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k a May Highlights and 2025 AoPS Online Class Information
jlacosta   0
May 1, 2025
May is an exciting month! National MATHCOUNTS is the second week of May in Washington D.C. and our Founder, Richard Rusczyk will be presenting a seminar, Preparing Strong Math Students for College and Careers, on May 11th.

Are you interested in working towards MATHCOUNTS and don’t know where to start? We have you covered! If you have taken Prealgebra, then you are ready for MATHCOUNTS/AMC 8 Basics. Already aiming for State or National MATHCOUNTS and harder AMC 8 problems? Then our MATHCOUNTS/AMC 8 Advanced course is for you.

Summer camps are starting next month at the Virtual Campus in math and language arts that are 2 - to 4 - weeks in duration. Spaces are still available - don’t miss your chance to have an enriching summer experience. 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 upcoming events:
[list][*]May 9th, 4:30pm PT/7:30pm ET, Casework 2: Overwhelming Evidence — A Text Adventure, a game where participants will work together to navigate the map, solve puzzles, and win! All are welcome.
[*]May 19th, 4:30pm PT/7:30pm ET, What's Next After Beast Academy?, designed for students finishing Beast Academy and ready for Prealgebra 1.
[*]May 20th, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 1 Math Jam, Problems 1 to 4, join the Canada/USA Mathcamp staff for this exciting Math Jam, where they discuss solutions to Problems 1 to 4 of the 2025 Mathcamp Qualifying Quiz!
[*]May 21st, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 2 Math Jam, Problems 5 and 6, Canada/USA Mathcamp staff will discuss solutions to Problems 5 and 6 of the 2025 Mathcamp Qualifying Quiz![/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
May 1, 2025
0 replies
k i Peer-to-Peer Programs Forum
jwelsh   157
N Dec 11, 2023 by cw357
Many of our AoPS Community members share their knowledge with their peers in a variety of ways, ranging from creating mock contests to creating real contests to writing handouts to hosting sessions as part of our partnership with schoolhouse.world.

To facilitate students in these efforts, we have created a new Peer-to-Peer Programs forum. With the creation of this forum, we are starting a new process for those of you who want to advertise your efforts. These advertisements and ensuing discussions have been cluttering up some of the forums that were meant for other purposes, so we’re gathering these topics in one place. This also allows students to find new peer-to-peer learning opportunities without having to poke around all the other forums.

To announce your program, or to invite others to work with you on it, here’s what to do:

1) Post a new topic in the Peer-to-Peer Programs forum. This will be the discussion thread for your program.

2) Post a single brief post in this thread that links the discussion thread of your program in the Peer-to-Peer Programs forum.

Please note that we’ll move or delete any future advertisement posts that are outside the Peer-to-Peer Programs forum, as well as any posts in this topic that are not brief announcements of new opportunities. In particular, this topic should not be used to discuss specific programs; those discussions should occur in topics in the Peer-to-Peer Programs forum.

Your post in this thread should have what you're sharing (class, session, tutoring, handout, math or coding game/other program) and a link to the thread in the Peer-to-Peer Programs forum, which should have more information (like where to find what you're sharing).
157 replies
jwelsh
Mar 15, 2021
cw357
Dec 11, 2023
k i C&P posting recs by mods
v_Enhance   0
Jun 12, 2020
The purpose of this post is to lay out a few suggestions about what kind of posts work well for the C&P forum. Except in a few cases these are mostly meant to be "suggestions based on historical trends" rather than firm hard rules; we may eventually replace this with an actual list of firm rules but that requires admin approval :) That said, if you post something in the "discouraged" category, you should not be totally surprised if it gets locked; they are discouraged exactly because past experience shows they tend to go badly.
-----------------------------
1. Program discussion: Allowed
If you have questions about specific camps or programs (e.g. which classes are good at X camp?), these questions fit well here. Many camps/programs have specific sub-forums too but we understand a lot of them are not active.
-----------------------------
2. Results discussion: Allowed
You can make threads about e.g. how you did on contests (including AMC), though on AMC day when there is a lot of discussion. Moderators and administrators may do a lot of thread-merging / forum-wrangling to keep things in one place.
-----------------------------
3. Reposting solutions or questions to past AMC/AIME/USAMO problems: Allowed
This forum contains a post for nearly every problem from AMC8, AMC10, AMC12, AIME, USAJMO, USAMO (and these links give you an index of all these posts). It is always permitted to post a full solution to any problem in its own thread (linked above), regardless of how old the problem is, and even if this solution is similar to one that has already been posted. We encourage this type of posting because it is helpful for the user to explain their solution in full to an audience, and for future users who want to see multiple approaches to a problem or even just the frequency distribution of common approaches. We do ask for some explanation; if you just post "the answer is (B); ez" then you are not adding anything useful.

