Mathematical Tools for the Digital Age

Université Catholique de Lille

Course Description

  • Course Name

    Mathematical Tools for the Digital Age

  • Host University

    Université Catholique de Lille

  • Location

    Lille, France

  • Area of Study

    Mathematics

  • Language Level

    Taught In English

  • Prerequisites

    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.

    Hours & Credits

  • Contact Hours

    46
  • Recommended U.S. Semester Credits
    3
  • Recommended U.S. Quarter Units
    4
  • Overview

    Content:
    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

    Learning Outcomes:
    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

    EDUCATIONAL METHODS
    Interactive class, lab, problem solving, presentations, projects, group work, case study

    RESOURCES
    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.

Course Disclaimer

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