Wow!!! If this was intended to be an introduction to Programming then what would a special/advance topic in programming be??

Operational & denotational semantics, for example...

Dana S. Scott. Outline of a mathematical theory of computation. Technical Monograph PRG-2, Oxford University Computing Laboratory, Oxford, England, November 1970.

Dana Scott and Christopher Strachey. Toward a mathematical semantics for computer languages Oxford Programming Research Group Technical Monograph. PRG-6. 1971.

Gordon D. Plotkin. A Structural Approach to Operational Semantics. (1981) Tech. Rep. DAIMI FN-19, Computer Science Department, Aarhus University, Aarhus, Denmark

I don't wanna sound off-topic but I liked your suggestions, they're great actually... Can you please provide me with some suggestions on the following topics? An introduction to Programming Languages Design theory. Computer Science Mathematics, introductions and advanced topics.

If you're interested in books, I like these.

Intro to programming books:

Matthias Felleisen, Robert Bruce Findler, Matthew Flatt, and Shriram Krishnamurthi. How to Design Programs: An Introduction to Programming and Computing.

Daniel P. Friedman (Author), Matthias Felleisen (Author), Duane Bibby (Drawings), Gerald J. Sussman (Foreword). The Little Schemer.

Programming language principles & implementation books:

Daniel P. Friedman, Mitchell Wand, and Christopher T. Haynes. Essentials of Programming Languages.

Shriram Krishnamurthi. Programming Languages: Application and Interpretation.

Matthias Felleisen, Robby Findler, and Matthew Flatt. Semantics Engineering with PLT Redex

These are all by pretty much the same group of people (but distributed across the US: http://racket-lang.org/people.html) so the books all go together really well.

our of curiosity, have you read "Types and Programming Languages", and if so, what is your opinion?

I haven't, but I should. Everyone I know who's read it says it's great.

Intro to Computer Science, not programming. Different subjects.