716939937510 5820974944 5923078164062862089986280348253421170679$

This post has been edited 1 time. Last edited by greenplanet2050, Today at 12:10 AM

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959 posts

#2 h Today at 1:42 AM • 1 Y

Y by At777

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639 posts

#3 h 6 hours ago

Y by

happy pi day!!!!!!

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639 posts

#4 h 5 hours ago

Y by

this is all the pi numbers I remember 3.14159265

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174 posts

#5 h 5 hours ago

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3.1415926535893238…..

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374 posts

#6 h 5 hours ago

Y by

arsenal2012 wrote:

3.1415926535893238…..

bro, pi day was yesterday.

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