One-dimensional objects | Algebraic Topology 1 | NJ Wildberger

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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[steffenkarl]

Professor Wildberger reminds me of Captain Janeway 's doctor on Star trek.
He will be teaching forever 😊❤

[UFOOOS]

Amazing series. For those like me who are really bothered by the camera moving all the time, it gets better in the next videos.

[FaizanKhan-jnfi]

Excellent lecture! Clear exposition and great motivating examples!

[kish]

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.

[feraudyh]

That e function around 7:40 is interesting. I wonder if it has advantages when it comes to geometrical algorithms.

[darkdevil]

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.

[patrick]

dude I love your videos so much! you explain everything so simply and it makes perfect sense

[njwildberger]

@bewertow69 Are you sure about that? See my MathFoundations series for a more sensible approach to analysis, coming up in the New Year.

[seneca]

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.

[loicetienne]

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.

[njwildberger]

What happens if I replace ``real numbers'' with ``Easter Bunnies" in your statement?
Do you still hold to it?

[martinworrell]

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