I'd like some advice on my approach to learning mathematics (e.g. is this reasonable).
Right now I'm interested in computing. I understand basic algorithms such as how quick, heap, merge, insertion and bubble sort work. But that is the extent--I'd love to learn more about algorithms, computability and complexity topics.
interests are centered around learning Mathematical Logic for the Prolog programming language (which, from what I understand, is based on first-order predicate calculus). I'd like to work on some *very*
minimal AI systems and other things that build directly on top of Mathematical Logic.
In 2-3 years time, I plan to pursue my interests in science. At that time I will focus on other areas such as calculus, algebra, differential equations, differential geometry, topology... (this is according to the curriculum for the programme I wish to enter).
Recalling that some great mathematicians attempted to axiomize the logic and suggest that everything comes from the foundations--mathematical logic and set theory--I wondered if it would be wise to start off with logic? Would it benefit me for my later studies (re: science). More importantly, would it make me much stronger with the math?
I have a background in programming. Not computer science. I have minimal exposure to algorithms and my bachelors program did not contain any
math offerings. My math abilities end at the high school level.
So I would like to know whether or not it is a good idea to dabble with logic, algorithms, (and time permitting) computability and complexity theory and then to later (~2-3 years) try my hand at the other topics listed.
Is this a "sound" approach, or should I be doing it another way? I really have no concept of how difficult these topics are, so please enlighten me
Best regards and thanks for your thoughts.
P.S. How deep does the rabbit hole go with regard to the topic of Mathematical Logic?
(Can anyone recommend David Hilbert's Principles of Mathematical Logic
? I've managed to read the first 6 pages (of ~170) on Amazon and they are quite accessible--would it get very difficult after that? The TOC reads: I. The Sentential Calculus, II. The Calculus of Classes (Monadic Predicate Calculus), III. The Restricted Predicate Calculus, IV. The Extended Predicate Calculus.)