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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Apr 2, 2025
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]
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All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.

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0 replies
jlacosta
Apr 2, 2025
0 replies
the circle problem
miquelmas   0
an hour ago
Source: Olympiad of the city of Almaty (selection for the IZhO) 2010
The circle ω is centered at the quadrilateral ABCD. The lines AB and CD meet at point K, and the lines AD and BC meet at point L. A line passing through the center of ω and perpendicular to KL intersects KL, CD and AD at P, Q and R respectively. We need to prove that the lines QL, BP and KR all intersect at the same point.
0 replies
miquelmas
an hour ago
0 replies
How many approaches you got? (A lot)
IAmTheHazard   84
N 2 hours ago by User141208
Source: USAMO 2023/2
Let $\mathbb{R}^+$ be the set of positive real numbers. Find all functions $f \colon \mathbb{R}^+ \to \mathbb{R}^+$ such that, for all $x,y \in \mathbb{R}^+$,
$$f(xy+f(x))=xf(y)+2.$$
84 replies
IAmTheHazard
Mar 23, 2023
User141208
2 hours ago
MasterScholar North Carolina Math Camp
Ruegerbyrd   5
N 3 hours ago by ohiorizzler1434
Is this legit? Worth the cost ($6500)? Program Fees Cover: Tuition, course materials, field trip costs, and housing and meals at Saint Mary's School.

"Themes:

1. From Number Theory and Special Relativity to Game Theory
2. Applications to Economics

Subjects Covered:

Number Theory - Group Theory - RSA Encryption - Game Theory - Estimating Pi - Complex Numbers - Quaternions - Topology of Surfaces - Introduction to Differential Geometry - Collective Decision Making - Survey of Calculus - Applications to Economics - Statistics and the Central Limit Theorem - Special Relativity"

website(?): https://www.teenlife.com/l/summer/masterscholar-north-carolina-math-camp/
5 replies
Ruegerbyrd
Today at 3:15 AM
ohiorizzler1434
3 hours ago
9 Physical or online
wimpykid   0
4 hours ago
Do you think the AoPS print books or the online books are better?

0 replies
wimpykid
4 hours ago
0 replies
Three variables inequality
Headhunter   6
N 4 hours ago by lbh_qys
$\forall a\in R$ ,$~\forall b\in R$ ,$~\forall c \in R$
Prove that at least one of $(a-b)^{2}$, $(b-c)^{2}$, $(c-a)^{2}$ is not greater than $\frac{a^{2}+b^{2}+c^{2}}{2}$.

I assume that all are greater than it, but can't go more.
6 replies
Headhunter
Apr 20, 2025
lbh_qys
4 hours ago
Sequence
lgx57   8
N 5 hours ago by Vivaandax
$a_1=1,a_{n+1}=a_n+\frac{1}{a_n}$. Find the general term of $\{a_n\}$.
8 replies
lgx57
Apr 27, 2025
Vivaandax
5 hours ago
AMSP Combo 2 and Alg 2.5
idk12345678   4
N 6 hours ago by Bread10
Im gonna be taking Geo 2 and i was deciding if to take combo 2, alg2.5, both, or neither.

My main goal is to qualify for JMO in 10th grade(next yr). Ive done aops int c+p but i didnt fully understand everything.

Would combo 2 and/or alg 2 be good for jmo qual?
4 replies
idk12345678
Yesterday at 2:12 PM
Bread10
6 hours ago
Geometric inequality
ReticulatedPython   3
N Today at 4:27 AM by ItalianZebra
Let $A$ and $B$ be points on a plane such that $AB=n$, where $n$ is a positive integer. Let $S$ be the set of all points $P$ such that $\frac{AP^2+BP^2}{(AP)(BP)}=c$, where $c$ is a real number. The path that $S$ traces is continuous, and the value of $c$ is minimized. Prove that $c$ is rational for all positive integers $n.$
3 replies
ReticulatedPython
Apr 22, 2025
ItalianZebra
Today at 4:27 AM
Transformation of a cross product when multiplied by matrix A
Math-lover1   1
N Today at 1:02 AM by greenturtle3141
I was working through AoPS Volume 2 and this statement from Chapter 11: Cross Products/Determinants confused me.
[quote=AoPS Volume 2]A quick comparison of $|\underline{A}|$ to the cross product $(\underline{A}\vec{i}) \times (\underline{A}\vec{j})$ reveals that a negative determinant [of $\underline{A}$] corresponds to a matrix which reverses the direction of the cross product of two vectors.[/quote]
I understand that this is true for the unit vectors $\vec{i} = (1 \ 0)$ and $\vec{j} = (0 \ 1)$, but am confused on how to prove this statement for general vectors $\vec{v}$ and $\vec{w}$ although its supposed to be a quick comparison.

