The n-th harmonic number is the sum of the reciprocals of the first n natural numbers and is related to the harmonic mean. It is important in various branches of number theory and approximates the natural logarithm function. It is also used in Zipf's law distribution and the Bertrand-Chebyshev theorem.

This course explores the relationship between algebra and computation, focusing on algorithms used for symbolic computation and modern algebra concepts. Subjects covered include proving combinatorial identities, Gröbner bases, symbolic integration, and experimental mathematics. Prerequisites suggest this is a mid-level course.