The Numbers: Season 1

Charlie assists Don on a serial rapist case by calculating a "hot zone", an area where the rapist is most likely to live. Don is removed from the case after Charlie's formula fails to turn up any leads but later a comment from their father then leads Charlie to change the equation to calculate two points of origin, instead of one, leading to a new suspect. Anthony Heald guest stars. Mathematics used: Geographic profiling, probability theory, 11-dimensional supergravity theory and projectile moti

Charlie successfully predicts the time and place of a bank robbery using what he says are elements of Heisenberg's uncertainty principle, but when the planned arrest goes bad, he retreats into the math problem P vs. NP. Mathematics used: P vs. NP and Heisenberg's uncertainty principle

A deadly strain of influenza is spreading through Los Angeles, killing many people. Don investigates whether the strain was released deliberately, and Charlie tries to calculate the origin and likely spread of the virus. Guest stars include CCH Pounder, J.K. Simmons, and Rainn Wilson. Mathematics used: Patient Zero, Viral vector, Vector and SIR model

An engineering student dies by what is ruled a suicide, but Charlie suspects foul play. Don disagrees, but he agrees to help Charlie investigate whether the student was murdered because of his research into a building's structural integrity. Alyson Reed, Douglas Sills, and David Hunt guest star. The Hyatt Regency walkway collapsed in 1981 as did the Hartford Civic Center in 1978. The episode concludes with Don Eppes saying that Occam's razor says "that the simplest answer is usually the right on

A young girl is kidnapped, but her parents refuse to cooperate with Don's investigation. The girl's father (Neil Patrick Harris) is an innovative mathematician, and the kidnapping may be related to his work on the Riemann hypothesis. Mathematics used: Cryptography, prime numbers, Riemann hypothesis and Riemann zeta function

Don is investigating a series of train accidents which are recreations of previous wrecks. The saboteur leaves a note composed entirely of numbers. Keith Szarabajka guest stars. Mathematics used: Kasiski examination, Cryptography, Fibonacci sequence, golden ratio and Beale ciphers

A strange series of robberies leads Don into a case involving counterfeit money, kidnapping and murder. Don is assisted by Secret Service agent Kim Hall (Sarah Wayne Callies) while Charlie uses math to analyze fake bank notes and track their spread. Mathematics used: Guilloché pattern and wavelet analysis

A new murder with disturbing similarities to an old case leads Don to question whether he put the right man in jail. While Don tries to find the connection between the two cases, he asks Charlie to look for mistakes or flaws in the first case. Luis Antonio Ramos, Dominic Fumusa, Marek Probosz and Molly Hagan are among the guest stars. Mathematics used: Poker, geometric progression – paper folding, pyramid scheme, fingerprint and Schrödinger's cat

Don is investigating a series of sniper killings, and Charlie is searching for an underlying pattern to the attacks. What appears to be bad data can't be eliminated from the analysis, because it fits the only pattern he can find. Lou Diamond Phillips guest stars as FBI sniper and tracker Agent Ian Edgerton. Mathematics used: Projectile motion, Tipping point, regression toward the mean and exponential growth

A truck carrying radioactive nuclear waste disappears, and Don figures that a dirty bomb will be set off in downtown Los Angeles. When three suspects are caught but refuse to turn on each other, Charlie must try to convince one of them to give up the others and also the location of the waste. David Marshall Grant and Roxanne Hart guest star. In 1946 Manhattan Project physicist Louis Slotin used his body to protect fellow scientists during an accident with a plutonium experiment at Los Alamos; he

A researcher is murdered in his home, and Charlie must reconstruct data erased from his computer while Don investigates possible suspects. Guest stars include Joseph Gordon-Levitt, Corey Stoll, Bruce Davison, and Elizabeth Dennehy. David Krumholtz and Joseph Gordon-Levitt co-starred in the 1999 film 10 Things I Hate About You. Final appearance of: Sabrina Lloyd as Terry Lake Mathematics used: Sabermetrics and econometrics; bathythermograph; Van Eck phreaking

An unidentified flying object travels over Los Angeles and then disappears. Don suspects terrorist activity, and Charlie tries to find out more about the object and its flight path. Guest stars include Gloria Reuben, Bill Smitrovich, and Ethan Embry. Mathematics used: Combinatorics and conditional probability distribution – "squish-squash" with Fourier analysis

A prison bus crashes, allowing two dangerous convicts to escape. Don is joined by his former Fugitive Recovery partner Billy Cooper (Max Martini) as the Bureau launches an effort to recapture them. Guest stars include Christina Cox and Jennifer Westfeldt. Mathematics used: Bayesian inference, Markov chain, Chapman–Kolmogorov equation and Monty Hall problem