Explore the fundamental concepts of circuit analysis and Boolean functions in this comprehensive mathematics lecture. Learn about canonical forms for logic circuits, including the use of logic gates like AND, OR, NOT, XOR, NAND, and NOR. Discover how to associate algebraic expressions with logical circuits to capture their effects on all possible inputs. Examine the geometric interpretation of Boolean functions and compare the traditional Boolean algebra approach with the more powerful original Algebra of Boole. Delve into topics such as the 16 connectives/operations, three-dimensional representations, and methods for expressing Boolean functions. Gain valuable insights into circuit analysis and Boolean algebra that will enhance your understanding of mathematical foundations in logic and computation.