You are also encouraged to post questions about a specific problem in the specific thread for that problem, or about previous user's solutions. It's almost always better to use the existing thread than to start a new one, to keep all the discussion in one place easily searchable for future visitors.
-----------------------------
4. Advice posts: Allowed, but read below first
You can use this forum to ask for advice about how to prepare for math competitions in general. But you should be aware that this question has been asked many many times. Before making a post, you are encouraged to look at the following:
[list]
[*] Stop looking for the right training: A generic post about advice that keeps getting stickied :)
[*] There is an enormous list of links on the Wiki of books / problems / etc for all levels.
[/list]
When you do post, we really encourage you to be as specific as possible in your question. Tell us about your background, what you've tried already, etc.

Actually, the absolute best way to get a helpful response is to take a few examples of problems that you tried to solve but couldn't, and explain what you tried on them / why you couldn't solve them. Here is a great example of a specific question.
-----------------------------
5. Publicity: use P2P forum instead
See https://artofproblemsolving.com/community/c5h2489297_peertopeer_programs_forum.
Some exceptions have been allowed in the past, but these require approval from administrators. (I am not totally sure what the criteria is. I am not an administrator.)
-----------------------------
6. Mock contests: use Mock Contests forum instead
Mock contests should be posted in the dedicated forum instead:
https://artofproblemsolving.com/community/c594864_aops_mock_contests
-----------------------------
7. AMC procedural questions: suggest to contact the AMC HQ instead
If you have a question like "how do I submit a change of venue form for the AIME" or "why is my name not on the qualifiers list even though I have a 300 index", you would be better off calling or emailing the AMC program to ask, they are the ones who can help you :)
-----------------------------
8. Discussion of random math problems: suggest to use MSM/HSM/HSO instead
If you are discussing a specific math problem that isn't from the AMC/AIME/USAMO, it's better to post these in Middle School Math, High School Math, High School Olympiads instead.
-----------------------------
9. Politics: suggest to use Round Table instead
There are important conversations to be had about things like gender diversity in math contests, etc., for sure. However, from experience we think that C&P is historically not a good place to have these conversations, as they go off the rails very quickly. We encourage you to use the Round Table instead, where it is much more clear that all posts need to be serious.
-----------------------------
10. MAA complaints: discouraged
We don't want to pretend that the MAA is perfect or that we agree with everything they do. However, we chose to discourage this sort of behavior because in practice most of the comments we see are not useful and some are frankly offensive.
[list] [*] If you just want to blow off steam, do it on your blog instead.
[*] When you have criticism, it should be reasoned, well-thought and constructive. What we mean by this is, for example, when the AOIME was announced, there was great outrage about potential cheating. Well, do you really think that this is something the organizers didn't think about too? Simply posting that "people will cheat and steal my USAMOO qualification, the MAA are idiots!" is not helpful as it is not bringing any new information to the table.
[*] Even if you do have reasoned, well-thought, constructive criticism, we think it is actually better to email it the MAA instead, rather than post it here. Experience shows that even polite, well-meaning suggestions posted in C&P are often derailed by less mature users who insist on complaining about everything.
[/list]
-----------------------------
11. Memes and joke posts: discouraged
It's fine to make jokes or lighthearted posts every so often. But it should be done with discretion. Ideally, jokes should be done within a longer post that has other content. For example, in my response to one user's question about olympiad combinatorics, I used a silly picture of Sogiita Gunha, but it was done within a context of a much longer post where it was meant to actually make a point.

