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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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0 replies
jlacosta
Apr 2, 2025
0 replies
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Generating Functions
greenplanet2050   4
N an hour ago by greenplanet2050
So im learning generating functions and i dont really understand why $1+2x+3x^2+4x^3+5x^4+…=\dfrac{1}{(1-x)^2}$

can someone help

thank you :)
4 replies
greenplanet2050
3 hours ago
greenplanet2050
an hour ago
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Transformation of a cross product when multiplied by matrix A
Math-lover1   1
N an hour ago 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
4 hours ago
greenturtle3141
an hour ago
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Geometry books
T.Mousavidin   4
N 2 hours ago 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
2 hours ago
J
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trigonometric functions
VivaanKam   3
N 4 hours ago by aok
Hi could someone explain the basic trigonometric functions to me like sin, cos, tan etc.
Thank you!
3 replies
VivaanKam
6 hours ago
aok
4 hours ago
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CG / DE > = 2\sqrt 3/ 3 Almaty City MO 2024 p4
parmenides51   0
May 5, 2024
Inside the convex quadrilateral $ABCD$, let $G$ be the point of intersection of the medians of triangle $ABC$. It turned out that $G \in [BD]$ and $\angle DCG = \angle BAC$. From point $D$ a perpendicular $DE$ is dropped on the segment $CG$. Prove that $\frac{CG}{DE} \ge \frac{2\sqrt 3}{3}.$
0 replies
parmenides51
May 5, 2024
0 replies
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CG / DE > = 2\sqrt 3/ 3 Almaty City MO 2024 p4
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parmenides51
#1 h  May 5, 2024, 3:28 PM
Y by
Inside the convex quadrilateral $ABCD$, let $G$ be the point of intersection of the medians of triangle $ABC$. It turned out that $G \in [BD]$ and $\angle DCG = \angle BAC$. From point $D$ a perpendicular $DE$ is dropped on the segment $CG$. Prove that $\frac{CG}{DE} \ge \frac{2\sqrt 3}{3}.$
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