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Various topics are covered including sectional curvature and Ricci curvature, minimal submanifolds, Atiyah-Singer index theorem and eta invariant, Einstein manifold, symplectic geometry, geometry of gauge theories, geometric PDE, Morse theory and Floer theory.

Prerequisites: Mathematics 240A-B-C.

4

Units

Optional

Grading

1, 2, 3

Passtime

None

Level Limit

Letters and science

College
Xianzhe Dai
2.9
110 reviews
Winter 2026 . Wei G
GIRV 1108
T R
12:30 PM - 13:45 PM
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MATH 241B Dai X Z Winter 2025 Total: 0
MATH 241B Dai X Z Winter 2020 Total: 1
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110
2.9
147 . 5 Months Ago

He was an amazing lecturer who really wanted everyone to succeed, you could tell he cared so much about all of his students. He was really helpful in office hours and gave homework hints during lecture. The homework was super hard, midterm was chill, final was brutal but fair if you did all of the homework/went over examples from lecture.

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147a . 5 Months Ago

I really really like this professor. His lectures were really nice and he made the material approachable. It is a pretty difficult course and you definitely need to spend time outside of class reading the textbook and understanding the material, but the midterm/final were both very fair, though challenging.

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147a . 3 Years Ago

Almost failed his class, dropped halfway through, took it with another professor later and got A. Gives trivial examples in class while homework seem like rocket science. This guy is too busy to accommodate students for extra office hours. Had other classes during his office hours so I had no chance to ask him questions, consequently the near fail.

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147a . 3 Years Ago

hypocritical

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MATH8 . 5 Years Ago

Very clear lecture notes. Lots of homework but exams are not that hard as homework.

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MATH4A . 6 Years Ago

Math major. Took this as my first math class at UCSB. I didn't do well for the midterm, but I studied hard for the final and got an A. After taking a lot of math courses, I think he is one of the several professors that explain things clear and organized. If you want to get an A, just do all the homework and all the recommended exercises!

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