On the other hand, there are many threads which consist largely of posts whose only content is an attached meme with the word "MAA" in it. When done in excess like this, the jokes reflect poorly on the community, so we explicitly discourage them.
-----------------------------
12. Questions that no one can answer: discouraged
Examples of this: "will MIT ask for AOIME scores?", "what will the AIME 2021 cutoffs be (asked in 2020)", etc. Basically, if you ask a question on this forum, it's better if the question is something that a user can plausibly answer :)
-----------------------------
13. Blind speculation: discouraged
Along these lines, if you do see a question that you don't have an answer to, we discourage "blindly guessing" as it leads to spreading of baseless rumors. For example, if you see some user posting "why are there fewer qualifiers than usual this year?", you should not reply "the MAA must have been worried about online cheating so they took fewer people!!". Was sich überhaupt sagen lässt, lässt sich klar sagen; und wovon man nicht reden kann, darüber muss man schweigen.
-----------------------------
14. Discussion of cheating: strongly discouraged
If you have evidence or reasonable suspicion of cheating, please report this to your Competition Manager or to the AMC HQ; these forums cannot help you.
Otherwise, please avoid public discussion of cheating. That is: no discussion of methods of cheating, no speculation about how cheating affects cutoffs, and so on --- it is not helpful to anyone, and it creates a sour atmosphere. A longer explanation is given in Seriously, please stop discussing how to cheat.
-----------------------------
15. Cutoff jokes: never allowed
Whenever the cutoffs for any major contest are released, it is very obvious when they are official. In the past, this has been achieved by the numbers being posted on the official AMC website (here) or through a post from the AMCDirector account.

You must never post fake cutoffs, even as a joke. You should also refrain from posting cutoffs that you've heard of via email, etc., because it is better to wait for the obvious official announcement. A longer explanation is given in A Treatise on Cutoff Trolling.
-----------------------------
16. Meanness: never allowed
Being mean is worse than being immature and unproductive. If another user does something which you think is inappropriate, use the Report button to bring the post to moderator attention, or if you really must reply, do so in a way that is tactful and constructive rather than inflammatory.
-----------------------------

Finally, we remind you all to sit back and enjoy the problems. :D

-----------------------------
(EDIT 2024-09-13: AoPS has asked to me to add the following item.)

Advertising paid program or service: never allowed

Per the AoPS Terms of Service (rule 5h), general advertisements are not allowed.

While we do allow advertisements of official contests (at the MAA and MATHCOUNTS level) and those run by college students with at least one successful year, any and all advertisements of a paid service or program is not allowed and will be deleted.
0 replies
v_Enhance
Jun 12, 2020
0 replies
k i Stop looking for the "right" training
v_Enhance   50
N Oct 16, 2017 by blawho12
Source: Contest advice
EDIT 2019-02-01: https://blog.evanchen.cc/2019/01/31/math-contest-platitudes-v3/ is the updated version of this.

EDIT 2021-06-09: see also https://web.evanchen.cc/faq-contest.html.

Original 2013 post
50 replies
v_Enhance
Feb 15, 2013
blawho12
Oct 16, 2017
Angle Relationships in Triangles
steven_zhang123   0
33 minutes ago
In $\triangle ABC$, $AB > AC$. The internal angle bisector of $\angle BAC$ and the external angle bisector of $\angle BAC$ intersect the ray $BC$ at points $D$ and $E$, respectively. Given that $CE - CD = 2AC$, prove that $\angle ACB = 2\angle ABC$.
0 replies
steven_zhang123
33 minutes ago
0 replies
acute triangle and its circumcenter and orthocenter
N.T.TUAN   6
N an hour ago by MathLuis
Source: USA TST 2005, Problem 2
Let $A_{1}A_{2}A_{3}$ be an acute triangle, and let $O$ and $H$ be its circumcenter and orthocenter, respectively. For $1\leq i \leq 3$, points $P_{i}$ and $Q_{i}$ lie on lines $OA_{i}$ and $A_{i+1}A_{i+2}$ (where $A_{i+3}=A_{i}$), respectively, such that $OP_{i}HQ_{i}$ is a parallelogram. Prove that
\[\frac{OQ_{1}}{OP_{1}}+\frac{OQ_{2}}{OP_{2}}+\frac{OQ_{3}}{OP_{3}}\geq 3.\]
6 replies
N.T.TUAN
May 14, 2007
MathLuis
an hour ago
Nice one
imnotgoodatmathsorry   3
N an hour ago by Bergo1305
Source: Own
With $x,y,z >0$.Prove that: $\frac{xy}{4y+4z+x} + \frac{yz}{4z+4x+y} +\frac{zx}{4x+4y+z} \le \frac{x+y+z}{9}$
3 replies
imnotgoodatmathsorry
May 2, 2025
Bergo1305
an hour ago
Imtersecting two regular pentagons
Miquel-point   2
N 2 hours ago by ohiorizzler1434
Source: KoMaL B. 5093
The intersection of two congruent regular pentagons is a decagon with sides of $a_1,a_2,\ldots ,a_{10}$ in this order. Prove that
\[a_1a_3+a_3a_5+a_5a_7+a_7a_9+a_9a_1=a_2a_4+a_4a_6+a_6a_8+a_8a_{10}+a_{10}a_2.\]
2 replies
1 viewing
Miquel-point
5 hours ago
ohiorizzler1434
2 hours ago
ranttttt
alcumusftwgrind   40
N May 12, 2025 by ZMB038
rant
40 replies
alcumusftwgrind
Apr 30, 2025
ZMB038
May 12, 2025
HCSSiM vs other programs
MathWizardThatCanBeatYou   2
N May 9, 2025 by MasterInTheMaking
For anyone that has been to HCSSiM and other summer math programs like Canada/USA Mathcamp, Ross, PROMYS, etc. What's the difference and which would you consider more worth it?
2 replies
MathWizardThatCanBeatYou
May 6, 2025
MasterInTheMaking
May 9, 2025
How many people get waitlisted st promys?
dragoon   34
N May 2, 2025 by dragoon
Asking for a friend here
34 replies
dragoon
Apr 18, 2025
dragoon
May 2, 2025
PROMYS Europe
Taxicab-1211729   5
N Apr 28, 2025 by Alex-131
Is anyone attending Promys Europe this summer?
5 replies
Taxicab-1211729
Apr 19, 2025
Alex-131
Apr 28, 2025
2025 PROMYS Results
Danielzh   30
N Apr 23, 2025 by ilovepizza2020
Discuss your results here!
30 replies
Danielzh
Apr 18, 2025
ilovepizza2020
Apr 23, 2025
Hot Take: Mathcamps Don't Matter
alcumusftwgrind   7
N Apr 19, 2025 by cowstalker
Mathcamps mathcamps mathcamps.........

