Luckily there are a lot of introductory texts in logic. Logic With Trees is a popular undergraduate one covering propositional and predicate calculus - sequent calculus, semantic tableaux and elementary model theory for both. You'll also probably have to study modal logic at some point in your degree, this is a free introductory reference with a few citations.

More advanced logic classes might have you learn proof/model and category/topos theory, but I never got to those. :)

A youthful fascination with logic is akin to the young mechanic's fervor in the presence of a nice set of wrenches, especially if he - always a he - doesn't own them and cannot afford them, and often enough, has no immediate need of them. What's forgot in the passion of the moment is that they're both tools to be used, not contemplated in Socratic detachment. Well, actually, they can be so contemplated; no great harm comes from it; and it - they - have their uses. Indeed, the sheer velocity of your career through school will argue you away from any long-term obsessions, that and the allure of better subjects. The point here is to give the subject its due as necessary and as you're reasonably inclined, but to keep your gaze firmly fixed on worthier subject and goals. And don't forget girls. If you think I'm joking, I'm not.

Truly, logic is beautiful, as are the axioms of arithmetic and lots of other balanced, aesthetically pleasing things, and where you're going there are a lot of such things. And as logic is such a thing, so is philosophy. There's a real risk that a student grows out of logic (that's not the risk), and replaces it with the idol of philosophy, an altogether more difficult siren to get away from. Ahh!, the seductive charms of good thinking. Pah! The seductive charms of a good crossword puzzle!

The secret to keep on or near your person at all times is that the secret of this life lies in the doing. University offers a thousand doors that all enter into some kind of doing, often the best kind of doing. And another thousand doors that open into alleyways and dead ends of endless fascination.

Learning to deal successfully with fascinations isn't specifically on any college syllabus. It should be. Maybe it's enough at first to remember to do, that doing is what gets one anywhere, the lack of which gets one exactly nowhere. As it happens, logic, and philosophy, are great tarpits of doing nothing. Skirt them, visit them; stay out of them.

A phrase and a word: carpe diem. Everyone knows what this means: seize the day! Except that's not what it means. Carpe means pluck, in the sense of a ripe fruit. Nor is it about hedonism or epicureanism. Freely translated, the complete phrase means simply make the best and highest use of the opportunities of today, without undue reliance on the opportunities of tomorrow.

The word is liminal, (as) a term of art from anthropology. Wikipedia does a good job of it: "In anthropology, liminality (from the Latin word līmen, meaning "a threshold") is the quality of ambiguity or disorientation that occurs in the middle stage of rites, when participants no longer hold their preritual status but have not yet begun the transition to the status they will hold when the rite is complete. During a rite's liminal stage, participants "stand at the threshold" between their previous way of structuring their identity, time, or community, and a new way, which the rite establishes."

What this obscures is the sheer stress of being in a liminal state. The past is suspended, the future uncertain. All values shaken or unseated. Far from being a bad thing, it's merely an uncomfortable exhilarating thing, and a necessary thing. One finishes the traverse in all ways a different, better, and stronger person. College is a liminal state; is, should be, had better be. It is to be ridden. There is no true shelter or security in the ride, except perhaps for moments. And it is a fatal mistake to seek shelter, to escape the ride. Logic can be an early shelter, it just makes a man a fool. Philosophy is a later, far more dangerous shelter. Some never escape it.

I think your best bet is to start with a mathematics textbook that assists students in transitioning from computational classes to classes dealing with proofs. I think there are a number of good books out there, and one I have in my personal library is titled something like "Mathematical Reasoning," just not sure of the subtitle off the top of my head. Many books on logic do not provide answers, as do many math books on non-computational subjects, like in discrete mathematics, so you should see what the people reviewing such books say online. Is it self-study friendly? That's the main thing you need to make sure the book is good at --- allowing one to study it without an instructor, so the books will definitely need exercises along with answers. I'm teaching myself a lot of math in the hope of going to grad school in applied mathematics, and I have been burned a number of times by purchasing books online only to later discover that there are no answers to any of the exercises.

Thank you all! I have ordered some of the suggested books.