Start with some school textbooks for grades 8-12 i.e. Secondary Education. This is more for a refresher course in the absolute basics.
The above can be supplemented with the following books to develop intuition;
1) Who is Fourier - https://www.amazon.com/Who-Fourier-Mathematical-Adventure-2n...
2) Functions and Graphs - https://www.amazon.com/Functions-Graphs-Dover-Books-Mathemat...
After this is when you enter undergraduate studies and you have to fight the dragon of "Modern Maths" which is more abstract and conceptual. In addition to standard textbooks; i suggest the following;
1) Concepts of Modern Mathematics - https://www.amazon.com/Concepts-Modern-Mathematics-Dover-Boo...
2) Mathematics: Its Content, Methods and Meaning - https://www.amazon.com/Concepts-Modern-Mathematics-Dover-Boo...
3) Mathematical Techniques (i am linking this so you can see the reviews but get the latest edition) - https://www.amazon.com/Mathematical-Techniques-Dominic-Jorda...
Finally, if you would like to learn about all the new-fangled mathematics your best bets are;
a) The Princeton Companion to Mathematics - https://www.amazon.com/Princeton-Companion-Mathematics-Timot...
b) The Princeton Companion to Applied Mathematics - https://www.amazon.com/Princeton-Companion-Applied-Mathemati...
One important piece of advice that i have is to become comfortable with the Symbols, Notation and Formalism used in Mathematics. Most students are intimidated by the Formalism (which is nothing more than a precise form of shorthand to express abstract concepts) and give up on studying Mathematics altogether. This is a shame since it is merely the Form and not the Function of Mathematics.
The last time people asked, I collected the responses so I could do the same thing as you. Note that I'm wanting to learn it in a way where I can do proofs. So, I have general-purpose books and stuff for that. I just ordered the three books I've seen pop up the most. Although 2 are in the mail, Concepts of Modern Mathematics by Stewart just got here yesterday. It had an awesome opening that made me wish the math I was taught in school was done like this back when I went. Makes newer stuff make a lot more sense, too. I included a link to Dover that has a Google Preview button on it where you can read full, first chapter for free to see if it's what you like. Other two are more about exploring and proving things which may or may not interest you. I added them in case anyone is reading your question to learn that stuff.
I would recommend 'Concepts of Modern Mathematics' [1], by Ian Stewart. It has some very nice illustrations and humor, and reminds me of 'Learn You A Haskell For Great Good' (though I believe CoMM came out before LYaH). It's a wonderful preview of a variety of topics, and is intended to introduce someone with a poor math background to some of the different fields of math.
From the Amazon description:
In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts underlying "new math": groups, sets, subsets, topology, Boolean algebra, and other subjects. No advanced mathematical background is needed to follow thought-provoking discussions of such topics as functions, symmetry, axiomatics, counting, topology, hyperspace, linear algebra, and more. 200 illustrations.
To get better intuition without a math degree I'd recommend: Concepts of Modern Mathematics which only requires elementary algebra, but will give you great intro treatments of everything from groups to number theory.
Start with some school textbooks for grades 8-12 i.e. Secondary Education. This is more for a refresher course in the absolute basics.
The above can be supplemented with the following books to develop intuition;
1) Who is Fourier - https://www.amazon.com/Who-Fourier-Mathematical-Adventure-2n...
2) Functions and Graphs - https://www.amazon.com/Functions-Graphs-Dover-Books-Mathemat...
After this is when you enter undergraduate studies and you have to fight the dragon of "Modern Maths" which is more abstract and conceptual. In addition to standard textbooks; i suggest the following;
1) Concepts of Modern Mathematics - https://www.amazon.com/Concepts-Modern-Mathematics-Dover-Boo...
2) Mathematics: Its Content, Methods and Meaning - https://www.amazon.com/Concepts-Modern-Mathematics-Dover-Boo...
3) Mathematical Techniques (i am linking this so you can see the reviews but get the latest edition) - https://www.amazon.com/Mathematical-Techniques-Dominic-Jorda...
Finally, if you would like to learn about all the new-fangled mathematics your best bets are;
a) The Princeton Companion to Mathematics - https://www.amazon.com/Princeton-Companion-Mathematics-Timot...
b) The Princeton Companion to Applied Mathematics - https://www.amazon.com/Princeton-Companion-Applied-Mathemati...
One important piece of advice that i have is to become comfortable with the Symbols, Notation and Formalism used in Mathematics. Most students are intimidated by the Formalism (which is nothing more than a precise form of shorthand to express abstract concepts) and give up on studying Mathematics altogether. This is a shame since it is merely the Form and not the Function of Mathematics.
Concepts of Modern Mathematics by Stewart
https://www.amazon.com/Concepts-Modern-Mathematics-Dover-Boo...
Dover Version with Google Preview Button
https://www.amazon.com/Introduction-Mathematical-Reasoning-N...
How to Prove It by Velleman
https://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/...
From the Amazon description:
In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts underlying "new math": groups, sets, subsets, topology, Boolean algebra, and other subjects. No advanced mathematical background is needed to follow thought-provoking discussions of such topics as functions, symmetry, axiomatics, counting, topology, hyperspace, linear algebra, and more. 200 illustrations.
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[1]: http://www.amazon.com/Concepts-Modern-Mathematics-Dover-Book...
here's a whirlwind tour http://www.amazon.com/Concepts-Modern-Mathematics-Ian-Stewar...
http://www.amazon.com/Concepts-Modern-Mathematics-Ian-Stewar...