If you get into one, cool! If you don't that's okay. You don't need a mathcamp to learn math. You can grind AMC/AIME at home and qual for olympiad, and if you get into a mathcamp that doesn't guarantee you for olympiad.

If you get rejected, its not the end of the world! Over the summer, you can go play frisbee and hang out with your friends; you'll probably be happier this way than laboring over problems 8 hours a day.

Besides, you have next year! And if you are a rising senior, then you will go to college and none of this will matter. Don't take rejections as an evaluation on your qualities!

I'm coping rn
7 replies
alcumusftwgrind
Apr 18, 2025
cowstalker
Apr 19, 2025
questions from a first-time applicant to math camps
akliu   23
N Mar 21, 2025 by John_Mgr
hey!! im a first time applicant for a lot of math camps (namely: usa-canada mathcamp, PROMYS, Ross, MathILY, HCSSiM), and I was just wondering:

1. how much of an effect would being a first-time applicant have on making these math camps individually?
2. I spent a huge amount of effort (like 50 or something hours) on the USA-Canada Mathcamp application quiz in particular, but I'm pretty worried because supposedly almost no first-time applicants get into the camp. Are there any first-time applicants that you know of, and what did their applications (as in, qualifying quiz solutions) look like?
3. Additionally, a lot of people give off the impression that not doing the full problem set will screw your application over, except in rare cases. How much do you think a fakesolve would impact my PROMYS application chances?

thanks in advance!
23 replies
akliu
Mar 12, 2025
John_Mgr
Mar 21, 2025
SUMMER PROGRAMS THAT ARE STILL OPEN
itsjeyanth   7
N Mar 6, 2025 by fake123
HI!

I want to do a math summer program! I did awesomemath, applied for ross an and promys already, but need something else thats still open. Please suggest
7 replies
itsjeyanth
Mar 5, 2025
fake123
Mar 6, 2025
Proof-Writing
zoo1202   2
N Mar 6, 2025 by poodle2
Hi everyone!

My dream for this year (and the past year) has been to get into a math-related summer program (ROSS, PROMYS, SUMaC, etc.) However, one of the biggest parts of the application process is writing a killer problem set. To be honest (although I can hope), I do not think that any math camp will accept me this year.

To be frank, I do not have much experience writing proofs. Writing problem sets for summer camps is one of the only times that I ever formalize my ideas and put it into formatted latex. So, it usually takes me a ton of time to finish writing up one problem (2-3 hours) when I see other people speeding through and finishing everything within 3 days (and their solutions / formatting is way better than mine too). Usually, my solutions are also not with great 'mathematical' language and seem pretty hard to follow my ideas (which is not good)

While I understand that writing proofs and formulating creative ideas is extremely important, I am at a loss as to where to start. In comparison, competitive math kind of already has this 'path' laid out, but for proof writing practice/improvement it seems less so. How can I get started & improve to the point where I will be comfortable with writing by next year? One of my friends told me that USAMTS is a really nice way to practice (albeit all of the hate, it still has its merits), but I do not have a clear cut path ahead of me to really follow I guess.

