So having completed Calculus I-III, Linear Algebra, and Ordinary Differential Equations, I am looking at a 400 level math course as a freshman during my 1st semester at college. With this, what should I expect? I know my teacher said, the proofs are far more complex, so would you recommend going over college proofs, and if so what book or resource should I use?
@schakraborty560 your college likely offers some sort of logic, discrete math, or introduction to proof-writing course, so I would check out those syllabi and any textbooks they use. Many universities offer similar courses.
You’ll probably want to go over proof techniques (such as direct proof, induction, proof by contradiction, proof by cases, combinatorial/proof by bijection, etc.).
Of course, the best practice is actually writing out mathematical proofs, and it is often good to start with simpler problems first. Typically you will find such problems in an introductory discrete math course.
You should expect less calculations and more “essay” proof writing. Depending on what math course you’re taking now, you’ll probably have to memorize/understand some of the famous theorems relating to that subject.
What class is it?
I would talk to your advisor or the head of the math department and get their advice.
It should be fine if you did well in all the prerequisites.
It is an Intro to Partial Differential Eqs class @halcyonheather. Thanks everyone! The advice really helped 
!