Time: yellow
Thursdays, 14.15-16.00
Room: 606
Lecture notes: here
We started with a short informal introduction on TDA in general
and persistent homology in particular (slides).
We also covered abstract and geometric simplicial complexes, and
the relationship between them (Section 1.1 in the lecture
notes).
We covered filtrations of simplicial complexes, and
specifically Čech, Rips and Morse filtrations (Sections 1.2-1.4
in the lecture notes; slides).
We introduced chain complexes and homology groups (Sections
2.1-2.2 in the notes).
We studied Euler characteristic and maps induced in homology
(Sections 2.3-2.4 in the notes), as well as introduced the
notion of a module over a ring.
We introduced persistent homology, a.k.a. homology groups of a
filtration as a graded module over a polynomial ring, and talked
about structure theorem of such modules (Sections 3.1-3.2 in the
notes), ending with a brief introduction of persistence diagrams
and barcodes.
We discussed persistence diagrams a bit more extensively, and
introduced the bottleneck distance (Sections 3.3-3.5 in the
notes).
We introduced Wasserstein distances and discussed their
computations in practice (Sections 3.5-3.6 in the
notes).
Time: blue
Thursdays, 14.15-16.00
Room: 606
Problem lists: 1 2
3
Class test: during the class on 25 May 2023
(14.15-16.00, room 606).
The assessment for recitation classes will consist of:
For activity, you can get credit by solving the
exercises from the problem lists on the blackboard during
recitation classes. Each subproblem is worth roughly one
point (but may be more for longer or more difficult exercises);
the contribution to your grade is then computed as A =
min{P⋅S/TP, 1} ⋅ 25%, where
The class test will contain exercises similar in style to the exercises solved during the recitation classes. It will contribute up to 75% towards your grade.
To get a grade n/2 (where n is an integer and 5 < n < 11), you will need to score at least 10(n-2)%. In particular, the grade boundaries are as follows: