Obtaining a deeper understanding of lower level Mathematics

I am a college student, at a community college and I am in the process of obtaining an associates degree in general science with a specialization in mathematics in hope of transferring to a university to major in electrical-computer engineering.

When I first started community college about 3 years ago I entered with little no knowledge of anything(I was an extremely lazy high-school jock and a mediocre one at that), I took every introductory course basically except for in English. My first math class was learning basic arithmetic and now I am entering a Differential equations and Calculus III class next semester.

Now that my background is out of the way I would like to get my question. I am looking for books to help me obtain a deeper understanding of lower level mathematics, basically everything from Pre-Calculus and down. While I know enough(of algebra, geometry, trig, precalc) to excel in the courses at my school, which I think is fair to say are watered down. I feel like at my school the courses have only touched the surface of lower level mathematics and I would like to delve deeper into them.

I have done some research and think that the books I am looking for are Algebra, Trigonometry, Functions & Graphs, Method of Coordinates, Sequences-Combinations-Limits; all by Gelfand.

I am also looking for books, on geometry(Now I don’t know if I should find a classical Geometry book or a Euclidean Geometry book; I think the two are the same but I don’t know)

Also, I am looking for a book that teachers about the number system, like the difference between Real numbers and complex numbers, and how the Reals branch off between natural, rational, irrational, etc.

And a book on mathematical notation would nice.

Finally, I need to know what order would be best to read these books. Basically I want to know the order in which would provide the best flow or synergy with one another.

I am obviously not going to buy all these books at once and this list is by no means set in stone and is subject to change.

Another reason that I want to get a deeper understanding of these subjects is because I feel like my lack of depth is what hindered me in my linear algebra class this semester, I did okay overall but I had hard time because the book used a lot of notation and symbols with stuff that I didn’t know.

I eventually, after reading these books, is get better books for calculus, linear algebra, and discrete mathematics.


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