I am presently working on a series of math books that will consist of four volumes: (1) Algebra, (2) Geometry, (3) Precalculus, and (4) Calculus, all with the tag line of “For the Enthusiastic Beginner.” The books are aimed at middle-school and high-school students (along with anyone else who wants to learn some math!). They will include many examples and solved problems, so they should be great for self-study. They’ll also feature lots of limericks – the Algebra book will have more than 100 of them! For a sampling, click here: Math Limericks.
Like my other self-published books, these will be inexpensive. The completion date for the Algebra book will be June 2024. And then roughly yearly intervals for the others. In the meantime I’ll periodically post some chapters in draft form.
The Algebra book grew to be a bit long, so I’ll need to break it up into two volumes. The numbering of the chapters and pages runs straight through, so it’s really just one book, split into two physical volumes.
Volume 1:
1. Background, Part 1
2. Background, Part 2
3. Using letters, Part 1
4. Using letters, Part 2
5. Solving for x
6. Coordinate systems and lines
Appendix A: Geometry tools
Appendix B: Benefits of using letters
Glossary of notation
Volume 2:
7. General functions
8. Quadratic equations
9. Logs and exponentials
10. Means, sequences, and series
11. Miscellaneous topics
12. Slopes of general functions
Appendix C: Binomial coefficients
Glossary of notation (repeated)
Other topics that are sometimes considered to be part of “Algebra 2” will reside in the precalculus book (book #3 in the series): trigonometry, complex numbers (a little bit is done in Chapter 8 above, but there is much more to do), conic sections, probability, and other topics.
Stay tuned for some sample chapters from the Algebra book. For now here’s an early draft of the chapter on the Pythagorean theorem that will eventually appear in the Geometry book (book #2 in the series). The exercise solutions are at the end of the chapter.
Pythagorean theorem (draft)