Time for the october challenge! This time a lot of people sent me suggestions for challenges. I wish to thank them a lot! If you think of a good challenge that could be included here, don't hesitate to send me!
Ranking [and previous challenges] here...
September, schools restart, summer ends, but a new challenge is here:
Ranking here: https://www.physicsforums.com/threads/micromass-big-challenge-ranking.879070/
RULES:
1) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored.
2) It...
August is already well underway, so time for some nice challenges! This thread contains both challenges for high schoolers and college freshmen, and for more advanced people. Also some previously unsolved challenges are omitted.
Ranking here...
Here is a thread of challenges made especially for high school students and first year university students. All the following problems can be solved with algebra, trigonometry, analytic geometry, precalculus and single-variable calculus. That does not mean that the question are all easy.
For...
Summer, July, hot weather: every reason is good enough for some new challenge questions.
NEW: ranking can be found here: https://www.physicsforums.com/threads/micromass-big-challenge-ranking.879070/
For high school and first year university students, there is a special challenge thread for you...
List of challenges:
Integral Challenge: https://www.physicsforums.com/threads/micromass-big-integral-challenge.867904/
Counterexample Challenge: https://www.physicsforums.com/threads/micromass-big-counterexample-challenge.869194/
Counterexample Challenge 2...
In this thread, I present a few challenging problems from all kinds of mathematical disciplines.
RULES:
In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored.
It is fine to use nontrivial results without proof as long as you cite...
micromass submitted a new PF Insights post
How to self-study algebra. Part II: Abstract Algebra
https://www.physicsforums.com/insights/wp-content/uploads/2016/06/aastock6.png [Broken]
Continue reading the Original PF Insights Post.
We had integrals, so we have to have series as well. Here are 10 easy to difficult series and infinite products. Up to you to find out the exact sum.
Rules:
The answer must be a finite expression. The only expressions allowed are integers written in base 10, the elementary arithmetic...
Probability theory is very nice. It contains many questions which are very easy to state, but not so easily solved. Let's see if you can solve these questions.
For an answer to count, not only the answer must be given but also a detailed explanation.
Any use of outside sources is allowed, but...
And we continue our parade of counterexamples! Most of them are again in the field of real analysis, but I put some other stuff in there as well.
This time the format is a bit different. We present 10 statements that are all of the nature ##P## if and only if ##Q##. As it turns out, only one of...
Well, the last thread of counterexamples was pretty fun. So why not do it again! Again, I present you a list with 10 mathematical statements. The only rub now is that only ##9## are false, thus one of the statements is true. Provide a counterexample to the false statements and a proof for the...
I adore counterexamples. They're one of the most beautiful things about math: a clevery found ugly counterexample to a plausible claim. Below I have listed 10 statements about basic analysis which are all false. Your job is to find the correct counterexample. Some are easy, some are not so easy...