Measure and Integration

This is a third-year (Semester 5) fundamental course in Measure and Integration Theory.

The primary objective is to introduce students to a powerful and general framework for integration that extends beyond the classical Riemann integral. The core of the course is Lebesgue integration, developed within the context of measured spaces.

Students will learn about sigma-algebras, measures, and measurable functions, which form the foundation for modern probability theory and advanced analysis. The course covers key convergence theorems, such as the Monotone Convergence Theorem and the Lebesgue Dominated Convergence Theorem, which are essential tools for analysis. It also introduces the Fubini Theorem for integrating over product spaces.

This theory is crucial for a deep understanding of areas like functional analysis, probability, and partial differential equations. Prerequisites include Algebra and Topology.

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Unconstrained Optimization

Unconstrained Optimization

NORMED VECTOR SPACES

    General information
    This course covers the subject, Normed Vector Spaces, and is intended to the third year students in
    mathematics Licence LMD.
    Its objective is to teach stydents the importance of the Banach space and the specificity
    of the Hilbert space as a class of normed spaces.
    it will present results specific to this space. It is divided into two chapters:
    Chapitre 1: Banach Spaces.
    Chapitre 2: Hilbert Spaces.
    Each chapter is completed by a series of exercises with solutions.
    Bibliography
    1-H. BRESIS, Functional Analysis, Theory and Applications.
    2-G. Lacombe, P. Massat, Fuctional Analysis. Corrected Exercises, DUNOD.
    3-F. Riesz, B. Sz Nagy, Lectures on Functional Analysis.
    4-Y. Sonntag, Topology and Functional Analysis, Lectures and exercises, Ellipses, 1997, Gauthier&Villars.
    Semestre : 5th
    Teaching unit: Fundamental
    Matière : Normed Vector Spaces
    VHS: 14 weeks (42 hours)
    Lectures: 1h30 + Tutorial: 1h30
    Credits : 5
    Weighting: 3
    Assessment method: Exam (60%) , continuous assessment(40%).
    Recommended prior Knowledge: Analysis 1, Analysis 2, Analysis 3 and Topology.