I am a computer science student who, by nature of my major, am disallowed from taking all the of the math needed to get to algebraic topology for credit as an undergrad(there are a limited amount of credits I can take, and those credits will be eaten up by computer science classes at my university). Despite this I would like to build a path to understanding algebraic topology in my free time. There have been a lot of insights and inspirations from algebraic topology in my field in recent years and I see it as a good branch of mathematics to know generally for solving problems in computer science(proof writing, abstract thinking, etc).
I am finishing multivariate calculus, which covers some areas of elementary analysis, this fall alongside linear algebra. I have been doing linear algebra for a while now as I tutor it already and use a lot of it in my personal work/self study. I've also already done differential equations and numerical methods.
What will I need to ramp up to algebraic topology and is computational algebraic topology just an application of the theory? I noticed that Michael Robinson at American University posted his class online and I plan to watch that lecture or Norman Wildbergers once I get to the point to be able to do problems in algebraic topology.
I noticed that Michael just requires Calculus and Linear Algebra for his course but others on here seem to think an understanding of Groups is also necessary. How necessary are groups?