This was the most challenging math course I've ever taken. I took this course after receiving an A+ in Math 115A and was humbled; my advice is to only take this course if you love proofs, theory, and desire a challenge. The homework assignments are manageable, and the lectures are (for the most part) a heavy review of 115A content within a more theoretical framework. Lecture notes are great so attendance in lecture is not necessary unless you want to ask questions. The exams are extremely challenging and make up a majority of your grade. The homework and lectures on their own are not sufficient to prepare for the exams, so a strong understanding of all the theorems is absolutely necessary to pass. I would recommend concept mapping and discussing in a study group. Luckily, Kannan is a great guy and genuinely wants his students to succeed; he is more than willing to help if you reach out.

AVOID THIS CLASS.

Even though Professor Kannan is a good guy, his exams are certainly not. As a new professor, I'm afraid that he doesnt know how to control the difficulty level of his tests, making the average and median in the Failing range in the absolute scale. There are NO computational or simple proof questions on the exam at all, but every question require you to master the contents really well to know the tricks to solve them. To put it briefly, exam questions are FAR MORE DIFFICULT than 115A, and materials of this course is very managable but the exams are far beyond acceptable. NO practice exams, so you'll just have to guess what will be tested on the paper. Cotents of 115B should not be that difficult at all, and I am afraid that he just doesnt want to give simple questions or proofs he went over in class or on the text book. If you think mastering the notes and HWs, I can tell you that's still far from enough. Instead, you have to spent great amount of time practicing the problems at the end of every chapters to do a little better in the exam.
Overall, if you dont want to screw your GPA, and certainly this is not a mandatory elective, I suggest that DONT TAKE THIS CLASS. If you have any other options, go for it, just AVOID THIS CLASS.

Tests are really hard (midterm is more than doable if you just know the concepts, but the final requires a lot more in the realm of problem solving, so it's still a bit of time crunch). 115B's material isn't all that difficult since it has a ton of overlap with 115A. I got an A in 115AH a while back so I didn't really give this class the respect it deserved, but it's still a math upper div so you have to take it seriously. If you start reviewing and doing problems a few days before a test you should be fine.

Tests are hard af. Even if you the content of the course like the back of your hand, you have to make several deductive steps under a extreme time crunch(even during the final) to get the answer and there's very little partial credit. Lectures are good and his notes are very clear though. Homework is manageable.