Karthik started off this class not really on the best foot. But I think after the first midterm he got ten times better. Considering that I think this is his first time teaching I'd say that is a pretty good handle on things. He really wanted us to know the concepts behind the math and really do things the correct way, which I appreciate as a math major. His tests were not that hard, this does not mean you don't need to study. If you know the content and how to do the problems then you are good. Karthik was not an interesting lecturer and he rambled on for the most part but it was not too bad especially since the tests reflected what he taught. So yeah I would take this with him again.

Firstly, I want to preface this review by saying [I think] this is his first time teaching, like anywhere, so hopefully he will be better for future quarters when he works out the kinks in his teaching style. Also, prepare your inboxes for A LOT of emails from him.
In terms of the material itself, this class isn't necessarily hard, especially compared to other math classes here, but I feel that it was just confusing trying to navigate this class at the beginning, given that Karthik is new to teaching. We started off the quarter using the blackboard, where the professor would try to follow a lecture style consisting of theorems followed by relevant examples. Personally, I prefer math classes to use the blackboard, but that's just me (I find that for slides, I get lazy and tend to skip class as a result). You can tell that Karthik really does care about student learning, it's just sometimes he doesn't go about it the right way. He responded to feedback after the first midterm and proceeded to teach the rest of the quarter using lecture slides instead, which was a little more organized, but they're usually riddled with errors and typos (which he subsequently corrects before posting to CCLE), and he proceeds to lecture extremely fast with slides.
There are ten homeworks throughout the quarter, and starting with #3, we started uploading them to Gradescope (for the first two we were handing in hard copies before Karthik utilized Gradescope). The homeworks are usually textbook problems, and they should be free points (especially since the solution manual and textbook can be found online for free). However, sometimes he adds his own problems, which are more tricky and usually contain way too many words. Just like his emails, you have to really scour through the message and look for the important parts, and pick them out from the spam that's around them. Because he likes making a ton of announcements, and fixing his typos, and making updates, he usually sends out like 10 or so (probably more ) per week, so prepare your inboxes. The homeworks are graded for 50% accuracy and 50% correctness, so they should mostly be easy points.
The class also has two midterms, given during lecture time, and they each have a ~5 point bonus problem at the end. The first midterm was pretty easy, almost all computation, and he gives further extra credit for doing separable equations using the change of variable formula. The second midterm is a bit more difficult, as there are more conceptual questions, but overall it's still mostly computation, and likely not that bad. For the final, another part that was confusing was that Karthik sent out a list of practice conceptual questions, but strangely refused to provide an answer key (and also forbade the TAs from helping us out with those). The final consisted of a little more conceptual questions, and difficulty wise, wasn't that bad, but he seems to grade a little more strictly for the final. Karthik can come off as passive aggressive in his emails, saying that "don't use the excuse that you're in engineering", and usually after the midterm/final he sends out an email listing all the common mistakes.
There are two grading schemes, your classic 10% HW, 25% Each Midterm, 40% Final, or 10% HW, 35% Better Midterm, 55% Final. There's also 1% extra credit for filling out the instructor evaluation survey, as well as the bonus points you could potentially earn from the midterms. He grades on a standard straight scale (i.e. 93 is an A, 90 is an A-, etc.), which I think was acceptable since he stated that the averages for the midterms seemed to be quite high. Would I take this class with him again? Meh. I think he'll get better in the future and work out his issues, and as a person, he's not a bad guy (genuinely curious to meet people, watches anime, etc.). If you're willing, you could give him a shot.

The class was a bit of a mixed bag. The homework isn't very hard and his policy this quarter was to drop the two lowest scores, so that was nice. Lectures usually didn't cover anything that you wouldn't learn from reading the book carefully, but are still nice to listen to and may help you get a better grasp of some of the tricky concepts. Midterms were a bit wonky; he sent out long emails before the tests explaining what we were expected to know, but didn't provide much in terms of practice material. The midterms themselves had a mix of computational and conceptual problems, so I would recommend studying the textbook and lecture slides intently in addition to knowing how to do the homework problems. For the final he provided us a set of practice problems but didn't provide answers to it for some reason, which ended up being a bit confusing. The final itself was a bit tough, it covered a lot of material with an emphasis on generalized eigenvectors/matrix exponentials that weren't covered as much on the homework. After the tests he would send long emails discussing how we did on the problems and sometimes chewing us out for missing things.

Karthik is also a bit rigid in terms of the methods you solve your problems with on the tests, so be sure you understand how to use the change of variables formula for separable equations. It'll make more sense when you get to it and he gave us extra credit for using CoV on the tests. Overall I'd say he's not a bad professor, despite his teaching peculiarities he does genuinely care about your learning and most of the class is reasonable in difficulty, you just need to know what to expect.

Grading schemes: 10% HW, 25% midterm 1, 25% midterm 2, 40% final OR 10% HW, 35% better midterm, 55% final. Starting around Week 3, all homework assignments were submitted and graded via Gradescope (online), due Friday afternoon up through Week 10. All three exams were also graded and posted on Gradescope.

Overall, Karthik definitely had his strengths and weaknesses. I only attended lecture the first week, and stopped going because I thought it was very unorganized. However, it seems that his lectures became better organized as the quarter progressed, especially after he started making slides (and posting them to CCLE).

As a math major, I thought Karthik got too involved in some of the applications of the material; he would sometimes have chemistry/physics/engineering homework problems that he assigned in addition to the weekly textbook problems which had foreign concepts, like conservation of mass/energy. Also, from time to time he was heavily nitpicky when it came to some theoretical concepts. There was one theoretical question that he asked on midterm 1, a homework, and the final which was strange to say the least. He also asked on true/false question on the final that almost everyone got wrong, as it was true except in some extreme edge cases.

His exams had relatively high averages (~80s for both midterms) as well as a 5-point extra credit problem (out of 40). They were slightly on the computational side, but there was still a lot of theory. On one midterm, I gave a proof for the extra credit question that was mostly correct but took a different approach from what he'd taught. However, I came to Karthik in office hours to explain my process and he ended up adding a few points back, which saved me a lot of stress.

Before each exam, Karthik also sent out an email (via post on CCLE) stressing certain ideas, which was often very helpful. He would occasionally come off a little condescending about some theoretical idea (basically, not 'trusting' us to fully understand it), but towards the end of the quarter he added a bit of humor to his messages.

I don't know why the reviews seem lower than I had expected for this guy. Out of the 4 math classes I've taken here at UCLA, I think this was my favorite, largely due to Karthik's willingness and care towards adapting his teaching style for students. He's quite passionate about learning math the "right" way, and he does send out emails about what to look out for on exams and common mistakes that students had made previously- I think this is a very helpful and productive way to guide studying down the right lane. I ended up with a B in the class, because I'm not that smart, but I'm sure most of you would like this professor and do better than I did. I'd rate Professor Karthik 4/5 overall, and I'd say that he's very solid compared to what I got my last few quarters.