Introductory analytic geometry and calculus. Topics include limits, continuity, differential calculus of algebraic and trigonometric functions with applications to curve sketching, optimization ...

The binomial distribution is a key concept in probability that models situations where you repeat the same experiment several times, and each time there are only two possible outcomes—success or ...

Predicting how complex stochastic systems respond to small external perturbations is central in physics, climate science, and engineering. We combine the generalized fluctuation–dissipation theorem ...

Operational Laws: Little's Law, response-time law, asymptotic bounds, modification analysis, performance metrics. Markov Chain Theory: both discrete-time and ...

The Extreme Ultraviolet Imaging Spectrometer (EIS) on the Hinode spacecraft has substantially advanced our understanding of the Sun’s upper atmosphere. Unfortunately, after being in operation since ...

When is it appropriate to completely reinvent the wheel? To an outsider, that seems to happen a lot in category theory, and probability theory isn’t spared from this treatment. We’ve had a useful ...

If a new pathogen causes a large epidemic, then it might “burn out” before causing a second epidemic. The burnout probability can be estimated from large numbers of computationally intensive ...

Creative Commons (CC): This is a Creative Commons license. Attribution (BY): Credit must be given to the creator. As a supervised machine learning algorithm, conditional random fields are mainly used ...