<p>I recently switched from biochemistry to mathematics. Next semester, I was able to enroll in multivariable calculus and linear algebra since I took calculus two as a prequisite. I have yet to take discrete mathematics & proof writing. Is this necessary for linear or can I take discrete after linear algebra?</p>
<p>Linear algebra does not use material from Discrete Math and does not usually require it as a prerequisite. If your university teaches a rigorous proof-based linear algebra course, they might prefer students to get some exposure to proofs before enrolling in the class. In that case it would still be possible to take linear algebra without an intro-to-proofs class, but it might be a fair bit harder.</p>
<p>You will get better advice from someone at your own university who is familiar with your curriculum.</p>
<p>I concur, this is heavily university dependent. Discrete math was not required at my alma mater, and there was no intro to proofs class. You just learned it through algebra and analysis, the first year weed-out courses. Some places will let you do entire majors with applied courses and little in the way of proofs, while at other departments it’s all abstract everything (epsilon-delta proofs everywhere where you never actually have to compute, say, a double integral).</p>
<p>So regardless, I think the best way to do this is to practice writing some proofs in linear algebra and just take the course. I guess it’s nice to have some proof-writing practice from something like discrete math, but I learned proofs through basic linear algebra back in the day. </p>
<p>Be able to define a vector space and use its axioms to prove basic facts about it, be able to prove things about spanning sets and linear independence, and things like when linear maps surject, inject, etc and how to detect these things based on spanning sets and bases, that injectivity can be determined based on where zero goes, and you’ll be good to go without a question (in fact, even doing much less than this will likely be enough to get you familiar).</p>