Bachelor's degree Double degree in mathematics, physics and chemistry
Entry requirements
Scientific Baccalaureate (S) (Mathematics or Physics-Chemistry specialisation) or new general Baccalaureate (specialisations required are Mathematics and Physics-Chemistry, the Complementary Mathematics option is highly recommended).
Benefits of the program
Because of its specific nature (teaching in both Mathematics and Physics, Chemistry), our course provides a real alternative to traditional preparatory classes and offers a 3-year level diploma. Students' excellent level of knowledge and skills in mathematics and physical sciences offers them a wide range of opportunities for pursuing their studies. To facilitate transition from high school, a pre-term-start tutoring programme is organized and most modules during the 1st year are in small classes (Lessons-tutorials). To encourage students to work regularly and independently, regular checks are carried out and online exercises are proposed. During the programme, students may request to join the specific Mathematics or Physics, Chemistry pathways.
Acquired skills
Acquiring sound general scientific training on theoretical, experimental and digital levels. Ability to roll out a scientific and/or abstraction approach. Explaining and presenting a project in writing and orally. In Mathematics: proficiency in the fundamental concepts of analysis, probability, statistics and linear algebra. In Physics and Chemistry: solving theoretical problems from Newtonian physics to modern physics and understanding its applications. In Computer Science: mastering the Python language. In English: level B2 minimum.
Capacities
15
Course venue
Your future career
Double Mathematics - Physics Chemistry Degree students may pursue their studies with a Master's in Mathematics, a Master's in General Physics or a Master's in Applied Sciences or generalist or specialised course in an Engineering School by admission based on qualifications. The Master's accessible at Université Gustave Eiffel are: Mathematics and Applications Master's, Careers in Teaching, Education and Training Master's specializing in Mathematics, Actuarial Science Master's, Theoretical Chemistry Master's, Mechanics Master's, Risks and Environment Master's, Material Engineering and Sciences.
Professional integration
Continuation of studies with a Master's degree or at Engineering School
Study objectives
Provide rigorous dual-disciplinary training in mathematics and physics, allowing students to pursue their studies with a Master's degree or at engineering school
Major thematics of study
Mathematics - Physics - Chemistry - Electronics - Mechanics - Computer Science - English
Options
In the 3rd year, students choose optional classes (minimum 9 ECTS) in Mathematics or in Physics.
Semester 1
| Courses | ECTS | CM | TD | TP |
|---|---|---|---|---|
| MATHEMATIQUES | 24 | |||
|
Calculus
The objective of this EU is to deepen the concepts of analysis seen at the science terminal and to improve the computational skills of students. Complex numbers, derivability, primitive calculation, study of usual reciprocal functions, polynomials, as well as first and second order ordinary differential equations, linear and with constant coefficients are discussed.
Teaching language FRANÇAIS / FRENCH | 6 | 24h | 36h | |
|
Methodology
The learning outcomes of the "méthodologie des mathématiques" course are designed to acquire the mathematical method based on the unambiguous definition of notions, the formulation of conjectures, the formulation of mathematical propositions and their demonstration using logic from more basic propositions, going back to the axioms. To do this, learning and mastering the language of mathematics is fundamental (speech, syntax, objects, variables). This course aims to allow the acquisition of the basic elements of this language by its implementation in simple demonstrations addressing basic but new concepts that will be seen in class. Topics include naïve set theory, applications, binary relations, natural integers and groups. At the end of this course the students will be able to independently demonstrate simple original propositions concerning these notions. This course is built around three modalities: the lecture, the tutorials, and the personal work. These revolve around the elements transmitted in class and in Tds but also with the help of other educational resources, including self-correcting exercises.
Teaching language FRANÇAIS / FRENCH | 6 | 24h | 36h | |
|
Numerical sequences and real functions
Content: 1) Real numbers (upper and lower bound, absolute value, integer part, axiomatic of R, intervals, density of rational and irrational numbers)2) Real sequences: monotonicity, convergence (with epsilon), inductive and adjacent sequences, Cauchy sequences, Bolzano-Weierstrass theorem, arithmetic and geometric sequences. 3) Real functions (limit with Epsilon, delta), continuity, image of a compact and non compact interval through a continuous function, uniform continuity, Heine's theorem, bijections, homeomorphisms, lipschitzian functions. 4) Derivation of real functions: definition, Rolle's theorem, Mean value theorem, local extrema, Taylor-Lagrange and Taylor-Young formula, limited developments and application to local extrema.
