6 ECTS credits
180 h study time

Offer 1 with catalog number 1022970ANR for all students in the 2nd semester at a (A) Bachelor - preliminary level.

Semester
2nd semester
Enrollment based on exam contract
Impossible
Grading method
Grading (scale from 0 to 20)
Can retake in second session
Yes
Enrollment Requirements
Enrolling in 'Mathematics for Data Science' means that students bachelor mathematics and data science simultaneously follow 'Linear Algebra' and 'Mathematical Analysis I' and 'Mathematical Analysis II' or have successfully passed 'Linear Algebra' and 'Mathematical Analysis I' and 'Mathematical Analysis II'. Enrolling in 'Mathematics for Data Science' means that students bachelor computer science simultaneously follow 'Mathematics: Calculus and Linear Algebra' or have successfully passed 'Mathematics: Calculus and Linear Algebra'.
Taught in
Dutch
Faculty
Faculty of Sciences and Bioengineering Sciences
Department
Mathematics
Educational team
Jan De Beule (course titular)
Activities and contact hours
26 contact hours Lecture
26 contact hours Independent or External Form of Study
Course Content

The first objective of this course is to treat mathematical foundations of data science. These mathematical foundations are spread over different subdisciplines of mathematics.  Mathematical optimization is not possible without analysis of multivariate real functions, the determination of a best rank k approximation of a set of data points in the Euclidean space is a problem in linear algebra, and modelling the internet as a (directed) graph is necessary to develop any PageRank algorithm. Hence the courses Analysis, Linear Algebra and Discrete Mathematics are a very suitable base for students to set their first steps into the mathematics for data science. The second objective of this course is to use and develop the mathematical knowledge of the courses in the first term in the context of this course. Although this course is a mathematical course, the content will be rigorous from foundation to application. Hence for a topic like spectral clustering of data, the treatment will start with the mathematical foundations and end with an implementation in python 

Contents

1. Spectral graph theory (part 1): matrices associated to graphs, the spectrum of a graph, spectral properties of undirected graphs.

2. Linear Algebra (part 1): Perron-Frobenius theorem, Raleigh coefficients. Applications in spectral graph theory: equitable partitions, interlacing.

3. Spectral graph theory (part 2): spectra of graphs, cliques and co-cliques and the Delsarte-Hoffmanbound. Applications: the sensitivity conjecture, the chromatic number of a graph, the Shannon capacity of a graph.

4. Data clustering: k means algorithm, spectral clustering, mincut problem in graphs.

5. Linear Algebra (part 2): singular value decomposition. Applications: low rank approximations, principal component analysis, the power method, the Hypertext Induced Topics Search algorithm, google PageRank. 

6. Mathematical optimization: linear programming and discrete optimization.

Course material
Course text (Required) : Wiskunde voor Data Science, Jan De Beule, Digitale versie (pdf) beschikbaar via canvas
Additional info

None

Learning Outcomes

General Competences

  • To apply acquired knowledge from discrete mathematics, analysis/calculus and linear algebra in a context of algorithms
  • To apply results from lineair algebra to explain essential results from algebraic graph theory
  • To explain some particular algorithms and their complexity from graph theory
  • To explain some basic algorithms from optimization
  • To use mathematical software and to execute a custom made project related to the contents of this course.

 

Grading

The final grade is composed based on the following categories:
Oral Exam determines 60% of the final mark.
Other Exam determines 40% of the final mark.

Within the Oral Exam category, the following assignments need to be completed:

  • oral exam with a relative weight of 60 which comprises 60% of the final mark.

Within the Other Exam category, the following assignments need to be completed:

  • Project with a relative weight of 40 which comprises 40% of the final mark.

Additional info regarding evaluation

Additional information regarding evaluation (Engels): Theory Exam (oral with the opportunity for written preparation) 60% + permanent evaluation using project work 40%

Allowed unsatisfactory mark
The supplementary Teaching and Examination Regulations of your faculty stipulate whether an allowed unsatisfactory mark for this programme unit is permitted.

Academic context

This offer is part of the following study plans:
Bachelor of Computer Science: Default track (only offered in Dutch)
Bachelor of Mathematics and Data Science: Standaard traject (only offered in Dutch)