Reddit reviews Propositional and Predicate Calculus: A Model of Argument

I would guess that career prospects are a little worse than CS for undergrad degrees, but since my main concern is where a phd in math will take me, you should get a second opinion on that.

Something to keep in mind is that "higher" math (the kind most students start to see around junior level) is in many ways very different from the stuff before. I hated calculus and doing calculations in general, and was pursuing a math minor because I thought it might help with job prospects, but when I got to the more abstract stuff, I loved it. It's easily possible that you'll enjoy both, I'm just pointing out that enjoying one doesn't necessarily imply enjoying the other. It's also worth noting that making the transition is not easy for most of us, and that if you struggle a lot when you first have to focus a lot of time on proving things, it shouldn't be taken as a signal to give up if you enjoy the material.

This wouldn't be necessary, but if you like, here are some books on abstract math topics that are aimed towards beginners you could look into to get a basic idea of what more abstract math is like:

• theoretical computer science (essentially a math text)
  
  
• set theory
  
  
• linear algebra
  
  
• algebra
  
  
• predicate calculus
  
  Different mathematicians gravitate towards different subjects, so it's not easy to predict which you would enjoy more. I'm recommending these five because they were personally helpful to me a few years ago and I've read them in full, not because I don't think anyone can suggest better. And of course, you could just jump right into coursework like how most of us start. Best of luck!
  
  (edit: can't count and thought five was four)

For basic logic (first-order, classical) these are excellent textbooks...

• Goldrei, Propositional and Predicate Calculus
  
• Enderton, A Mathematical Introduction to Logic
  
• Smullyan, A Beginner's Guide to Mathematical Logic
  
  I should also mention that there are some free, open source textbooks on standard logic (good books, written by scholars in the field) such as the following...
  
  
• "Forall X" (Cambridge Edition)
  
  And if you want to go beyond classical logic, these are excellent textbooks...
  
  
• Priest, An Introduction to Non-Classical Logic
  
• Van Benthem, Modal Logic for Open Minds

> Second and third semester calculus

Is this vector calc? If so I enjoyed this book as it's very geometric, not at all rigorous and has lots of worked examples and exercises. Sorry it seems to be so expensive -- it wasn't when I bought it, and hopefully you can find it a lot cheaper if it's what you're looking for.

In general Stewart's big fat calculus book is a nice thing to have for autodidacts.

Obviously what you describe might include analysis, which these books won't help with.

>Formal logic theory (Think Kurt Godel)

I've heard Peter Smith's book on Godel is good, but haven't read it. Logic is a huge field and it depends a lot on what your background is and what you want to get out of it. You may need a primer on basic logic first; I like this one but again it's quite personal.