Informatics 3

Course info

Class hours: Tuesday (room 405A) & Thursday (room 207) 8.30-10.00
Location: BME campus, building H.

Neptun code: BMETE91AM44
Credits: 4
Final grade: Project + 2 midterms + participation

Content

Scientific programming in Python

Advanced features of NumPy and SciPy
Symbolic computations with SymPy
An outlook to SAGE

Computational topology

Basics of topology
Knots and links
2-manifolds
Triangulations and simplicial complexes

Notes

[SP] Ádám Gyenge, Ferenc Wettl: Scientific programming in Python
(Password: the programming language we use with small letters)
[EH] Edelbrunner-Harer: Computational topology
Solution to an exercise from Lab 4

Schedule

Week	Lecture	Lab	Notes
1	Python scientific ecosystem, advanced NumPy and SciPy	Lab 1	[SP] 5-6
2	SymPy: symbols	Lab 2	[SP] 7.1
3	Calculus, DE	Lab 3	[SP] 7.2, 7.3
4	Polynomials	Lab 4	[SP] 7.4
5	Algebra, number theory	Lab 5	[SP] 7.5, 7.6
6	SAGE	Midterm 1, project ideas	[SP] 7.5
7	Intro to topology	Lab 7	[EH] 1.1-1.2
8	Knots and links	Lab 8	[EH] 1.3
9	Two-dimensional manifolds	Lab 9	[EH] 2.1, 2.2
10	Simplicial complexes, homology	No lab, but here is a HW	[EH] 3.1, 3.2, 4.1
11	Break	No lab
12	Midterm 2	No lab
13	Projects	Projects
14	No class	No lab

Midterms

Format: 60 minutes, 4 questions

1st Midterm: NumPy, SciPy, SymPy, symbols, expressions, simplification, expression trees, substitution, lambdification, calculus, differential equations, polynomials, ring and integral domains, linear algebra (numerical and symbolic), ideals, modules, number theory

2nd Midterm: topological space, metric space, constructions (disjoint union, product space, subspace topology, quotient topology), connectedness, continuous map and homeomorphism, knots and links, knot invariants, Kauffmann bracket and Jones polynomial, surfaces, polygon construction, triangulation, simplical complex, chain complex, homology