if you're just looking for the fundamentals of logic and mathematic / programmatic reasoning, I suggest starting with a solid understanding of Discreet Math. Here is an excellent textbook on the subject which I used to teach myself the subject. Start at chapter 1 and move forward https://www.amazon.com/Discrete-Mathematics-Introduction-Mathematical-Reasoning/dp/0495826170?asin=0495826170&revisionId=&format=4&depth=1
I think that is the wrong book. The book is "Discrete Mathematics: Introduction to Mathematical Reasoning".
Unless "Discrete Mathematics: Introduction to Mathematical Reasoning" and "Discrete Mathematics: with Applications" are the same.