#7: Comparing the Arduino and Raspberry Pi

Patrick Pilarski Artificial Intelligence Part IV LABMP 590 2014 Feb 25

A working definition of NP-hard (Stephen Boyd, Stanford)

Board Building: Massimo Banzi, Arduino

What Computers Do: Model, Connect, and Engage

What Computers Do: Model, Connect, and Engage

5 Ways to Solve Recurrence Relations - wikiHow

5 Ways to Solve Recurrence Relations - wikiHow:

How to Solve Recurrence Relations

ArithmeticGeometricPolynomialLinearGenerating Functions

Edited by Peter, Molly, Jason, Teresa and 10 others

In trying to find a formula for some mathematical sequence, a common intermediate step is to find the n^th term, not as a function of n, but in terms of earlier terms of the sequence. For example, while it'd be nice to have a closed form function for the n^th term of the Fibonacci sequence, sometimes all you have is the recurrence relation, namely that each term of the Fibonacci sequence is the sum of the previous two terms. This article will present several methods for deducing a closed form formula from a recurrence.

Method 1 of 5: Arithmetic

1. 
   1
   Consider an arithmetic sequence such as 5, 8, 11, 14, 17, 20, ....
2. 
   2
   Since each term is 3 larger than the previous, it can be expressed as a recurrence as shown.
3. 
   3
   Recognize that any recurrence of the form a_n = a_n-1 + d is an arithmetic sequence.
4. 
   4
   Write the closed-form formula for an arithmetic sequence, possibly with unknowns as shown.
5. 
   5
   Solve for any unknowns depending on how the sequence was initialized. In this case, since 5 was the 0^th term, the formula is a_n = 5 + 3n. If instead, you wanted 5 to be the first term, you would get a_n = 2 + 3n.

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Ban Bossy. Encourage Girls to Lead

Ban Bossy. Encourage Girls to Lead:



When a little boy asserts himself, he's called a “leader.” Yet when a little girl does the same, she risks being branded “bossy.” Words like bossy send a message: don't raise your hand or speak up. By middle school, girls are less interested in leading than boys—a trend that continues into adulthood. Together we can encourage girls to lead.



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