Weeks 1/2: Solving Big Problems

As mentioned earlier, all BEAM students study problem solving throughout the program.  Beyond Math Team Strategies, the other option is Solving Big Problems: working on the same problem for 2+ hours and really working to understand it.

In today's class, students investigated the following problem:

Which positive integers can be written as the sum of consecutive integers?

SBP

Students had a number of early conjectures, including:

  • All odd integers have this property.
  • If a given number is composed only of factors without this property, then that number also won't be possible to write as the sum of consecutive integers (so, if 4 = 1 * 2 * 2 and 1 and 2 are impossible, 4 is also impossible). 

The class was quickly able to prove the first conjecture, and then spent the next 2 hours working on the second.  Can you figure it out?

BEAM Goes to the Opera- Wednesday, July 20, 2016

A concoction of perfumes filled the halls of the dorm, lip gloss was generously applied, shirts were tucked in, and hair was transformed into artful masterpieces as the students primped up for their night out. Everyone was finally ready, and the group walked towards the architecturally sublime Richard B. Fisher Center for the Performing Arts. The BEAMers, gawking at the sight of the place, entered the building. The dress rehearsal for the opera Iris was spectacular. The students were amazed with the wonderful scenery, impressive special effects, and beautiful music. What a night. 

Beginning of Week 2!- Tuesday, July 19, 2016

After two days of amazing field trips, the second academic week began. The courses being offered this week are: Solving Big Problems; Math Team Strategies; Voting Theory; Number Theory; Symmetries, Mosaics, and ¿Dancing?; and Programming.

Leon Botstein, the president of Bard College, gave the students a beginning-of-the-week commencement speech, during which he talked about the importance of academics and of programs like BEAM. Additionally, he invited the BEAMers to attend the dress rehearsal for the opera "Iris", which he will be conducting, on Wednesday evening. 

The good news just keeps rolling in: the fourth challenge problem has been solved by one of our BEAMers: Kenneth. The prize is yet to be announced. 

What a BEAMing start to the second week! 

 

Week 1/2 Class: Math Team Strategies

How do strong mathematicians think? How do they work? That's the goal of our problem solving classes at BEAM!

At the beginning of the program, students got to choose between Solving Big Problems and Math Team Strategies.  In Math Team Strategies, the goal is to prepare for math competitions, like MATHCOUNTS, the AMC 8, or Purple Comet. Math competitions and math teams praise clever, efficient thinking, finding solutions and shortcuts that save time and still make mathematical sense!

In class, students were working on problems like the following one, combining their knowledge of geometry and number theory:

Pentagonal Numbers

And here are the students hard at work, trying to break the problem down and explain their solution.