Introducing Math Problem of the Week

[Greg Bernhardt]

One of the best things to migrate over from MHB is their Problem of the Week program. Let me introduce the POTW directors @anemone and @Euge, who had been running the POTW at MHB for 8 years and we're very glad to have them continue the great program here. I'll let them say hi and tell you what to expect!

At the moment, the POTW forum is located in General Math.
https://www.physicsforums.com/forums/potw-for-secondary-and-high-school-students.348/

 

[anemone]

Hello to all!

I am anemone. I am from MHB and I wish to share a brief history regarding the ongoing problem of the week that we had at MHB.

Shortly after MHB's creation early in 2012, a feature was added whereby each week a challenging problem in each of three levels of expertise would be posted for consideration: Secondary/high school, Under graduate and Post graduate.

It was hoped this would engage the community and stimulate curiosity. Our POTW directors were dedicated and kept the problems flowing for ten years week after week.

Since MHB has been merged into PF, I would like to carry on this tradition that we started at MHB here. A new set of problems will be posted on every Monday and the solution, if no one solved the problem correctly, will be posted a week after. At PF, members can submit their solution by replying to the POTW thread, and you may use the spoiler tags to hide your solutions. However, collaboration between members is allowed by building on the replies.

I hereby welcome all members to participate in POTW section!

 

[WWGD]

Please excuse my ignorance: What/Who is MHB?

 

[Drakkith]

Please excuse my ignorance: What/Who is MHB?

MathHelpBoards.com
They merged with PF recently: https://www.physicsforums.com/threads/mathhelpboards-com-merges-with-pf.1044618/

 

[Drakkith]

@anemone Forgot to say welcome to PF!

 

[anemone]

Please excuse my ignorance: What/Who is MHB?

We used to be a mathematics forum that allowed members to get free math help or discuss any of the math problems.

 

[anemone]

@anemone Forgot to say welcome to PF!

@Drakkith, thanks for the welcome!

 

[Petek]

@anemone

Welcome to PF!. I think I solved some of your challenge problems on MHB.

 

[Borek]

Welcome!

 

[Borg]

Welcome to Physics Forums @anemone. Hope that your assimilation goes well.

 

[Borek]

Hope that your assimilation goes well.

Especially as resistance is futile.

 

[Drakkith]

Especially as resistance is futile.

Reference please. My book says resistance is voltage over current.

 

[Greg Bernhardt]

Everyone should feel free to try out the past POTW. The current POTW will always be stickied.

 

[jedishrfu]

Hello to all!

I am anemone. I am from MHB and I wish to share a brief history regarding the ongoing problem of the week that we had at MHB.

Shortly after MHB's creation early in 2012, a feature was added whereby each week a challenging problem in each of three levels of expertise would be posted for consideration: Secondary/high school, Under graduate and Post graduate.

It was hoped this would engage the community and stimulate curiosity. Our POTW directors were dedicated and kept the problems flowing for ten years week after week.

Since MHB has been merged into PF, I would like to carry on this tradition that we started at MHB here. A new set of problems will be posted on every Monday and the solution, if no one solved the problem correctly, will be posted a week after. At PF, members can submit their solution by replying to the POTW thread, and you may use the spoiler tags to hide your solutions. However, collaboration between members is allowed by building on the replies.

I hereby welcome all members to participate in POTW section!

Welcome to PF!

 

[anemone]

@anemone

Welcome to PF!. I think I solved some of your challenge problems on MHB.

Yes, @Petek, you did indeed! I remember it!

 

[Greg Bernhardt]

First one is live!
https://www.physicsforums.com/threads/potw-about-product-of-real-roots.1044748/

 

[bhobba]

Indeed welcome. My background is math, but I became seduced by mathematical physics. However always loved math.

Thanks
Bill

 

[WWGD]

At least it was not called Math Forums Board, else we would have a mix up with our @mfb , having both a lower-case and capitalized version.

 

[scottdave]

Welcome @anemone

 

[topsquark]

Indeed welcome. My background is math, but I became seduced by mathematical physics. However always loved math.

Thanks
Bill

Good to meet you. I'm a Physicist that has become seduced by Mathematical Physics!

-Dan

 

[bhobba]

Good to meet you. I'm a Physicist that has become seduced by Mathematical Physics!

It's contagious. I caught it from Landau - Mechanics. If you haven't read it, please do, and then your conversion will be complete.

Thanks
Bill

 

[topsquark]

It's contagious. I caught it from Landau - Mechanics. If you haven't read it, please do, and then your conversion will be complete.

Thanks
Bill

Landau is good! Actually I've had the bug since High School but when I decided to go into QFT it almost became a necessity. For reasons I won't go into here I've had to teach myself the whole field of QFT (Weinberg is my current favorite for this) and I've found I needed a heck of a lot of Math just to read it, much less do anything with it.

