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Bayesian Inference - A statistical model where probability is based on belief, not frequency or proportion.
Markov Chain - A mathematical concept that states the past is irrelevant for predicting the future given knowledge of the present.
Monty Hall Problem - A problem with a counter-intuitive solution explained by Charlie in his lecture on odds using goats and automobiles.
Don was in Fugitive Recovery in Phoenix before he moved back to L.A.
Charlie finally teaches a class in this episode.
This was the first time Don and Alan beat Charlie in a game of chess.
Charlie has trouble with spelling. He spells the word 'anomaly' as 'anomoly' despite using it constantly as a mathematician.
The exact same example Charlie shows with the goat and the car is used in the movie 21.
The chess game in the ending scene is the famous chess game Morphy v. Duke of Brunswick and Count Isouard.
During the shootout in the end, a bullet hits a metal tube protruding from the ground a bunch of sparks fly off the tube. Technically, this shouldn't happen when a bullet is propelled from a gun like the one they were using.
Watch the chess pieces on the board in the final scene. Charlie's knight on his right side moves over two squares to the right after taking Alan's bishop, without taking anything. If it didn't move, Alan wouldn't have been able to checkmate Charlie.
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Conditional Probability Distribution
Combinatorics - A field of mathematics that studies data structures in computer science.
In the beginning Charlie claims that "every problem has a solution" and that "if there is any limitation, it's got to be in the mathematician, not the math". But in 1931 the mathematician Kurt Gödel found his so-called incompleteness theorems, which basically demonstrated that any finite axiom-set, the mathematical basis, must be incomplete and thus there will always be problems without a solution. This theorems together with later works by Alan Turing ended the so-called "Hilbert's Dream" of a complete and consistent math and seriously shook the foundations of the mathematical world at that time, so it is strange that Charlie, who is supposed to be a brilliant mathematician and often corrects misstatements made by people in his surrounding, would make a statement that contradicts this groundbreaking mathematical discovery.
Air traffic control radars do not, in normal operation, look for reflections off the aircraft (A "skin paint"). Rather, they send out much lower power transmissions than that would require, which are picked up by a transponder on the aircraft. The transponder transmits a reply, which the ATC radar uses to identify the flight.
An aircraft without a transponder, or with it turned off, will not show up on ATC radar in the first place.
This was even *mentioned* early in the episode, and yet, later on, they're all talking about how all the different radar systems "tracked the flight".
In the scene where the military liaison "Leader 1" is speaking with air traffic control, a close-up of a radio scanner appears on the screen with the following frequency "866.6125." This frequency is a public safety frequency used mostly by police. If Leader 1 had actually been talking to air traffic controllers, he would have used a military UHF frequency in the 225-400 AM range instead of the 866 FM public safety range.
When Alan hits the golf ball in the first golf scene, he doesn't even hit it but Charlie still calls out nice shot!
The military officer in the opening tells Don Eppes there are F-16s patroling the area looking for the UFO. However, the fighter jets shown in the opening are not F-16s. One giveaway was their general shape. They resembled F-18s. Also, there is a scene showing the jets flying past and away revealing the afterburner in the night sky. These jets had twin-engine afterburners while F-16s are single-engine jets. The script doesn't match the special effects.
The reason why the characters talk about F-16s and we see F-18s is because the script was written with the F-16 references. When the effects company that did the jet fighter footage finished its work, F-18s had been substituted for the F-16s - most likely because the same company did the effects for JAG and there were a lot more F-18 models, which are Navy fighters.
In the original flight of the plane in the first scene, it's the same graphic footage used over and over.
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Van Eck Phreaking
Sabermetrics - The study of baseball performance through statistical analysis.