Don races to capture a serial rapist who has begun to murder his victims. Charlie is recruited by Don to help track the killer. He creates a mathematical equation to identify the killer’s point of origin by working back from the crime scene locations. Charlie’s obsession with the case leads him to seek the insight of his colleague, physicist Dr. Larry Fleinhardt. Meanwhile, their father, Alan, is pleased to see his sons working together but fears their competitive nature will lead to trouble.

While consulting with the National Transportation Safety Board (NTSB) at the scene of the wreck, Don learns that this tragedy is one of a series of recreated accidents involving railroad negligence. As is the pattern with the previous train wrecks, an undecipherable numerical code is left at the site, which Don recruits Charlie to solve. By breaking the code, Charlie is able to establish that this accident was a recreation of a deadly wreck that left only one survivor several years ago. Don's investigation leads him and his team to a dangerous standoff with their suspect, who has surprising ties to the railway system.

When people start mysteriously dying in Los Angeles, Don and his FBI team are called in by the Public Health Service to determine if it is an act of bio-terrorism. Using Charlie's knowledge of the mathematics of diseases, they attempt to track the virus not only to stop it, but to find the point of origin in order to determine who is responsible and why -- only to be surprised by the motive of the suspect. Meanwhile, Don is surprised to learn that Charlie has been keeping a secret from him.

When Don and his team attempt to catch a pair of repeat bank robbers in Los Angeles, Charlie devises an equation using probability and statistical analysis to pinpoint the location of their next robbery. Although his prediction for the next robbery is correct, his mathematical model turns out to be useless when the robber’s true motives are revealed. His frustration growing, Charlie’s desire to continue to help the FBI falters when a stake-out goes bad, leaving one agent dead and his brother, Don, with a gunshot wound.

After an engineering student at CalSci is found dead from an apparent suicide, Charlie convinces Don to launch an investigation after he reads the student’s thesis that asserted that the architecturally magnificent Cole Center in Los Angeles is structurally unstable. Although reluctant at first, Don and his FBI agents discover that the student’s findings were correct and uncover a dangerous and surprising conspiracy. Meanwhile, Alan prepares for a first date and convinces Don and Terry to join them, hoping they might rekindle their old romance.

When a 5-year-old girl is kidnapped from her birthday party, Don and Terry lead the investigation but must rely on Charlie's help, as the girl's father, Ethan, is also a mathematician. Charlie realizes the kidnapper's motive when Ethan reveals that he is close to solving Riemann's Hypothesis, a difficult math problem. If solved, the solution could not only earn him with $1 million but could break the code for Internet security, unlocking the world's biggest financial secret.

Charlie is called in to use his mathematical expertise to pinpoint the location of the counterfeiters by analyzing the dispersion of the bogus money. In addition, he also discovers a surprising connection to the disappearance of a local artist. Meanwhile, Charlie realizes how little he knows about his brother when he meets someone from Don’s romantic past.

When a recent murder bears a strong resemblance to a murder case he closed a year ago, Don questions whether he sent the wrong man to jail. As a favor to Don, Charlie examines the old case and finds flaws in the fingerprint and eyewitness systems that put their reliability into question.

Pressed for time to find the sniper, Don calls in a senior Sniper Instructor from Quantico (guest star Lou Diamond Phillips) to assist on the case, causing Charlie to feel insecure about his role as special consultant to the FBI. Feeling animosity towards Agent Edgerton at first, Charlie learns from him that human behavior could make his mathematical equations useless. Instead Edgerton encourages Charlie to get inside the head of the killer.

Don and his team are called when it is discovered that a truck driver and his big rig carrying radioactive material have been hijacked and are now missing. They are pressed for time to find the truck when the hijackers threaten to detonate a dirty bomb in an undisclosed location in Los Angeles if they don't receive $20 million in 12 hours.

After an independent computer researcher with a contract with the Defense Department is found murdered, Don and his team are called in to find out who is responsible. After Don recruits Charlie to decode the murder victim's cryptic computer data, Charlie uncovers he was working on a secret and potentially damaging project, forcing Charlie to question the impact of his own life's work.

Don and Agent Quimby of the NTSB investigate eyewitness accounts of a mysterious unidentified object flying dangerously close to downtown Los Angeles that has raised concern of a terrorist attack. After Charlie is recruited to help with the investigation, it is discovered that the flying object is part of a new technology that could revolutionize air travel. But the investigation takes a turn when they learn that the lead engineer is found murdered.

As Don investigates the prison bus crash, Charlie uses of probability analysis to conclude that the bus crash was not an accident, but part of a conspiracy to free a dangerous killer. Now, Don and Charlie must discover the killer's lethal agenda and stop him before he is able to carry it out.