-Dan

 

[WWGD]

Landau is good! Actually I've had the bug since High School but when I decided to go into QFT it almost became a necessity. For reasons I won't go into here I've had to teach myself the whole field of QFT (Weinberg is my current favorite for this) and I've found I needed a heck of a lot of Math just to read it, much less do anything with it.

-Dan

I'm still trying to figure out how the bra and ket thing works.

 

[Thytanium]

Hello to all!

I am anemone. I am from MHB and I wish to share a brief history regarding the ongoing problem of the week that we had at MHB.

Shortly after MHB's creation early in 2012, a feature was added whereby each week a challenging problem in each of three levels of expertise would be posted for consideration: Secondary/high school, Under graduate and Post graduate.

It was hoped this would engage the community and stimulate curiosity. Our POTW directors were dedicated and kept the problems flowing for ten years week after week.

Since MHB has been merged into PF, I would like to carry on this tradition that we started at MHB here. A new set of problems will be posted on every Monday and the solution, if no one solved the problem correctly, will be posted a week after. At PF, members can submit their solution by replying to the POTW thread, and you may use the spoiler tags to hide your solutions. However, collaboration between members is allowed by building on the replies.

I hereby welcome all members to participate in POTW section!

Welcome anémone. Thank you for being here collaborating with PF. Very grateful for your presence.

 

[bhobba]

I'm still trying to figure out how the bra and ket thing works.

Before I learned QM I used to use the standard bracket thing for the inner products. After I always use bra-ket notation. It's contagious.

Thanks
Bill

 

[WWGD]

Before I learned QM I used to use the standard bracket thing for the inner products. After I always use bra-ket notation. It's contagious.

Thanks
Bill

I'm kind of embarrassed that I've gone over explanations several times, but maybe I did not pay enough attention.

 

[bhobba]

(Weinberg is my current favorite for this)

I like Wienberg too, but he is a bit advanced for my QFT level which is about at QFT For The Gifted Amateur. We have a high-powered researcher, from I think Oxford, who sporadically posts here. He is very good, and I eagerly wait for anything he writes. He called Wienberg - the old man - when Wienberg was alive.

Thanks
Bill

 

[bhobba]

I'm kind of embarrassed that I've gone over explanations several times, but maybe I did not pay enough attention.

Seriously it's easy. First, read the following even though it seems to not be relevant:
https://www.amazon.com/dp/0521558905/?tag=pfamazon01-20

The Kets are simply the test functions, the Bras are the distributions (or dual space as it's sometimes called). Hilbert spaces have the interesting property that the Bra's and Kets can be placed in 1-1 correspondence. This is the origin of the so-called Gefland Tripple you can look into if you wish.

Thanks
Bill

 

[Wrichik Basu]

I'm still trying to figure out how the bra and ket thing works.

Modern QM by Sakurai has an excellent detailed explanation on the bra, kets, operators and the like.

 

[Euge]

Hi Everyone,

I am Euge, MHB POTW director for university and graduate level POTW. I plan to post problems biweekly on Sundays. Hopefully, you'll enjoy tackling some of them! Of course, open collaboration and multiple solutions are welcome. Please use spoiler tags to hide your solutions.

I look forward to getting to know you!

 

[I like Serena]

@Euge! You've made it over here! Thank you for joining!

You're pretty much the smartest mathematician that I've ever seen and I've always been impressed that you were willing to put up the university and graduate POTW's on a regular basis.
So I hope the people here will welcome you, and give your problems at least a try. I won't hold my breath if they can solve your graduate POTW's though, or even your university POTW's.

 

[Euge]

@Euge! You've made it over here! Thank you for joining!

You're pretty much the smartest mathematician that I've ever seen and I've always been impressed that you were willing to put up the university and graduate POTW's on a regular basis.
So I hope the people here will welcome you, and give your problems at least a try. I won't hold my breath if they can solve your graduate POTW's though, or even your university POTW's.

Thanks! Well, I suspect that several members are capable of solving both of the advanced POTWs, considering the mathematical talent displayed on this site.

 

[julian]

Welcome to the PF @Euge! It is exciting to have somebody with your abilities joining the forum!

I have a PhD in theoretical physics and enjoy tackling undergraduate maths problems. But I fear that your postgraduate problems will be beyond me. Just checking, so you will you be giving us 2 weeks to solve the problems?

 

[Euge]

Thanks @julian! I will not be so stringent with the POTW. If no one answers the POTW in 2 weeks, then I will post my solution. Other solutions are still welcome after the two-week period.

 

[Greg Bernhardt]

Graduate POTW just kicked off today!
https://www.physicsforums.com/threads/potw-in-a-category-with-fibered-products.1044934/