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
2.6
172 reviews
Spring 2024 . Dai X Z
HSSB 1207
T R
11:00 AM - 12:15 PM
Spring 2025 . Wink M
HSSB 1206
T R
12:30 PM - 13:45 PM
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MATH 241C Wink M Spring 2025 Total: 5
MATH 241C Dai X Z Spring 2024 Total: 2
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172
2.6
MATH4A . 9 Days Ago

Thick accent, difficult to understand. Used Khan Academy to pass the class, waste of time and money.

0 helpful 0 unhelpful
MATH4A . 25 Days Ago

too easy to get an A. All the things on canvas. better than 95% courses in ucsb

0 helpful 1 unhelpful
MATH4A . A Month Ago

Dai is funny at times and clearly had good intentions. However his inability to lecture and lack of clear explanations on almost everything means self-study is required. Homeworks are very difficult, while midterms are easy. The final counts for most of the grade and is challenging, but doable. This is only my opinion. Your experience may differ.

0 helpful 0 unhelpful
MATH4A . A Month Ago

So that just happened

0 helpful 0 unhelpful
MATH4A . A Month Ago

Dai's lectures were often very convoluted and hard to understand without external resources. Lectures were almost always pretty unhelpful. If you put in a lot of work outside of class and attend CLAS / use CLAS online resources it isn't hard to get an A. Lots of partial credit is given on tests, I got multiple problems wrong and got a 4/5 or a 3/4.

0 helpful 0 unhelpful
MATH4A . A Month Ago

The professor seems very smart and knowledgable, but he cannot speak English. If you take this professor for 4A, sign up for CLAS group instruction and attend those instead of lectures/sections. The lectures are just him reading off the slides (which are posted), so I skipped most of them and did fine. Weekly homework, 2 online midterms, and final.

0 helpful 0 unhelpful
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