I want to learn abstract linear algebra. Do I require the knowledge of discrete mathematics before I start? I have the impression that abstract maths and their proofs can be understood easily by the concepts of discrete mathematics
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Lots of people use discrete mathematics as a first proof-based class. However, it's not strictly required for linear algebra. A good chunk of linear algebra is computational, and not really focused on theorems and proofs but on solving problems. You could really just dive in and see how much of it makes sense. You might find that a lot of it does.
Other common places to get to know proofs in a familiar context are geometry and elementary number theory. Like discrete math, these are both quite approachable for lots of people.