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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.

Thanks.

Matty D
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  • I find this question both very broad and very opinion-based in terms of expected answers. As such, I consider it a rather poor fit for this Q&A format, despite the hight number of upvoters who obviously think differently. – MvG Dec 11 '13 at 11:11
  • You're entitled to you're opinion and it seems like people don't even want to answer it anyway, thanks though. I'll just have to go with what I've found through my searches and decide for myself. – Matty D Dec 11 '13 at 22:00
  • If you want to review highschool math, the Gelfand books that you mentioned are great. Also check out the book "Lines and Curves" by Gutenmacher. The books by Art of Problem Solving are fantastic, as well. These would cover all you need, really. –  Sep 14 '14 at 03:55
  • See the books I mention in my answer to Preparing For University and Advanced Mathematics as well as the books at the other math StackExchange questions I direct you to in my answer. – Dave L. Renfro Sep 15 '14 at 18:04

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