tl:dr
1) How can I learn to write proofs more efficiently?
2) How can I learn some of the more advanced topics required for some elegant proofs (that you see in math camp sets)

thank you!
2 replies
zoo1202
Mar 6, 2025
poodle2
Mar 6, 2025
query about computing for summer program application psets
Possible   2
N Feb 28, 2025 by Yiyj1
Hello AoPSers,

I am applying for PROMYS this year. For some of the problems in the application problem set, I have considered writing out some code to I can notice certain patterns within smaller test cases more efficiently. Would this be acceptable as long as I include mathematical justification?

Best, Possible
2 replies
Possible
Feb 25, 2025
Yiyj1
Feb 28, 2025
Inspired by GeoMorocco
sqing   3
N Apr 21, 2025 by sqing
Source: Own
Let $x,y\ge 0$ such that $ 5(x^3+y^3) \leq 16(1+xy)$. Prove that
$$  k(x+y)-xy\leq  4(k-1)$$Where $k\geq  2.36842106. $
$$  5(x+y)-2xy\leq 12$$
3 replies
sqing
Apr 20, 2025
sqing
Apr 21, 2025
Inspired by GeoMorocco
G H J
G H BBookmark kLocked kLocked NReply
Source: Own
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sqing
42169 posts
#1
Y by
Let $x,y\ge 0$ such that $ 5(x^3+y^3) \leq 16(1+xy)$. Prove that
$$  k(x+y)-xy\leq  4(k-1)$$Where $k\geq  2.36842106. $
$$  5(x+y)-2xy\leq 12$$
Z K Y
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sqing
42169 posts
#2
Y by
Let $x,y\ge 0$ such that $ 5(x^3+y^3) \leq 27(1+xy)$. Prove that
$$  k(x+y)-xy\leq  3(2k-3)$$Where $k\geq   3.461539. $
$$  7(x+y)-2xy\leq 24$$$$  4(x+y)- xy\leq 15$$Let $x,y\ge 0$ such that $ 5(x^3+y^3) \leq 27(1+xy)$. Prove that
$$  k(x+y)-xy\leq  3(2k-3)$$Where $k\geq   4.568. $
$$  5(x+y)- xy\leq 24$$
This post has been edited 1 time. Last edited by sqing, Apr 20, 2025, 12:56 PM
Z K Y
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lbh_qys
579 posts
#5
Y by
sqing wrote:
Let $x,y\ge 0$ such that $ 5(x^3+y^3) \leq 16(1+xy)$. Prove that
$$  k(x+y)-xy\leq  4(k-1)$$Where $k\geq  2.36842106. $
$$  5(x+y)-2xy\leq 12$$

Let \( u = x + y \), \( v = xy \). Then, \( 5(x^3 + y^3) \leq 16(1 + xy) \) implies \( v \geq \frac{5u^3 - 16}{16 + 15u} \).

According to \( v \leq \frac{u^2}{4} \), we have \( \frac{u^2}{4} \geq \frac{5u^3 - 16}{16 + 15u} \), which leads to \( (u - 4)(5u^2 + 4u + 16) \leq 0 \), and thus \( u \leq 4 \).

At this point,

\( k(x + y) - xy \leq 4(k - 1) \) is equivalent to \( (4 - u)k \geq 4 - v \).

Since \( 4 - v \leq 4 - \frac{5u^3 - 16}{16 + 15u} = \frac{5(4 - u)(u + 2)^2}{15u + 16} \),

it suffices to have \( k \geq \frac{5(u + 2)^2}{15u + 16} \). Let \( f(u) = \frac{5(u + 2)^2}{15u + 16} \). Then, \( f'(u) = \frac{5(u + 2)(15u + 2)}{(15u + 16)^2} > 0 \), indicating that \( f(u) \) is monotonically increasing. Therefore,

\( f(u) \leq f(4) = \frac{45}{19} \), and it is sufficient to have \( k \geq \frac{45}{19} \).
Z K Y
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sqing
42169 posts
#6
Y by
Very very nice.Thank lbh_qys:
Let $x,y\ge 0$ such that $ 5(x^3+y^3) \leq 16(1+xy)$. Prove that
$$  k(x+y)-xy\leq  4(k-1)$$Where $k\geq    \frac{45}{19}. $
This post has been edited 1 time. Last edited by sqing, Apr 21, 2025, 5:09 AM
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