Math at Andrews University
Math at Andrews University
Andrews University is a national university in southwest Michigan, recognized for its commitment to excellent Christian education and ranked the nation's most ethnically diverse campus, serving students from across the world. The department of mathematics offers degrees in mathematics (theoretical, applied, and statistics) and data science, preparing undergraduates for highly competitive graduate programs and impactful careers.
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Thanks for the video 😊 Are you able to number your calculus playlists so we know which order to watch them in?
Wonderful Presentation. Best ever for my self taught efforts, in rounding out my understanding of several topics all at once!
Beautiful presentation sir
Babylonian school (physics) against Greek School (mathematics)
I LOVE WHEN THIS DUDE TEACHES ALGEBRAIC TOPOLOGY
Great lecture. Its very clear. He/ him is less common for referring to objects than she/ her, because relationships (ie in graph theory) are feminine by default. But, that has no affect on the topic. I just thought it was interesting.
Great..... lecture.... Its a key to entering in the modern mathematics
You're a great lecturer, thank you for making these available! I've always struggled with this subject and this has made it much more accessible to me.
The best explanation of linear form and bilinear form that I have found. I would have a much harder time understanding my textbook had I not come across these KZread videos.
There is the hard problem of consciousness for today’s philosophers; what is it? In the East Consciousness has been equated with God; was God. If Consciousness is universal; all there is and God is universal all there is; then the idea that they are one and the same makes sense. Mind will likely be found to be elementary; emerging with quantum events.
The conclusion strikes as Jesuitical Casuistry. The sq rte of 2 = 1.414....; so that raised to itself (1.414....^ 1.414...) would give an irrational #.
Points are dual to lines -- the principle of duality in geometry. Singular homology is dual to simplicial homology -- homology is dual. "Always two there are" -- Yoda. Injective is dual to surjective synthesizes bijection or isomorphism (duality). Homology is dual to co-homology. Categories (form, syntax) are dual to sets (substance, semantics) -- category theory.
Such a good lecture
This is so cool. Such a nice and cool concept. This video was phenomenal too. I read about linear forms in my linear algebra textbook and I didn't understand what was going on, then I watched this video and I understood everything. Not only that I think the concept is cool and I saw that is is isomorphic before he said it. I like this professor and how he explains it. Studying university is easier in today's day and age because you can watch lessons from other professors from all over the world explaining the same topics.
Nice suit and nice lecture! Thanks.
Excellent 👍👌
Topological holes cannot be shrunk down to zero -- non null homotopic. The big bang is a Janus point/hole (two faces = duality) -- Julian Barbour, physicist. "Always two there are" -- Yoda.
That is the most epic sweater viz ever
Im in Calculus 1 right now, and this video helps a lot.
Please, the name of this teacher
I wish I could've had this lecture 10 years ago. Enlightening stuff!
Deck transformations are dual to permutations. Rotations are dual to reflections. Symmetry is dual to anti-symmetry -- permutation groups. "Always two there are" -- Yoda. Subgroups are dual to subfields -- the Galois correspondence.
clean explanation thank youuu
its booring because need for clear concept
The isomorphism at 31:00 is independent of the path if the fundamental group is abelian. Not in general.
22:00 how do we know that [f] * ([g] * [h] ) even exists though? We should probably prove it.
I think we already proved that the binary operation is well defined and it is clearly closed given the definition so then it should exist
My best attempt to put this in layman’s terms: Given 2 “spaces”, for example, the space of two unlinked rings and the space of 2 linked rings, the fundamental group is a way of classifying all loops in this space. A loop here is a curve that starts and ends at the same point (not the same as the rings themselves). More specifically, we say 2 loops are equivalent if you can continuously deform one into another. If 2 spaces have a different fundamental group, you cannot continuously transform one of the spaces into another. Here, by showing that the fundamental groups are different because one is abelian and the other is not, we can deduce that you cannot continuously transform 2 linked rings into 2 unlinked rings
Why there are so many ads inside this video, it is like every 3-5 minutes 😢
quebec
اتمنى لو لديك ترجمة عربية شرحك رائع لكن لا افهم اغلب الكلام
knowledge of English is necessary for professional courses
Just a quick off-the-cuff comment after seeing cohomology for the first time: since elements of the chain groups are Z-linear combinations of the generators (same thing as maps from the generators to Z), and elements of the cochain groups are homomorphisms from the free groups on the generators into Z (same thing as arbitrary maps from the generators to Z) and the addition operations on each coincide, aren’t they each (at least for Z coefficients) the same? I guess they might be, but the homology can differ because the boundary maps might differ. Also, I guess this has something to do with why the case of cohomology with Z coefficients is a special case and why in the torsion-free case they actually are the same.
I just realised I’m basically just observing that finite dimensional Z-modules are all isomorphic to their duals. Which is… I guess… a very standard fact.
30:48 Yes, you can check it if you like… but you can instead just remember that contravariant represented functors preserve coproducts 😉 (a fact I learnt only very recently!).
Amazing, regards from Spain, you are helping me a lot, thanks.
He has a special relationship with the book. That’s completely understandable. 😅
Very well explained, thank you!
Retraction (convergence, syntropy) is dual to inclusion (divergence, entropy). "Always two there are" -- Yoda. Attraction is dual to repulsion -- forces are dual!
Yeah, feeling bad about math, so hard and still learning. And hopefully get excited career like Sean said, just starting industry job.
Math is hard for all of us! Hang in there - half the battle is just sticking to it.
What is a Union of Union to Learn more about the Ambient Spaces?
Soooo it’s 0?
how is possible that with n-2 number in a sequence get n to the power of (n-2), with (n-2) position and with n as the highest value you can have (n-2) to the power of n that is totally different.
big galaxies are knots in process ?
Why the RHS solid torus behavior while filling space around the LHS torus (compactification 1h.02m ) resembles the shape of the magnetic field of a coil ?
at 39:00, when you said f and g are homotopy equivalent, did you mean to say homotopic?
and at 53:16, you meant "equivalence classes" not relations. Thank you for the great lectures!!
he did not prove that GF is perpendicular to AE.
Can i use max instead of sup bcz the image set is closed and bounded.
WTF 😮
we all know it's not possible without your group theories
The only thing that the book lacks is examples. Otherwise the theoretical content is intermediate friendly.
Isn't the boundary of a circle is itself? as any neighborhood of a point on the circle intersects both circle and its complement. It makes sense that the boundary of the circle is empty if we define the boundary of a set to be the boundary of its interior.
The circle is one-dimensional, and the neighborhoods of its points are too, and none of them contain any points not on the circle