Teaching language FRANÇAIS / FRENCH | 6 | 24h | 36h | |
|
Linear algebra 1
The course of Linear Algebra consists of three chapters. The first chapter defines the vector spaces, the bases, and introduces the notion of dimension.Then we deal with linear applications: kernel, image, rank, projectors. The last chapter is about matrices: their links to linear applications, base change, and linear systems.
Teaching language FRANÇAIS / FRENCH | 6 | 24h | 36h | |
| PHYSIQUE CHIMIE | 35 | |||
|
Geometric optics - Kinematics and dynamics of the material point
Observation of propagation phenomena; laws of reflection and refraction; propagation through diopters, lenses, a continuous medium modeled in layers; formation of sharp images . Position, velocity, acceleration; force; Newton's laws; friction (solids and fluids); conservative forces and potential energies; theorem of kinetic energy; conservation of mechanical energy; non -conservative forces cases.
Teaching language FRANÇAIS / FRENCH | 7 | 31h | 31h | 6h |
|
General chemistry 1
Structure of the material (carbon , covalent bonds, conformations and configurations, molecular interactions )
Teaching language FRANÇAIS / FRENCH | 5 | 20h | 22h | 6h |
|
Electricity - Electronics 1
Electrokinetic : continuous modes (magnitudes, dipoles real, sources, Kirchhoff's laws, resistance). electronics: study of combinatorial circuits (Boolean algebra, logic function, logic gates, encoder / decoder, transcoder, multiplexer / demultiplexer )
Teaching language FRANÇAIS / FRENCH | 5 | 18h | 20h | 8h |
|
Wave optics - Thermodynamics
Interference and diffraction experiments with light. Theoritical interpretation. pressure, temperature, thermodynamic state of a gas, equation of state ; internal energy, work , heat, first principle ; various types of processing ; entropy, the second principle ; thermal cycles and engines11/03/2019
Teaching language FRANÇAIS / FRENCH | 6 | 20h | 28h | 8h |
|
Fluid and solid mechanics
Basic concepts used in fluid and solid mechanics. Kinematics. Forces and moments. Energy. Fundamental principle of dynamics.
Teaching language FRANÇAIS / FRENCH | 2 | 8h | 8h | 2h |
|
General chemistry 2
basis of chemical kinetics and application to simple cases; major reaction types in inorganic chemistry in aqueous solution (redox reactions, acid-base reactions); composition of equilibrium systems.
Teaching language FRANÇAIS / FRENCH | 6 | 22h | 22h | 10h |
|
Electricity - Electronics 2
Circuits in sinusoidal regime (rms value, phase shift, associated complex, coil and capacitor impedance and admittance, associations, powers, resonance). Study of sequential circuits (evolution, timing, synchronous and asynchronous technology flops, registers, counters)
Teaching language FRANÇAIS / FRENCH | 4 | 14h | 16h | 8h |
| COMPETENCES TRANSVERSES | 8 | |||
|
Computer science 1
This course prepares to C2i certifcation and introduces the basics of Python programming (variables, types, conditional structures, loops, functions, modules, lists, reading/writing in a file). The concepts and tools essential to scientific computing are emphasized (float type, SciPy and Matplotlib modules). The course has no prerequisite in programming.
Teaching language FRANÇAIS / FRENCH | 2 | 24h | ||
|
English 1
The teaching of English during the bachelor's degree aims to improve written and oral skills so that students become more autonomous. The aim is to be able to understand and communicate in future professional exchanges, as well as to be able to understand the scientific articles that they may encounter during their studies and/or professional lives. Throughout the bachelor's degree, English courses focus on providing an opening to different cultures in order to encourage exchanges between countries. Level groups are set up during the first semester to enable everyone to approach English courses in the best possible conditions. The emphasis is on oral participation thanks to a quality policy of the UFR which organises English courses in half groups.
