# Basic Introduction to University Level Mathematics [closed]

I'm looking for a script/ book on a very basic level. I am going to finish high school soon and go to university to study mathematics. The books I tried to read (mainly in German, so naming them won't be of any help) are very difficult to understand. I am willing to try out reading a book in English, so if you have a suggestion, please let me know!

In school, we learned about integrals and derivatives, and the Gauß-Algorithm.

## closed as unclear what you're asking by hardmath, Claude Leibovici, user91500, E. Joseph, mlcJun 9 '17 at 12:53

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• I don't understand: where are you studying? Why did you even take books in german if you understand, apparently, english better?\ – DonAntonio Jun 5 '17 at 11:59
• Do you about sequences and series? – Omnomnomnom Jun 5 '17 at 12:02
• Basic introduction to "University Level Mathematics" could mean several things. For some students (not you necessarily) it means coursework to remediate a poor high school math background. For others it will mean a calculus textbook. If you have studied calculus already and Gaussian elimination (solving linear systems of equations), you might be wanting to either review that material or to move on to (say) multidimensional calculus or abstract linear algebra. So its hard to recommend books without more focus. – hardmath Jun 5 '17 at 12:15
• @hardmath It means a textbook. – A. Pavlaković Jun 5 '17 at 12:48
• @A.Pavlaković Actually, it would be good if you could say what the books in German are that you're finding too hard. Otherwise, that really gives people no idea of what level you're at. – user49640 Jun 6 '17 at 2:20

Here I'll introduce some books, and (maybe) lecture notes, not oriented to promote any specialized topics in mathematics, but a necessary knowledge base that I think is good for pre-freshman in university-level mathematics.

Furthermore, I'll continuously update this post, unless it is disagreed.

General $$\textbf{ How to study for a mathematics degree }$$ Lara Alcock, $OUP, 2013$. Though the name of the book is not as interesting, it is, definitely, a good way to introduce one to a thinking style of advanced mathematics.

Analysis $$\textbf{ Analysis I }$$ Terence Tao, $Springer, (III\ Edition)2016$. A really good book in introducing the way of thinking in a constructive, based-on-axiom ways. No need further introduction, as the name of its author is enough to explain. You may also find Tao's lecture notes here at UCLA.

$$\textbf{ Mathematical Analysis I }$$ Vladimir A. Zorich $Springer, 2002$. My self-introducing book during my first year of high school, while I've finished all A-level syllabus. It gives a relatively fine way of teaching, with a level of difficulty, and also thanks to the use of logical notation by Zorich, it may give some awkwardness when first seeing it. But if you have familiarized with it, and also, trained yourself with the exercises, it must give you a better and wider view for your future studies, at least for myself.

Some other lecture notes

Calculus (Preliminary level): $Oxford$

Calculus (differential equation): $Oxford$

Calculus (vector calculus): $Cambridge$

Group theory: $Cambridge$

Tbc.

I suggest you just have fun and wait for University learn the formal stuff. Here's a related question and answers:

What books should I get to self study beyond Calculus for someone about to start undergrad mathematics?

I highly encourage you to study some logic if you haven't already done so in highschool.

My favourite 'first book' on the subject is Sweet Reason by Henle, Garfield, and Tymoczko. I think every student wanting to study mathematics and computer science beyond an elementary level should read this book!

The book covers sentential, predicate, modal logic, many-valued logics, and general argument and reasoning skills. It has many exercises and an accompanying website.

The book will make you get comfortable with things like quantifiers and when it comes time to do some mathematics, you can focus on the mathematics instead of the language(s) of mathematics.