Suggestions to Learn Math Beyond Engineering Mathematics

[medwatt]

Hello
I have to say I am a mathematics fanatic but my frustration stems from the fact that I teach myself mathematics meaning that I am basically lost what to do when I am impeded by an obstacle.
To cut a long story short, I have knowledge in calculus, complex analysis, linear algebra etc and most of the knowledge I have acquired is from books like Engineering Mathematics, Advanced Engineering Mathematics by Stroud and schums etc. I had decided lately to start some real analysis. Though the initial pages of the real analysis books were fine but after like 50 pages things got very rough. To put my points straight I am unused to the abbreviated languages used in these books such as leaving hanging sentences and a lot of mathematical notations which I'm not used to. I have also looked at other books and also in number theory but really the result is pretty much the same.
What I want is a suggestion of intermediary books which can take someone from books like Engineering Mathematics, Advanced Engineering Mathematics to books difficult writing styles. What I really want is books which can make me understand the notations and stuffs in Analysis books and other higher mathematics books. Books that are really meant for self study which are very lucid and with detailed explanations.

Thanks for reading

 

[micromass]

For analysis, you should try "Understanding analysis" by Abbott. Very nice book.

Another suggestion is to read "calculus" by Spivak. This book is very rigorous (and almost a real analysis book), but with topics you already know something about (and other topics which are likely new).