The Right Way to Do a Math Major (Connor Mooney) | Ep. 14
Connor Mooney is an assistant professor of mathematics at UC Irvine. We talk about formative experiences in mathematics and our paths through the math major in college.
0:00 Intro
2:55 First mathematical inspirations. Einstein, da Vinci. Wanting to be a scientist.
5:45 Gauss, arithmetic progressions, sums of powers, and the 12 Days of Christmas.
10:46 Less inspiration from grade school mathematics. Our experiences in AP Physics. Physics with and without calculus. Archimedes and Mercator. Richard Borcherds' channel.
20:00 Starting college as a physics major. The advantage of taking math courses designed for scientists and engineers.
26:00 Turning towards mathematics. PDE course. Strauss's PDE book and Stein and Shakarchi's Fourier Analysis.
28:54 My awakening to math at the PROMYS program.
34:50 More math inspirations, the maximum principle. Dissatisfaction with sweeping math under the rug in physics classes.
42:15 Unresolved issues in calculus class. My Tricky Parts of Calculus series. Importance of asking theoretical questions.
44:13 Computer programming in math and physics. Missing out on applied and computational mathematics.
47:31 Algebra and other high-level courses. Differential geometry. Graduate real analysis.
55:17 Math for application vs. math for its own sake. Appreciating abstractions. Terry Tao: Reaching the post-rigorous stage.
1:02:48 Nontrivial results vs. formalism.
1:05:10 Bad or useless math courses?
1:11:27 The value of doing an honors thesis. Curve-shortening flow. REUs. Writing mathematics.
1:18:02 Giving math talks.
1:22:10 Taking graduate-level math courses as an undergraduate. Evans' PDE book.
1:25:29 Choosing what kind of math to do. Choosing a graduate school and an advisor.
1:28:27 Undergraduate advisors and forging a path through math
1:37:04 Making sure that the math major program is useful to graduates. Lack of statistics in a math major.
1:43:18 Teaching differently from how we learned subjects. Motivation, training, and choosing the right content.
1:50:09 How too much abstraction in math hurts math majors
1:55:03 The social element and taking on responsibilities
Check out my channel for more great conversations and math content: / @danielrubin1
Daniel Rubin Show full episodes playlist: • Daniel Rubin Show, Full episodes
My previous conversation with Connor about Elliptic PDE: • Elliptic PDE (Connor Mooney) | Ep. 7
My Tricky Parts of Calculus playlist: • Tricky Parts of Calculus
This is a series of lectures on subtle parts of calculus that are rarely covered in a calculus class. Includes complete proofs and perspective from history on how problems were first solved.
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Books mentioned:
Strauss, Partial Differential Equations: An Introduction https://amzn.to/3kHK7zt
Stein and Shakarchi: Fourier Analysis: An Introduction https://amzn.to/3wMijvW
Evans, Partial Differential Equations https://amzn.to/2VOu6gt
Hatcher, Algebraic Topology (not recommended) https://amzn.to/3z5XHQU
(I get a small commission from purchases made from these links.)
See also:
Richard Borcherds' channel (math lectures): / @richarde.borcherds7998
Terry Tao's blog, There's more to mathematics than rigour and proofs: https://terrytao.wordpress.com/career...
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