math - Bits & Bytes

CS-7638: Artificial Intelligence for Robotics

Instructor(s): Jay Summet / Sebastian Thrun Course Page: Link CS-7638 is an introductory course that covers basic techniques used in robotics. Throught its 16-week span, the instructors cover various techniques/algorithms used in the field of robotics such as: Bayes Filters: Histogram, Kalman & Particle FiltersPID (Proportional–Integral–Derivative) ControllersPath

math

Birthday Attack

Alot of the crypotgraphic software we use relies on hashing and it's uniqueness guarantees to provide core functionality, such asauthentication, message integrity, message fingerprinting, data corruption detection, etc... Guaranteeing this uniqueness however is fundamentally impossible following from the Pigeonhole Principle if your input data size is going to be larger

math

Space Race

Another FiveThirtyEight Riddler.The President has bestowed upon you 1 billion dollars with the mission of getting us to an alien artifact as fast as possible! Here's whats available to you: Big Russian engines costing 400 million each. Buying one will reduce the trip time by 200 days. Buying two

riddle

Impossible Puzzle

Another weekly FiveThirtyEight riddler, and this one's a mind-bender. Three very skilled logicians are sitting around a table — Barack, Pete and Susan. Barack says: “I’m thinking of two natural numbers between 1 and 9, inclusive. I’ve written the product of these two numbers on this paper that I’

math

Casino Game

The solution for this weeks FiveThirtyEight riddler is pretty nutty. The riddle is essentially: If you drew random numbers from a uniform distribution from [0,1], what is the expected number of draws you would perform until their sum exceeds 1? So let us define $$S_{n}$$ as the sum

math

1 + 2 + 3 + ...

Here's something mind-blowing: If you take the sum of the first couple of natural numbers you get the triangle numbers: $$T_{1} = 1$$ $$T_{2} = 1 + 2$$ $$T_{3} = 1 + 2 + 3$$ $$T_{n} = (n)(n-1)/2$$ So essentially the series 1 + 2 + 3 + 4 + ... is the area of an