Students are encouraged to widen and expand their knowledge base through a series of elective classes chosen within the six thematic modules offered: Mathematics; Physics; Mechanics; Engineering; Electronics, Control Systems, and Computer Science; and Economy and Business Management.

The activities proposed in each module take three forms:

• seminars and tutorials: years 1 and 2 - each year, 2 series of tutorials of 24 hours each

• supervised research and bibliographical studies (with report): years 1 and 2 - 30 hours

• laboratory-based experimental research: years 1 and 2 - 30 hours

During their first two years at Ecole Centrale, students are required to undertake at least one activity in each of the six modules, and to have completed at least two series of tutorials, one report, and one cycle of experimental work.

A list of activities proposed in 1998-1999 for each thematic module is presented below. Several modules are cross-disciplinary.

Applications of Differential Calculus in Physics

Examples of Hilbert Bases

Mathematica

Multivariate Statistical Theory

Nonlinear Models in Mathematics and Physics

Polls, Modeling

Reliability

From the Microscopic to the Macroscopic

Introduction to Atomic and Molecular Physics

Introduction to Electron Microscopy

Introduction to Fourier Optics

and Optical Image Processing

Introduction to Non-linear Physics

Phase Transitions and States of Matter

Physical Methods of Materials Characterization

Quantum Correlation and Interaction Observer/Observed System in

Measurement Theory

Radioactivity: from Principles to Applications

Spectroscopy: Quantum and Statistical

Physics Applications

Structures, Chemical Properties,

and Molecular Symmetry

Mechanics of High Performance Materials

Formation and Mechanical Behavior

of Granular Materials

Gyroscopic Systems

Mechanism Theory

Architecture and Building Techniques

Gas Transport Phenomena

Instabilities of Chemical Reactors

Membrane Separative Processes

Process Design and Selection in Materials Production

Signal Processing

Elements of Law for the Engineer

Environmental Economics

Labor Economics

Protection of Innovation

Applications of Differential Calculus

to Physics (Ma, Ph)

Calculability, Algorithms,

and Decision Analysis (Ma, ECS)

Computational Fluid Dynamics (Me, ECS)

General Relativity, Cosmology (Ma, Ph)

Group and Representational Theory

Non-linear Analysis

Recent Applications of Mathematics to Industry

Defects in Crystals (Ph, Me)

Electron Densities: A Simple Measurable Link between Microscopic Properties and the Macroscopic Behavior of Matter

Experimental Methods and the Structure of Matter

General Relativity, Cosmology (Ph, Ma)

High-Flux Sources of X-Rays and Neutrons

as Tools for Investigating Condensed Matter

Illustrations in Solid State Physics: a Study of the Silicon Crystal by Computer Simulation and X-Ray Diffraction

Introduction to the Study of Electronic

Properties of Solids

LASER: Principles of Operation, Application

of Optical Techniques (Ph, ES)

Spectroscopic Techniques:

from Principles to Applications

Supraconductors, Semiconductors, Metals

The Cost of the Electric kWh (Ph, EBM)

Advanced Strength of Materials

Automotive Vehicle Dynamics

Computational Fluid Dynamics (Me, Ma, ECS)

Defects in Crystals (Me, Ph)

Architectural Design and Building Techniques

Civil Engineering Research Applications

LASER: Principles of Operation, Application

of Optical Techniques (ES, Ph)

Calculability, Algorithms,

and Decision Analysis (ECS, Ma)

Computational Fluid Dynamics (ECS, Ma, Me)

Digital Signal Processing

Electronic Circuit Design

Fiber Optics

Flat Systems

High Frequency Electronics

HInfinity and Robust Control

Neural Networks: Theory and Applications

Observers

Optimal Control

Opto-electronics, CCD

Finance and Management

The Cost of the Electric kWh (EBM, Ph)

The European Economy

The Firm: Environment and Constraints