How do I prove this statement easily with any two 2D vectors?
1 reply
Math-lover1
Yesterday at 10:29 PM
greenturtle3141
Today at 1:02 AM
Geometry books
T.Mousavidin   4
N Today at 12:10 AM by compoly2010
Hello, I wanted to ask if anybody knows some good books for geometry that has these topics in:
Desargues's Theorem, Projective geometry, 3D geometry,
4 replies
T.Mousavidin
Yesterday at 4:25 PM
compoly2010
Today at 12:10 AM
trigonometric functions
VivaanKam   3
N Yesterday at 10:08 PM by aok
Hi could someone explain the basic trigonometric functions to me like sin, cos, tan etc.
Thank you!
3 replies
VivaanKam
Yesterday at 8:29 PM
aok
Yesterday at 10:08 PM
Inequalities
sqing   16
N Yesterday at 5:25 PM by martianrunner
Let $ a,b \in [0 ,1] . $ Prove that
$$\frac{a}{ 1-ab+b }+\frac{b }{ 1-ab+a } \leq 2$$$$ \frac{a}{ 1+ab+b^2 }+\frac{b }{ 1+ab+a^2 }+\frac{ab }{2+ab }  \leq 1$$$$\frac{a}{ 1-ab+b^2 }+\frac{b }{ 1-ab+a^2 }+\frac{1 }{1+ab  }\leq \frac{5}{2}$$$$\frac{a}{ 1-ab+b^2 }+\frac{b }{ 1-ab+a^2 }+\frac{1 }{1+2ab  }\leq \frac{7}{3}$$$$\frac{a}{ 1+ab+b^2 }+\frac{b }{ 1+ab+a^2 } +\frac{ab }{1+ab }\leq \frac{7}{6 }$$
16 replies
sqing
Apr 25, 2025
martianrunner
Yesterday at 5:25 PM
Geometry Angle Chasing
Sid-darth-vater   6
N Yesterday at 2:18 PM by sunken rock
Is there a way to do this without drawing obscure auxiliary lines? (the auxiliary lines might not be obscure I might just be calling them obscure)

For example I tried rotating triangle MBC 80 degrees around point C (so the BC line segment would now lie on segment AC) but I couldn't get any results. Any help would be appreciated!
6 replies
Sid-darth-vater
Apr 21, 2025
sunken rock
Yesterday at 2:18 PM
BABBAGE'S THEOREM EXTENSION
Mathgloggers   0
Yesterday at 12:18 PM
A few days ago I came across. this interesting result is someone interested in proving this.

$\boxed{\sum_{k=1}^{p-1} \frac{1}{k} \equiv \sum_{k=p+1}^{2p-1} \frac{1}{k} \equiv \sum_{k=2p+1}^{3p-1}\frac{1}{k} \equiv.....\sum_{k=p(p-1)+1}^{p^2-1}\frac{1}{k} \equiv 0(mod p^2)}$
0 replies
Mathgloggers
Yesterday at 12:18 PM
0 replies
2025 Math and AI 4 Girls Competition: Win Up To $1,000!!!
audio-on   63
N Yesterday at 12:56 AM by RainbowSquirrel53B
Join the 2025 Math and AI 4 Girls Competition for a chance to win up to $1,000!

Hey Everyone, I'm pleased to announce the dates for the 2025 MA4G Competition are set!
Applications will open on March 22nd, 2025, and they will close on April 26th, 2025 (@ 11:59pm PST).

Applicants will have one month to fill out an application with prizes for the top 50 contestants & cash prizes for the top 20 contestants (including $1,000 for the winner!). More details below!

Eligibility:
The competition is free to enter, and open to middle school female students living in the US (5th-8th grade).
Award recipients are selected based on their aptitude, activities and aspirations in STEM.

Event dates:
Applications will open on March 22nd, 2025, and they will close on April 26th, 2025 (by 11:59pm PST)
Winners will be announced on June 28, 2025 during an online award ceremony.

Application requirements:
Complete a 12 question problem set on math and computer science/AI related topics
Write 2 short essays

Prizes:
1st place: $1,000 Cash prize
2nd place: $500 Cash prize
3rd place: $300 Cash prize
4th-10th: $100 Cash prize each
11th-20th: $50 Cash prize each
Top 50 contestants: Over $50 worth of gadgets and stationary


Many thanks to our current and past sponsors and partners: Hudson River Trading, MATHCOUNTS, Hewlett Packard Enterprise, Automation Anywhere, JP Morgan Chase, D.E. Shaw, and AI4ALL.

