>>13514142>>13514275Somewhere along your path of Algebra to Precalculus, you will want to study Geometry. The AoPS book is good, but it's aim is targeted towards math competitions. This is fine, but your interest is in Pure Mathematics and there are better choices. Geometry serves as an excellent introduction to basic proof writing and mathematical logic. If you want to give yourself a challenge, Euclid's Elements, while not totally mathematically sound by today's standards, was the defacto book for hundreds of years, for good reason. It captures what Pure Mathematics is like in a microcosm, isn't absurdly difficult, and, most importantly, it lays out an axiomatic foundation and uses mathematical logic to justify every statement. The Green Lion Press version of the text is the best I have ever seen so that would be my recommended version.
However, being a 2000 year old text does have it's issues. There are many modern Geometry texts that are rigorous and use mathematical logic and proofs just as effectively. Kiselev's Planimetry and Stereometry texts are a personal favorite of mine. The former covering 2D plane geometry, the later covering 3D solid geometry with excellent rigor and wonderful illustrations (this is crucial in a good geometry text!) Another option that I like is "Basic Geometry" by Birkhoff and Beatley. It uses a different axiomatic framework than tranditional Euclidean geometry, but still provides the rigor that you want form a Geometry text.
If you want a totally non-tradition way of seeing Geometry, Gelfand's Geometry book, which was recently released. It puts aside the axiomatic approach of the other texts, so you don't receive much of the mathematical logic end, but it presents geometry through constructions, and could be considered "Projective Geometry" rather than the traditional Euclidean version, and it can be a nice way to see how you can capture the same topic with totally different framework
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