# Adventures in Math by Matt McGann '00

Conversations in the world of math.

I’ve had some great conversations over the past few weeks with folks in the math community.

A couple weeks ago, I had the opportunity to sit down with Richard Rusczyk and Dave Patrick PhD ’97, two of the folks behind The Art of Problem Solving (AoPS). The fantastic AoPS offerings include great textbooks for gifted math students, an active and interactive forum (merged with MathLinks) for discussions of math and math problems, and online classes. I’m very excited about what Richard, Dave, and the entire AoPS crew are doing. I hope that if you’re interested in and excited about math, you’ll check it out.

The Art of Problem Solving folks also run the San Diego Math Circle, which I had a chance to visit. A Math Circle (like the ones in Berekeley and Boston) is a gathering of K-12 students for the purpose of exploring math. On the Saturday morning that I visited, more than 100 people were in attendance (including parents), the plurality of whom where students in grades 6-10. I spoke briefly to the group, talking about how students should follow their passions and not take a formulaic approach to life for the purpose of college admissions. I may have been preaching to the choir — these students were already following their passion for math.

Earlier this week, I had the opportunity to sit in on a high school math class taught by Zuming Feng. Dr. Feng is the coach of the US International Math Olympiad team, author of a number of math books, and a great math teacher at Phillips Exeter Academy in New Hampshire. The class is a proof-based number theory class and is very interactive. The problems presented on this day were well beyond the level we ever talked about in my high school math classes, such as, “Let *p* be a prime. Show that there are infinitely many positive integers *n* such that *p* divides 2^{n} – n.”

And finally, on Wednesday night, I did an online chat with the AoPS community called a “Math Jam. I co-hosted the Math Jam with MIT Math professor Kiran Kedlaya. What was this like, you ask? It was like the Questions Omnibus Olympics. People posed so many questions so quickly that I had trouble keeping up! Anyway, Kiran and I did as best we could keeping order and answering questions without making too many typos. Anyway, you may be interested in checking out the Math Jam transcript for even more Q&A fun.

And finally tonight, what better link to leave you with tonight but the MIT Math Department?

What amuses me most about mathematics are the humble, understated names of courses:

One post-calculus math course at Jefferson Science and Tech is called Linear Algebra.

Recently, I’ve been reading a book that was referenced in some economics models I was studying. The title of the referenced book: Simple Algebra.

Does MIT have any hilariously understated math courses?

math is my favorite subject!!!

Hey Matt,

how does one sign up to talk to admitted students back home? Is there a party bus of some sort we get to paint and tour around the country?

Thanks for the transcript! I wanted to attend but was unable. Also…I just cant resist…sorry.

Matt Wrote:

“Let p be a prime. Show that there are infinitely many positive integers n such that p divides 2n – n.”

Consider fermats little theorem which states that that if p is prime for any integer a. a^p is congruent to a mod p. Or the equivalent statement that if p is a prime and a is an integer coprime to p then a^p-1 is congruent to one mod p.

Therefore 2^p-1 is congruent to 1(mod p)

Let f(n)=(np-1)(p-1) hence for every n f(n)is congruent to 1(mod p)

2^f(n)=(2^p-1)^np-1

random question: do you have any pet peeves when it comes to reading apps (ex: excessive use of ! marks, mispelled words, colloquial acronyms, cliches, common grammar errors)?

Nehalita…I just wanted to chirp in here. I think your writing is certainlly dependant upon your personality and can say alot about it…however I would take the time to run it through a spell checker at the very least. Cliches? I would guess that it depends on how they are used…I am sure its a bit of a turn off if they, at the risk of being horribly hyperbolic, read:

“Did I mention how PASSIONATE I am about MIT? I am also REALLLLLY PASSIONATE about computer science. I am really PASSIONATE about everything in general PASSION…and did I mention how im soooooo passionate about computer science?…PASSION!!”

However if used appropriately cliches could add more insight into your personality…all in all I think you want to find a balance. Informal enough that your personality shows through…but not TOO informal. Again this is just my advice…

Quick addon: That of course does not really answer your question…but it looks at the core issue

Quote:

“”Did I mention how PASSIONATE I am about MIT? I am also REALLLLLY PASSIONATE about computer science. I am really PASSIONATE about everything in general PASSION…and did I mention how im soooooo passionate about computer science?…PASSION!!””

In replying to Robb Carr:

This is very funny, and good point. Though, in my own essays, I’ve always joked a bit, because I find humor to be of second nature to me. However, I’ve never let the humor overtake how serious I am about what I am interested in. So, I agree wholeheartedly that subject-rabidness might not be appealing, but I personally would not place my interests on the back burner. In my opinion, passion is good. Rabies is not.

I didnt mean as much subject rabidness as much as SPECIFICALLY using the word passion, over…and over…and over. I mean, on my interview report the words “Mathematical Fetishm” appear (apparently) so showing “passion” in what you are intrested in, is definetly wonderful…but it seems like it might be better to let it speak for itself.