Foundations

This is written to be a general introduction to mathematical logic and proofwriting. The vehicle by which this is explored will mostly be through elementary number theory, however there will be some combinatorics topics covered as well.

Following the basic introduction will follow undergraduate-level introductions into the mathematical subjects of Algebra, Analysis, and Topology. Each of these will build on the skills earlier developed while also holistically presenting the material in each subject.

Over the course of these lessons, the reader will gain a level of understanding of mathematics commensurate to an introductory-level exploration of the topics aforementioned. There will not be enough problems, nor topics explored in enough detail, to allow the student ample experience to form a complete knowledge-base. Rather, by reading this, a student should be primed to know if he or she wishes to seek out a proper textbook and begin learning more deeply.