Calculus in high school is often taught as a set of rules. Analysis is the branch of math that proves those rules. It deals with limits, continuity, and the nature of real numbers.
Topology studies the properties of spaces that remain unchanged under continuous deformation (stretching or twisting, but not tearing). higher mathematics books
A fantastic, often free alternative that covers set theory, logic, and various proof techniques with clear, approachable examples. 2. Analysis: The Rigor Behind Calculus Calculus in high school is often taught as a set of rules
If you prefer a more computational and intuitive approach, Strang’s book (and his famous MIT OpenCourseWare lectures) is the gold standard for practical application. 5. Topology: "Rubber Sheet" Geometry Topology studies the properties of spaces that remain
This is widely considered the gold standard for students moving from calculus to abstract math. It deconstructs the logical syntax of proofs, teaching you how to communicate complex ideas with rigor.