Topics include geometry of surfaces, manifolds, differential forms, Lie groups, Riemannian manifolds, Levi-Civita connection and curvature, curvature and topology, Hodge theory. Additional topics such as bundles and characteristic classes, spin structures, and Dirac operator, comparison theorems in Riemannian geometry.

No Prerequisites

4

Units

Optional

Grading

1, 2, 3

Passtime

None

Level Limit

Letters and science

College
Unlocks MATH 241A
Xianzhe Dai
2.9
108 reviews
Fall 2024 . Wink M
HSSB 1207
T R
11:00 AM - 12:15 PM
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MATH 240A Dai X Z Fall 2023 Total: 13
MATH 240A Dai X Z Fall 2022 Total: 6
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108
2.9
MATH240A . 20 Years Ago

Small class, professional invironment. Lectures are rather introductory and supplementary for a lot of reading and exersizing (what is good for me). The course is extremely difficult unless you are fluent in algebra, analysis, and topology.

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147a . 2 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 . 2 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 . 5 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!

1 helpful 0 unhelpful
MATH4A . 5 Years Ago

do not take his class

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