This textbook offers a unique exploration of analytic number theory that is focused on explicit and realistic numerical bounds. By giving precise proofs in simplified settings, the author strategically builds practical tools and insights for exploring the behavior of arithmetical functions. An active learning style is encouraged across nearly three hundred exercises, making this an indispensable resource for both students and instructors.Designed to allow readers several different pathways to progress from basic notions to active areas of research, the book begins with a study of arithmetic...

This textbook examines the Hamiltonian formulation in classical mechanics with the basic mathematical tools of multivariate calculus. Graduate and advanced undergraduate students in physics or mathematics who are interested in mechanics and applied math will benefit from this treatment of analytical mechanics.