Reddit reviews Abstract Algebra

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)

There is a book that is a little more of a "lay-person"'s guide to this stuff and I think you should check it out and read through it before going onto some more technical stuff. It'll give you an idea and overview of some of the more interesting parts of the subject.

It's also a book that I think every mathematician should read, too, but I won't get on my soapbox here.

The book's called Symmetry by Hermann Weyl, who was a world-class mathematician.

For more advanced references that will work for your level I would recommend the Gallian or Beachy and Blair which are better suited for someone without an extensive math background. Many of the texts that have been suggested so far are better suited for someone who is either an honors undergrad with a strong background or a first-year grad student. The Beachy and Blair is cheap new, I would look around for a used copy if you want to go for the Gallian. There's no reason you need the most recent edition, either.

If you have questions about the material I'd actually be happy if you PM'd me, it's always good to go over this stuff again for a mathematician.

Source: I'm a PhD student in math and professional nerd, and apparently this qualifies me to tell people what books to read and not read.

When I was in undergrad we used Abstract Algebra by Beachy and Blair.