Thanks for the Category Theory Prof Mac Lane

"You're giving a talk for non-mathematicians." "Can I use differential equations?"

What year was this taken in? Thanks

This lecture is more historical the mathematical. Mathematicians don't pay much attention to history they name theories after someone and sometimes they have call something to do with it and sometimes they do not. They never go to the first time sources they usually read up on the second or third. You can't write about it unless you understand it.

I guess this is grandpa Rudin.

Bob Ross of mathematics

What is the obsession with time?

I love blurry videos and french clowns trying to make american idiots laugh about italian mathematicians.Very good ,my eggs have been swelling and swelling,until I had an ejaculation! Make more such stupid videos!

A nice historical document showing a real master mind of mathematics. However the visual and audio quality is quiet bad.

There’s a wonderful little paper by Maclane, Maclane and Warfield. Ginger Maclane is Saunders’ daughter. Bob Warfield is her husband, a brilliant algebraist who sadly passed away much too young. Ginger has since made remarkable contributions to the Discovery Method approach to math education.

Maestro.

Terrible 🎉

Neither real analysis nor set theory are to be called mathematics because mathematics is the abstract science of measure and number. Georg Cantor is the father of all mainstream mathematics cranks.

To learn Real Analysis from Rudin himself -the man who wrote the definitive text book- is something truly special.

Many people attending the lecture aren't mathematicians, so only use the Schroedinger's Equation for simplicity.

Was the first guy Micromachines Guy?

OMG, This is the Rudin that has me suffering. Just kidding, I love his book even though it's insanely difficult.

0:21 prehistory (-400-+1650) Pure geometry never existed. Greeks used algebra for theory of conics, which were invented to solve of algebraic problem (double proportion). Only later did they notice relationship between conics and slices of a cone. 3:50 exploration (1630-1795) Invention of analytic geometry by Decarte and Fermat independently. Classification and transform problems. Fermat expresses dimension. Some classification theorems accordion to degree. Simple types of singularities. Newton discovers bound on the intersection of curves. Bezout shows newton's bound has equality for Bezout's theorem. Not quite what we call Bezout's theorem nowadays only the beginning. 6:23 golden age of projective geometry (1795-1850) Gaspard Monge publishes Descriptive geometry. Jean-Victor Poncelet develops Monge's idea. Scalars are complex and point at infinity in space. For 100 years only problems immersed in P^2(C) and P^3(C). Simplifies theory. Beginning of study of surfaces of low degree 3 and 4. Linear transformations. Duality. Introduce dual curve. One to many correspondences. What we would call linear algebra or linear geometry nowadays. 9:57 Riemann and birational geometry (1850-1866) Riemann studies abelian integrals invented by Abel. Abel tried to classify abelian integrals but didn't know projective geometry or theory of Cauchy integrals. Riemann defines Riemann surface to classify abelian integrals. Riemann surfaces are single valued with sheets. Sheets are joined together at ramification point. Branch points. Riemann shows on Riemann surfaces one can use the Cauchy integrals theory of the complex plane. Riemann invents algebraic topology via the classification of compact orientable surfaces. Defines the genus. Shows genus is related to ramification and number of sheets. Integrals of the first and second kind. Riemann attempts Dirichlet problem (Hilbert solved 50 years later). 22:40 Development and Chaos (1866-1924?) 24:15 Kronecker paper (1882) Kronecker gives a definition of dimension. Points that satisfy a number of polynomial equations will break up into a variety of irreducible components which vary in dimension. 25:04 Dedekind and Weber (1882) Birational transformations were a fundamental idea of Riemann. Want to recover Riemann surface from ... Valuation. Introduced notion of divisor. 37:20 Started an interpretation of Riemann's results only in geometric terms. Only wanted positive divisors. Auxiliary curves. Studied singularities more than had been done before. Work in n dimensional space. 1870 consider surface. 47:10 new structures in algebraic geometry (1920)

Are Battenburg cakes just another name for Hadamard matrices (but tastier)?

Eugenia is amazing!!! I only discovered her a few months ago when I watched a video on how to apply category theory to society, which made category theory make sense to me for the first time! I love the intuition she has about abstract mathematical concepts such as groups and braids in terms of Battenburg cakes and Bach fugues! I wish I had her kind of intuition about math!

Nice talk.

He ended before the embarrassing part for mathematics, when Bertrand Russell showed set theory was inconsistent, and it all comes crashing down.

Legend

This man is a legend.

❤🌷❤

She didn’t mention Sierpinski 😢

Such a master, thank you for your legacy sir!

This guy has horrible books

Please to hear from legend Rudin

Little did they know the mastery of Rust in Peace was on its way.

LEGEND

When was this recorded?

이 사람이 그 책을 쓴 Rudin 이로구만!!!

Great lecture

Here is a cool fact concerning Walter Rudin: he lived in a house that Frank Lloyd Wright designed -- en.wikipedia.org/wiki/Walter_Rudin_House

SOMEONE NEEDS TO FIND A VIDEO OF GROTHENDIECK HOW WAS HE NEVER CAUGHT ON CAMERA LIKE COME ON

Fourier DID prove the theorem, in the special case that f(x) is given by a power series. He showed that the trig series using the convergent power series will reproduce the original power series.

I'm grateful to hear from Walter Rudin in lecture form but I can't help but make a meme of this. Rudin: So I've been told there are a lot of non-mathematicians in the audience and that I'm only limited to writing one equation. *Writes down the wave differential equation* Layman Audience: :I *Proceeds to write down Fourier series expansion without defining/breaking down the symbols:* Layman Audience: :( This lecture is a good recap of real analysis for people already familiar with Fourier series but not good for a laypeople audience. In terms of presentations I've seen of mathematicians presenting to laypeople - Michael Atiyah's presentation for his attempted proof of the Riemann Hypothesis was better. He actually spelled out that "analytic" means the function can be represented as a power series which is an infinite long polynomial - now pray tell he could elaborate on what polynomial is but I saw a good attempt there. Pray tell I did skim through this video a bit on key portions so maybe upon hearing the whole thing I might not be judging Rudin's presentation skills fairly but these are my thoughts.

Reminds me of Carl Sagan somehow. Thanks for posting!

I was over the moon to watch RUDIN as I own his book Mathematical Analysis since 1962! However, I was thrilled to see Prof D Patil (introducing RUDIN) who was my professor in Mumbai teaching Pure Mathematics in the late 50’s and early 60’s and who I knew personally. I wonder if it is possible to contact him and convey my gratefulness

Amazing video!

Mr. Baby Rudin

Can anyone provide a link of her other lectures?

Amazing to see the giants of mathematics.

This was a complete surprise. She is a superior lecturer to Walter, and I was enthralled by her humble enthusiasm to the subject that she quite evidently loves. Well, I love analysis and topology and now, Mary Rudin also.

One of the most influential ladies in Mathematical Analysis

rudolph langer book?????? name please

He is a man of clarity ! This is reflected in his analysis textbook!

Extremely well balanced. The audio is quite nearly as bad as the video.

I have an addiction to buying his books! Classy as site