Don and his team hunt for the killers of two rock climbers found in possession of a large diamond. Charlie decides he should get his FBI clearance reinstated while a new agent joins the team.

First appearance of: Sophina Brown as Nikki Betancourt

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Mathematics used: Percolation Threshold and geometrical analysis

After a woman is murdered in what appears as an ATM robbery a series of kidnaps, rapes and murders turns into a hunt for the gang leader. New girl Nikki agrees to be the decoy, and Charlie's involvement leads to trouble for Don.

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Mathematics used: Decoy effect, Hall effect and scheduling algorithm

When eight people, including two LAPD police officers, are executed in a coffee shop, a detective (D. B. Woodside) gets the team on the case, and they uncover a trail of blackmail, romance and corruption. Also, McGowan's (Keith Carradine) investigation of Charlie and Don deepens.

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Mathematics used: Aggregation modeling and Hidden Markov model

Don's team joins FBI Agent Bloom (Henry Winkler) in tracking an elusive con man. Meanwhile, decisions are announced on Charlie's FBI clearance and disciplinary action for Don.

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Mathematics used: Belief propagation

The team hunts a crew stealing high-end goods from a shipping service and looks to an employee with savant-like abilities to lead them to those behind the scheme.

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Mathematics used: Geographic network, supply chain analysis and fractals

While on a date, David catches a disappearing act at a magic show but quickly becomes involved in the performance when the magician really vanishes.

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Mathematics used: Design Recovery

One of Don and Charlie's friends dies in what is deemed an accident. Not convinced, the brothers investigate further.

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Mathematics used: Deconvolution, neural network, hyperspectral imaging and site-prediction modeling

The team is sent to investigate and help with the recovery at a train crash; however, the train is carrying dangerous chemicals.

Note: During its original run, David Krumholtz gave a public service announcement stating that the episode was not in fact based on a similar train crash in the California area that occurred after taping, but before the episode aired.

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Mathematics used: Infotaxis and swarm robotics

A bomb goes off during a high profile meeting and a documentary film maker has a conspiracy theory about it.

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Mathematics used: Simpson's paradox, Rationality theorem

Charlie and his rival Marshall Penfield race against time to solve a case.

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Mathematics used: Group Dynamics and Three Way Duel

Buck Winters escapes from prison, consumed by getting revenge against Don, forcing Don to face his past and turn to his new-found religious beliefs.

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Mathematics used: Hidden Markov model, Maxwell's Demon and the Viterbi algorithm

When 18 tourists on a bus are taken hostage, the team has only four hours to stop the hijackers.

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Mathematics used: Articulate and Inverse Game Theory

An undercover agent disappears, leading the FBI team deep into Chinatown's black market. The FBI gets help from the returning psychic Simon Kraft (John Glover).

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Mathematics used: digital signal processing and Lévy flight

When a pair of valuable sneakers is stolen from the vault of a foreign ambassador, the team delves into the world of sneaker collecting.

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Mathematics used: Pinball

When Robin's seemingly bulletproof case fails and a dangerous weapons smuggler is released, the team investigates the possibility of jury tampering.

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Mathematics used: Probability, Mersenne twister, scientific jury selection and social networking potential

Liz goes undercover in an operation to stop a new illegal drug from hitting the streets after Charlie predicts that the drug in question will be the next "big thing" to hit the drug market. During the operation, David is assigned to be Liz's handler but he grows concerned for her safety after she ignores his plan and begins trusting a fellow undercover agent who may or may not be an addict himself.

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Mathematics used: Supply & Demand Theory

The FBI team investigates the death of visionary scientist Daniel Robertson; the prime suspect is Robertson's AI computer program, while Charlie considers an enticing job offer.

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Mathematics used: Turing test

The FBI team rushes to track down evidence that could save a mob boss from the death penalty. New information comes in that could exonerate him, leaving the team with only hours to run down the new lead.

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Mathematics used: Light Refraction and Voice Analysis

The investigation into the death of a CalSci professor exposes possible links to animal rights extremists.

Things go terribly wrong when Don gets injured during an investigation. Charlie and Alan have to put things into perspective, when the thought of possibly having to lose a part of their family comes to face them.

Charlie focuses his attention on tracking a previously undetected serial killer to help deal with his guilt over Don's almost-fatal stabbing. He receives help from a geeky amateur sleuth and a retired accountant, who each research serial murders as a hobby. The investigation reveals that the killer may be responsible for over two dozen unsolved deaths.

The team investigates a string of bank robberies and believe that ex-FBI Agent Roger Bloom (played by Henry Winkler) is responsible for them. The episode then ends with Amita being abducted at gunpoint as she and Charlie leave CalSci.

With Amita having been kidnapped by the leader of a cult with female followers, the whole team including Ian Edgerton race against the clock to bring Amita home safely before it's too late.

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Mathematics used: Angel problem and burr puzzle