I am delighted to announce that my first book, Linear Fractional Transformations: An Illustrated Introduction, has now been published Springer’s Undergraduate Texts in Mathematics. You can find the product page here: Springer Product Page. It is available both as a hardback and e-book. If you are interested in the book but are unsure if you want to purchase it, an excerpt from the preprint of this book can be found here: LFT Chapter 2. (But do bear in mind that the finished product is of a significantly higher quality: you can see a preview on the Amazon page.)

Linear Fractional Transformations is aimed primarily at an undergraduate audience, such as first-year mathematics students who wish to see some beautiful mathematics beyond the calculus/linear algebra curriculum. It is lovingly illustrated: in the final ~250-page manuscript, there are over a hundred different figures (many of which are made of several individual drawings). There were, in fact, too many illustrations and too much material in the original preprint, and almost half of it had to be cut.

Some of that material was repackaged, rearranged, rethought, and significantly expanded upon to produce a second book with the tentative working title A Projective Perspective on Linear Fractional Transformations, most likely to be changed at a later point. Aside from presenting some of the material from the first from a very different and more abstract perspective, there is additional material aimed at older undergraduate students, such as Fuchsian groups. It is currently under review by the Mathematical Association of America, but I cannot say much more at this time.

There is also a third book, co-authored with my PhD advisor, Alex Kontorovich that is under contract with the Princeton University Press. It is intended as a crash course in analytic number theory, aimed at the lower graduate/advanced undergraduate audience. We think that it will be a valuable addition to the literature, providing a resource that delves deeply into advanced material while still providing intuition about the broader picture.