Math and AI 4 Girls is a nonprofit organization aiming to encourage young girls to develop an interest in math and AI by taking part in STEM competitions and activities at an early age. The organization will be hosting an inaugural Math and AI 4 Girls competition to identify talent and encourage long-term planning of academic and career goals in STEM.

Contact:
mathandAI4girls@yahoo.com

For more information on the competition:
https://www.mathandai4girls.org/math-and-ai-4-girls-competition

More information on how to register will be posted on the website. If you have any questions, please ask here!


63 replies
audio-on
Jan 26, 2025
RainbowSquirrel53B
Yesterday at 12:56 AM
2025 Math and AI 4 Girls Competition: Win Up To $1,000!!!
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EvaLin
6 posts
#74 • 1 Y
Y by PikaPika999
should i still submit if i can't finish all the problems?
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stuffedmath
550 posts
#75 • 1 Y
Y by PikaPika999
EvaLin wrote:
should i still submit if i can't finish all the problems?

Yes! The problems are designed to be difficult and we would love to see any progress you have made on the problem set!
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WhitePhoenix
42 posts
#76 • 1 Y
Y by PikaPika999
There is about a week left before the submission deadline. Please make sure to submit before April 26th 11:59 PM EST!

We give a lot of prizes in addition to our cash prizes and merchandise for top scorers. Last year, we gave the Passion Award (additional $50 cash prize and certificate) to the student who submitted first, as well as Rising Star Awards for 5th and 6th graders who were not in the top 50 overall but impressed judges by showing tremendous promise.
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mkwhe
168 posts
#77 • 1 Y
Y by PikaPika999
JOIN OUR DISCORD FOR ANY UPDATES, FAQs, AND ANNOUNCEMENTS: https://discord.com/channels/1188231285521535006/1188234090739150950
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mkwhe
168 posts
#78 • 1 Y
Y by PikaPika999
Entries are due in ONE WEEK!
Just a reminder that you can still get partial credit for questions even if you get it wrong! Make sure to submit it, though, so that you can get the credit in the first place! For example, if you show your thought process or get to a certain valuable step in your explanation, you can get points for this!
https://xmathandai4girls.submittable.com/submit
This post has been edited 1 time. Last edited by mkwhe, Apr 19, 2025, 11:46 PM
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audio-on
513 posts
#79 • 2 Y
Y by mathfan2020, PikaPika999
Just an FYI - there are a limited number of spots for this! I'd recommend that participants submit their applications a couple of days prior to the actual submission deadline as spots will be filling up quickly.
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eyzMath
8 posts
#80 • 1 Y
Y by PikaPika999
do the essay questions count in our final score?
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WhitePhoenix
42 posts
#81 • 1 Y
Y by PikaPika999
eyzMath wrote:
do the essay questions count in our final score?

Yes!
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WhitePhoenix
42 posts
#82 • 1 Y
Y by PikaPika999
Also, as a reminder, there are only about 3 days left before the submission deadline. Please make your final revisions in the next day or two and submit! There is a limit to the number of submissions we can take.
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audio-on
513 posts
#83 • 1 Y
Y by PikaPika999
2 days left! If you haven't started your application, there is still time! :) Problem set is doable in a few hours. If you have any questions, please feel free to ask here or on our discord.
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WhitePhoenix
42 posts
#84 • 1 Y
Y by PikaPika999
IMPORTANT ANNOUNCEMENT: We are extending the competition by one week. The new submission deadline is 5/3/25 at 11:59 PM EST. Please make sure to submit by then. That is the hard deadline.
This post has been edited 1 time. Last edited by WhitePhoenix, Apr 25, 2025, 3:54 PM
Reason: Typo
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Penguin117
236 posts
#85 • 1 Y
Y by PikaPika999
WhitePhoenix wrote:
There is a limit to the number of submissions we can take.

How many submissions can you take, ooc :)
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WhitePhoenix
42 posts
#87 • 2 Y
Y by PikaPika999, Penguin117
350 submissions.
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alextheadventurer
74 posts
#88 • 1 Y
Y by PikaPika999
fossasor wrote:
Please read through the thread - this argument has already been had and in any case, arguing about the validity of girl's math competitions does not belong on this thread and is disrespecting the work of the people who have spent so much time putting this contest together.

There's a significant gender gap in STEM, which is why girl-only math competitions make sense: by providing more opportunities for girls, they narrow the gap.

Ah ok, thanks, I perfectly understand
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RainbowSquirrel53B
590 posts
#89 • 3 Y
Y by awesometriangles, PikaPika999, Gabrielle.Esther
WhitePhoenix wrote:
350 submissions.
uhhh how many slots are left ;-;
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