34

Answers
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10
How should one present curl and divergence in an undergraduate multivariable calculus class?
3
Theorems for nothing (and the proofs for free)
0
Examples where it’s useful to know that a mathematical object belongs to some family of objects
2
Efficiently sampling points uniformly from the surface of an n-sphere
2
What is your favorite isomorphism?
2
Do the empty set AND the entire set really need to be open?
1
Are all mathematical theorems necessarily true?
4
Why should I prefer bundles to (surjective) submersions?
3
Subset of the plane that intersects every line exactly twice
0
When shorter means smaller? (2)
3
What do people mean by “subcategory”?
4
Clearing misconceptions: Defining “is a model of ZFC” in ZFC
2
How to motivate the skein relations?
1
Side-Angle-Side Congruence and the Parallel Postulate
0
A canonical and categorical construction for geometric realization
0
Exact short sequences of vector spaces
7
When is a Riemannian manifold an open subset of a complete one?
1
Boundary of planar region
1
Heuristic explanation of why we lose projectives in sheaves.
2
Homology or cohomology?
2
When and why do universal objects have extra properties?
7
A programming language that can only create algorithms with polynomial runtime?
2
What is the earliest definition given by a universal mapping property?
7
Thom’s Principle: rich structures are more numerous in low dimension
0
Where does the generic triangle live?
11
Geometric meaning of torsion in homotopy groups
0
A conceptual proof that local fibrations over paracompact spaces are global fibrations?
2
Testing for Riemannian Isometry
2
Is there a category-theoretic definition of the arithmetic Grothendieck group
3
Tracking spectral sequence differentials
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