The book comprises notes are of several varieties. Some are merely to introduce and to whet the appetite for further investigation. The author has chosen to include elementary material with definitions and derivations relevant to understanding time and space, as well as ancient civilization calendars. The bio-mathematics of seed dispersal is presented with calculus. The scope of topics I believe reflects our times of an expanding knowledge universe and understanding of a complex world in a digital age of global images and communications. Several original ideas and contributions include: the calendar analysis of Mayan and Peruvian civilizations using arithmetic and algebra concepts of modulo n, as well as an insight on the term Golden portion is explained. A novel application to pyramid angles and arrangement seen best from a top view perspective is given. The envelope of trajectories of a bio-projectile with wind is calculated with fractional calculus. This natural evolution of calculus derives from arithmetic sums and algebra. Altogether these notes are intended to enliven and enlighten the application of mathematical sciences describing architecture and civilizations.