Mathematical Tools for the Digital Age
Université Catholique de Lille
Area of Study
Taught In English
Students undertaking this course should have a basic familiarity with the mathematical concepts
of vector, matrices, differentiation, integration, and so forth at the level of a first-year Calculus and
Linear Algebra class. They must have some ability to work as a group and be able to communicate
easily in English at a standard university level. Some experience with programming (at least one
computer science-oriented course) is highly recommended.
Recommended U.S. Semester Credits3
Recommended U.S. Quarter Units4
Hours & Credits
This course will provide students with an overview of a number of today’s commodities to
underline the mathematical concepts that make them work. Students will review some math
notions and apply them to concrete technological tools.
Algorithms are so prevalent around us these days that we often barely notice them, let alone think
about how they work. Many of today’s commodities rely on deep and interesting mathematical
ideas, yet most people would be hard-pressed to explain how the math they learn in school relates
in any way to the inner workings of today’s technologies.
The goal of this course is to bridge that gap, and allow curious students to gain, in the land of
Cauchy and Fourier, an understanding and appreciation of the computations that underlie some
applications, in an interactive and hands-on manner.
Class sessions may cover the following topics, depending on student interests:
- GPS geolocalization (solving linear equations)
- Google’s PageRank algorithm (Markov chains, graph theory)
- Audio CDs (Shannon’s theorem, error correction)
- MP3 files and JPEG images (data compression)
- Camera movement in animation (projective geometry, splines)
- Securing an e-commerce site (cryptography)
- Machine learning (data analysis, optimization)
- Wrap-up and evaluation
At the end of the course, the students should:
- have some understanding of the breadth and depth of abstract mathematical ideas involved in
modern consumer technology, and
- a capacity to understand the inner workings and details of some of these algorithms
- understand how the mathematical models apply to the reality they describe, and
- be able to explore how they behave on computer simulations
Interactive class, lab, problem solving, presentations, projects, group work, case study
All course materials will be supplied in class. Reference may be made to the following resource:
C. Rousseau et Y. Saint-Aubin, Mathématiques et Technologie, Springer Undergraduate Texts in
Mathematics and Technology, 2008.
Courses and course hours of instruction are subject to change.
Eligibility for courses may be subject to a placement exam and/or pre-requisites.
ECTS (European Credit Transfer and Accumulation System) credits are converted to semester credits/quarter units differently among U.S. universities. Students should confirm the conversion scale used at their home university when determining credit transfer.
Availability of courses is based on enrollment numbers. All students should seek pre-approval for alternate courses in the event of last minute class cancellations