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数学及其应用
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数学及其应用
https://youtu.be/X2p5eMWyaFs
YouTube
Day 2 - The notorious Collatz conjecture - Terence Tao
at Liceo Scientifico Galileo Ferraris
数学及其应用
https://youtu.be/4dyytPboqvE
YouTube
The Langlands Program - Numberphile
Professor Edward Frenkel discusses the famed Langlands Program - "a kind of grand unified theory of mathematics". More links & stuff in full description below ↓↓↓
Edward Frenkel is a professor of mathematics at the University of California, Berkeley - h…
数学及其应用
https://youtu.be/htTL0VvfsvM
YouTube
Jacob Lurie - Bezout's theorem and nonabelian homological algebra (Derived algebraic geometry)
An accessible lecture by Jacob Lurie from about 2005.
The motivations behind derived algebraic geometry are presented, starting with Bezout's theorem for intersections.
A generalization of algebraic geometry using derived (topological) coordinate rings…
数学及其应用
https://en.wikipedia.org/wiki/Integration_Bee
Wikipedia
Integration Bee
Annual integral calculus competition
数学及其应用
https://youtu.be/oDyviiN4NVo
YouTube
Grant Sanderson (3Blue1Brown) - Past, Present, & Future of Mathematics
I had a lot of fun chatting with Grant Sanderson (who runs the excellent 3Blue1Brown YouTube channel) about:
- Whether advanced math requires AGI
- What careers should mathematically talented students pursue
- Why Grant plans on doing a stint as a high school…
数学及其应用
https://youtu.be/szMaPkJEMrw
YouTube
Padé Approximants
In this video we'll talk about Padé approximants: What they are, How to calculate them and why they're useful.
Chapters:
0:00 Introduction
0:33 The Problem with Taylor Series
2:11 Constructing Padé Approximants
4:50 Why Padé Approximants are useful
5:45…
数学及其应用
https://mathstodon.xyz/@tao/111247716134350297
Mathstodon
Terence Tao (@
[email protected]
)
Attached: 1 image
Continuing to make progress on my #Lean4 formalization project. Thanks to a tip from a follower here, I was able to complete the proof that the derivative of a polynomial that splits of the reals, also splits over the reals, and as such…
数学及其应用
https://youtu.be/krtf-v19TJg
YouTube
When CAN'T Math Be Generalized? | The Limits of Analytic Continuation
There's often a lot of emphasis in math on generalizing concepts beyond the domains where they were originally defined, but what are the limits of this process? Let's take a look at a small example from complex analysis where we actually have the tools to…
数学及其应用
https://youtu.be/yckPYJgjXeY
YouTube
Writing a math research paper: start to finish!
A quick look at the process of writing and publishing a math research article from start to finish. This paper was typical in some ways, atypical in other ways.
The paper: https://doi.org/10.1016/j.topol.2023.108644
Chris Staecker webarea: http://cstae…
数学及其应用
https://francisrlb.com/2023/02/25/how-does-a-lie-algebra-encode-a-space-part-1/
Francis Bischoff
How does a Lie algebra encode a space? (Part 1)
A fundamental principle of derived deformation theory is that a formal “space” (i.e. formal moduli problem) can be encoded by a differential graded Lie algebra, or more generally, an $l…
数学及其应用
https://francisrlb.com/2023/07/29/how-does-a-lie-algebra-encode-a-space-part-2/
Francis Bischoff
How does a Lie algebra encode a space? (Part 2)
In my last post, I told you how to encode the zero locus of a polynomial function $latex f: V \to E &fg=000000$ in terms of an $latex L_{\infty} &fg=000000$-algebra structure on $latex L = …
数学及其应用
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数学及其应用
https://youtu.be/4GJ4UQZvCNM
YouTube
Category Theory for Neuroscience (pure math to combat scientific stagnation)
sources and references, in temporal order:
Nature paper on the decline in disruptive science:
https://pubmed.ncbi.nlm.nih.gov/36599999/
Gordon Shepherd's book on the revolutionary 1950s "Creating Modern Neuroscience":
https://www.amazon.com/Creating-Modern…
数学及其应用
https://youtu.be/PPCfDe8TfJQ
YouTube
Four Ways of Thinking: Statistical, Interactive, Chaotic and Complex - David Sumpter
Mathematics is about finding better ways of reasoning. But for many applied mathematicians, the primary mission is to shape their minds in a way that gets them closer to the truth. The calculations are secondary, the real question is: how we can better understand…
数学及其应用
https://youtu.be/MTzYNwtK6u8
YouTube
how much i actually study as a maths student at oxford university | busy week in my life
how do i actually study?
#oxforduniversity #studywithme #oxbridge #univlogs
Keep in touch ;)
TikTok | lucywangyuxin
Instagram | lucyywangyuxin
https://linktr.ee/lucywangyuxin
If you would like help with your studies:
https://drive.google.com/file/d/1…
数学及其应用
https://youtu.be/ZFOPxZtlkig
YouTube
The Langlands Programme - Andrew Wiles
In this lecture, part of the celebration event for the tenth anniversary of the Andrew Wiles Building, home to Oxford Mathematics, Andrew himself traces the background to the one of the most famous series of conjectures in modern mathematics, starting in…
数学及其应用
https://www.youtube.com/live/FUY8BZ5WQko
YouTube
Recent Advances in Mathematics and Related Areas- 2022 (Hilbert's 13th problem by Benson Farb)
数学及其应用
https://terrytao.wordpress.com/2023/12/10/a-generalized-cauchy-schwarz-inequality-via-the-gibbs-variational-formula/
What's new
A generalized Cauchy-Schwarz inequality via the Gibbs variational formula
Let $latex {S}&fg=000000$ be a non-empty finite set. If $latex {X}&fg=000000$ is a random variable taking values in $latex {S}&fg=000000$, the Shannon entropy $latex {H[X]}&fg=00000…
数学及其应用
https://youtu.be/BhJJdN9eT2M
YouTube
Terence Tao - From Rotating Needles to Stability of Waves: Local Smoothing... (November 29, 2023)
Solutions to the wave equation preserve energy, and so, in some sense, they maintain their regularity over time. Nevertheless, there is a paradoxical local smoothing phenomenon: When measured in certain aspects, waves can become significantly smoother in…
数学及其应用
https://www.quantamagazine.org/a-team-of-math-proves-a-critical-link-between-addition-and-sets-20231206/
Quanta Magazine
‘A-Team’ of Math Proves a Critical Link Between Addition and Sets
A team of four prominent mathematicians, including two Fields medalists, proved a conjecture described as a “holy grail of additive combinatorics.”
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