Teaching language ANGLAIS / ENGLISH | 2 | 20h | ||
|
Computer science 2
This course offers an introduction to scientific computing through various topics.1. Solving nonlinear equations: bisection method, Newton method.2. Numerical integration: rectangle rule, trapezoidal rule.3. Solving differential equations with initial conditions : models in mechanics, chemistry, electricity; Euler method, Runge-Kutta methods, backward Euler method, symplectic methods.4. Solving differential equations with boundary conditions : 1D elasticity model, 1D advection-reaction-diffusion model; finite difference approximation.5. Data fitting: Lagrange interpolation, splines, least square fitting.The course is oriented toward practice and consists mostly of computer lab sessions where the students program and apply the numerical methods (using Python).
Teaching language FRANÇAIS / FRENCH | 2 | 24h | ||
|
English 1
The teaching of English during the bachelor's degree aims to improve written and oral skills so that students become more autonomous. The aim is to be able to understand and communicate in future professional exchanges, as well as to be able to understand the scientific articles that they may encounter during their studies and/or professional lives. Throughout the bachelor's degree, English courses focus on providing an opening to different cultures in order to encourage exchanges between countries. Level groups are set up during the first semester to enable everyone to approach English courses in the best possible conditions. The emphasis is on oral participation thanks to a quality policy of the UFR which organises English courses in half groups.
Teaching language ANGLAIS / ENGLISH | 2 | 20h |
Semester 2
| Courses | ECTS | CM | TD | TP |
|---|---|---|---|---|
| SEMESTRE 3 | 36 | |||
|
Linear Algebra 2
Teaching language FRANÇAIS / FRENCH | 6 | 24h | 36h | |
|
Multivariable analysis
Teaching language FRANÇAIS / FRENCH | 5 | 20h | 30h | |
|
Numerical sequences and series
Teaching language FRANÇAIS / FRENCH | 2 | 18h | ||
|
Computer science 3
Teaching language FRANÇAIS / FRENCH | 4 | 12h | 24h | |
|
English 3
Teaching language ANGLAIS / ENGLISH | 2 | 20h | ||
|
Electromagnetism
Teaching language FRANÇAIS / FRENCH | 6 | 24h | 30h | 6h |
|
Solid mechanics
Teaching language FRANÇAIS / FRENCH | 5 | 22h | 28h | |
|
Thermodynamics and reactivity in chemistry
Teaching language FRANÇAIS / FRENCH | 6 | 24h | 24h | 12h |
| SEMESTRE 4 | 35 | |||
|
Sequences and series of functions
Teaching language FRANÇAIS / FRENCH | 6 | 24h | 36h | |
|
Computer science 4
Teaching language FRANÇAIS / FRENCH | 4 | 12h | 24h | |
|
English 4
Teaching language ANGLAIS / ENGLISH | 2 | 20h | ||
|
Probability modeling
Teaching language FRANÇAIS / FRENCH | 6 | 24h | 36h | |
|
Differential equation 1
Teaching language FRANÇAIS / FRENCH | 3 | 12h | 18h | |
|
From vibrations to waves
Teaching language FRANÇAIS / FRENCH | 3 | 14h | 16h | |
|
Fluid mechanics
Teaching language FRANÇAIS / FRENCH | 3 | 12h | 12h | 6h |
|
Thermodynamics 2
Teaching language FRANÇAIS / FRENCH | 3 | 14h | 16h | |
|
Mineral chemistry
Teaching language FRANÇAIS / FRENCH | 5 | 18h | 18h | 12h |
Semester 3
| Courses | ECTS | CM | TD | TP |
|---|---|---|---|---|
| Mathématiques | 39 | |||
|
Normed vector spaces
Normed vector spaces, compact, connected, complete, functions of several variables, differientiability, gradient, Taylor’s formulas, hessian matrix, extrema, inverse function theorem, implicit functions theorem.
Teaching language FRANÇAIS / FRENCH | 6 | 24h | 36h | |
|
Integration and probabilities
Measure, sigma-algebra, Lebesgue’s integral, convergence theorems, integrals with parameters, multiple integrals. Random variable, independence, usual distributions, characteristic functions, law of large numbers, central limit theorem.
Teaching language FRANÇAIS / FRENCH | 9 | 36h | 54h | |
|
Hilbert analysis
Lp spaces, Hilbert spaces, Fourier series, projection on a closed convex set, distance to a sub-space, Fourier transform on L2, Parseval’s formula.
