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If you are not prepared for hard, upper div courses, then DO NOT TAKE THIS CLASS. ONLY TAKE THIS CLASS IF YOU THINK YOU ARE THE BEST STUDENT IN THIS DEPARTMENT. Jens is my favorite professor in maths department but there are just so many students doing much better.
For Math 115AH:
As my first proof based and upper division math course, this class was a real challenge and as it was Honors it moves through material so much more quickly (though I have no doubt the 131H/110H series are much more difficult), so I really had to dedicate a lot of my time to this class. In addition to the Math 115A curriculum, the class also went into much detail on dual spaces, invariant subspaces, and orthogonal projections, and touched upon unitary/orthogonal operators and the Spectral Theorem, which all serve as part of the Math 115B curriculum.
That being said, the increased level of abstraction attained by this class's material, was incredibly interesting and definitely worth my time, and Prof. Eberhardt is undoubtedly one of the best math professors at UCLA for linear algebra. He is a very nice and approachable guy who is always happy to help, no matter how dumb you think your questions may be lol. His lectures are very neat and well structured, and an extra hour is also offered for the class, that serves as a Q&A session where he won't cover anything new, and just answer any questions you may have.
For the exams, the midterms were incredibly difficult to finish within the time allotted (50 mins for 4 medium-length proofs and 40 mins for 3 medium-length proofs), but the final was much more chill (3 hours for 3 longer proofs). Medians were like 60, 75, and 78 I believe, and the two grading schemes (homework is not a part of grade) are 22.5-22.5-55 and 35-65, allowing for you to bomb one of the midterms, the way I did lol.
Very much recommended.