One-dimensional objects | Algebraic Topology 1 | NJ Wildberger
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- čas přidán 27. 07. 2024
- This is the full first lecture of this beginner's course in Algebraic Topology, given by N J Wildberger at UNSW. Here we begin to introduce basic one dimensional objects, namely the line and the circle. However each can appear in rather a remarkable variety of different ways.
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Elementary Mathematics (K-6) Explained: / playlist
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Year 9 Maths: • Year9Maths
Ancient Mathematics: • Ancient Mathematics
Wild West Banking: • Wild West Banking
Sociology and Pure Mathematics: • Sociology and Pure Mat...
Old Babylonian Mathematics (with Daniel Mansfield): / playlist
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Math History: • MathHistory: A course ...
Wild Trig: Intro to Rational Trigonometry: • WildTrig: Intro to Rat...
MathFoundations: • Math Foundations
Wild Linear Algebra: • Wild Linear Algebra
Famous Math Problems: • Famous Math Problems
Probability and Statistics: An Introduction: • Probability and Statis...
Boole's Logic and Circuit Analysis: • Boole's Logic and Circ...
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Differential Geometry: • Differential Geometry
Algebraic Topology: • Algebraic Topology
Math Seminars: • MathSeminars
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Six: An elementary course in pure mathematics: • Six: An elementary cou...
Algebraic Calculus One: • Algebraic Calculus One
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I am not saying it is pointless to study "real numbers". There is a lot of point to it in fact, since that is the current foundation for modern analysis! The problem is that it does not work logically. So if one is interested in pure mathematics and its validity, one must look for alternatives. However the current knowledge about ''real numbers'' is an important guide to such a search. See my MathFoundations series for a lot more discussion.
Let as us learn it
Professor Wildberger reminds me of Captain Janeway 's doctor on Star trek.
He will be teaching forever 😊❤
Absolutely incredible series.
Amazing series. For those like me who are really bothered by the camera moving all the time, it gets better in the next videos.
Excellent lecture! Clear exposition and great motivating examples!
19:08
"We're going to talk about knot-theory"
"Why not?"
They are knot equal.
dude I love your videos so much! you explain everything so simply and it makes perfect sense
Now i feel the need to watch your video series on rational trig, it looks like Dr. Wildberger created an amazing alternative tool for simplifying problems. I imagine taking the volume integral over this region enclosed by the rational circle much easier to compute.
The statement ``pi is just the ratio of the circumference of a circle to its diameter' might make naive physical sense, but to pin down exactly what we are talking about here turns out to be highly challenging.
I have two tests tomorrow, Mechanics an probability theory and its 2:30 am now but this is very interesting. thanks
Don't worry, I didn't think you were being rude. A robust discussion is something I would like to encourage. I do think some of the issues we deal with in MathFoundations will interest you.
I appreciate your videos Dr. Wildberger, and you obviously know a lot more mathematics than me, so I'll take your word for it. I understand that rationals may be better suited for describing reality, but I still stand to my statement. If the easter bunny could be described by a finite set of axioms and was in someway intellectually interesting, then one could study it. However, I do think there is value as well in the approach of using rational numbers to prove things normally done with reals.
Great lectures btw!
I think that, for the parameter θ of the (cos(θ), sin(θ)) parametrization of the circle, the range 0 ≤ θ < 2π (with one of the inequalities being strict) is more exact than 0 ≤ θ ≤ 2π, for the sake of bijectivity.
Brilliant !
That e function around 7:40 is interesting. I wonder if it has advantages when it comes to geometrical algorithms.
Sure, that seems a reasonable statement.
Thx. Dr. Wildberger
Thanks so much for these lectures, Prof. Wildberger! I loved your two lectures on Knot Theory. I'm a little confused why you stated in 15:21 that a circle is equivalent to a Trefoil knot. I see how a circle is equivalent to a closed loop of string (you can essentially make the string have zero width and shape it into a circle), however, I don't see how you can shape a Trefoil knot into a circle without cutting it. Could you please clarify what you meant by "we can draw circles in novel ways"? Sorry, it has been a while since I studied topology formally, so perhaps I'm missing something.
You can cut things to make homomorphisms as long as you glue the two sides back together in exactly the same place afterward. This is a continuous mapping because nearby points, in the end, still get mapped to nearby points.
@@bobbicals exactly, this is the reason why, for instance, cutting a rubber band and turning it a half-turn before gluing it back is different from turning it a full turn before gluing it (a typical example)
@bewertow69 Are you sure about that? See my MathFoundations series for a more sensible approach to analysis, coming up in the New Year.
good info..
Fantastic videos, I actually understand it. My thinking has become homeomorphic with his lecture. He's definitely the man with two brains !, oops another topological equivalence
What happens if I replace ``real numbers'' with ``Easter Bunnies" in your statement?
Do you still hold to it?
powerful illustration of formalism vs intuitionism.