Two suggestions: Elements of Programming (by Alexander Stepanov and Paul McJones) takes a mathematical approach to programming. Since its only prerequisite is a basic understanding of high school algebra, the book is very accessible and easy to follow. Digital Design and Computer Architecture (by David Harris and Sarah Harris) is a great book on computer architecture that starts with digital logic design (i.e. gates and transistors) and ends with a subset of the MIPS instruction set. Though, it probably won't help you much in 'daily work'.
Also recommended in this reply