Knowledge-based events generally have two participants either taking a test or mathematically analyzing data.

The "capture histories" generated are analyzed mathematically to estimate population size, survival, or movement.

This allows even very complex optical systems to be analyzed mathematically or simulated by computer.

He developed the laws for falling bodies based on pioneering quantitative experiments which he analyzed mathematically.

He also explains the photoelectric effect by quantization and mathematically analyzes Brownian motion.

This impact can be analyzed mathematically by majorization of vectors with eigenvalues.

Kahn proved his ability to analyze mathematically and scientifically the problems that were constantly presented.

The computing technique can be analyzed mathematically.

An enormous variety of games that can be analyzed mathematically have been played around the world and through history.

Linear systems are easier to analyze mathematically.