What are the most important undergraduate courses for a non computer science person who plans to become a software engineer?

It depends on your interests. If you are interested in becoming a software engineer in a non-technical company (for example: PayPal etc.), doing Data Structures is probably enough, but is a must. This is anyway a prerequisite for most of the remaining CS courses, so consider it a foundation course. Doing this course is mostly enough to be competitive in the selection procedure of the companies I mentioned. But, if you are interested in a core CS job, like Google, you would be well served to pursue as many CS courses as possible, including, but not limited to, Design of Algorithms, Computer Architecture, Computer Networks and Programming Languages. Best of luck for your endeavours!! P.S.: I pursued this path myself while at IIT, so if you wish to talk about it, you can ping me anytime.

Data structures (CSL 201) is a must.

Data structures, Algorithm, Operating systems, Machine Learning (In that order, generally) Depending on the kind of job you are interested in, the value of (4) might change. But DS and Algorithms are definitely fundamental if you want to learn computer science.

I would recommend don't study any subject just for the sack of it. If you like to code pick up any problem you want to solve and solve it. This problem can be1) Anything you do everyday and want to automate it.2) Any problem you picked up for codechef or hackerearth or any competetive coding platform.3) Some random idea.And while solving these problem and researching about them, you can learn everything taught in pretty much every subject of computer science.