Review of Mathematics

The following pages contain notes from various math courses I've taken, as well as my own independent readings. I allocate what free time I can find each day learning something new in mathematics, then recording my findings here. I've made a separate page, Review of Computation, containing similar notes for computer science. Given my often hectic schedule, there may be errors or omissions. I try my best to correct these blunders during my week's end review, and during a broader cumulative review at month's end.

The notes are organized by volume (indicated by a Roman numeral), then by chapter (indicated by a Hindu-Arabic numeral). The organization attempts to mirror a typical course sequence for a mathematics education in the U.S. The volumes focus on a specific branch of mathematics, and the chapters focus on topics within that branch. For particularly long topics, an outline is provided at the beginning of the page.

Unlike many other fields and contrary to popular belief, mathematics doesn't necessarily require a linear learning path. Of course, some areas are easier to understand with knowledge from another area. Nevertheless, the reader is free to jump between the topics if they are interested in using these materials to self-learn mathematics. However, for the sake of expediency, the volumes are arranged (and written) with the assumption that the reader has knowledge from the previous volume. I try my best to make that assumption explicit by providing links to those areas.

I am so fortunate to have the time and opportunity to read mathematics, when so many of us go through life without ever getting the chance. I hope the materials evidence some of the field's beauty, and more importantly, provide others the opportunity.