Teaching language FRANÇAIS / FRENCH | 6 | 24h | 36h | |
|
Differential equations 2
Qualitative study of differential equations, Cauchy-Lipschitz theorem, Isomorphism theorem for homogeneous ODE, Wronskian, tangent field, autonomous differential equations, differential systems.
Teaching language FRANÇAIS / FRENCH | 6 | 24h | 36h | |
|
Optimisation Option A
Optimization for functions of several variables, Lagrangian, sub-differential and applications, stochastic optimization, gradient descent algorithms
Teaching language FRANÇAIS / FRENCH | 6 | 24h | 36h | |
|
Statistiques Option B
Parametric statistics: estimators by the method of moments and maximum likelihood, consistency of estimators, RMS convergence, test confidence interval, asymptotic and non-asymptotic.
Teaching language FRANÇAIS / FRENCH | 6 | 24h | 36h | |
| Compétences transverses | 9 | |||
|
English
Teaching language ANGLAIS / ENGLISH | 3 | 24h | ||
|
Numerical mathematics and Python
Machine representation of real numbers, numerical integration, interpolation, nonlinear equation solving (dichotomy and Newton methods), Euler methods for ODEs. Numerical simulation of probability distributions.
Teaching language FRANÇAIS / FRENCH | 6 | 24h | 24h | 12h |
| Physique | 48 | |||
|
Electromagnetism and electromagnetic waves
Equations de Maxwell locales et intégrales dans le vide, en régimes permanent et variable. Propagation d'ondes électromagnétiques planes dans le vide. Cas des milieux diélectriques. Cas des milieux magnétiques
Teaching language FRANÇAIS / FRENCH | 6 | 30h | 30h | |
|
Physics experiments
Etude, réalisation et exploitation d'expériences de physique en relation avec le cursus L3.
Teaching language FRANÇAIS / FRENCH | 3 | 28h | ||
|
Nuclear and particle physics
Structure nucléaire. Processus nucléaires. Energie nucléaire. Introduction aux Particules fondamentales. Modèles atomiques. Spectroscopie atomique.
Teaching language FRANÇAIS / FRENCH | 3 | 14h | 14h | |
|
Repositories and central fields
Changements de référentiels : composition des vitesses et des accélérations. Dynamique en référentiel non galiléen. Mouvement d'un point dans un champ de forces centrales. Application au mouvement des planètes.
Teaching language FRANÇAIS / FRENCH | 3 | 14h | 14h | |
|
Statistical Physics
Marches aléatoires et phénomènes de diffusion. Description statistique de l'état d'un gaz classique ou quantique. Travail et chaleur à l’échelle microscopique. Les ensembles statistiques et leurs applications.
Teaching language FRANÇAIS / FRENCH | 4 | 20h | 20h | |
|
Acoustic waves
Vibration transversale des cordes et des membranes. Equation d’onde acoustique dans les fluides. Vitesse du son et atténuation. Flux d’énergie et impédances acoustique. Réflexion et transmission.
Teaching language FRANÇAIS / FRENCH | 2 | 10h | 10h | |
|
Relativistic physic
Transformation de Lorentz pour les grandeurs cinématiques. Espace de Minkowski. Dynamique relativiste. Electromagnétisme et relativité.
Teaching language FRANÇAIS / FRENCH | 3 | 14h | 14h | |
|
Wave optics
Interférence, la lumière comme une onde, l'expérience de Young, cohérence, intensité de l'interférence produite par une fente double, interférences des films minces, interféromètre de Michelson. Diffraction et théorie ondulatoire de la lumière, diffraction par une fente, diffraction par une ouverture circulaire, critère de Rayleigh, diffraction par une fente double, fentes multiples, réseaux.
Teaching language FRANÇAIS / FRENCH | 3 | 14h | 14h | |
|
Project
Réalisation en binôme ou petit groupe d'un projet en physique, mettant en œuvre les concepts théoriques et les compétences acquises en licence. Il donne lieu à un rapport écrit et une présentation orale devant un jury.
Teaching language FRANÇAIS / FRENCH | 3 | 60h | ||
|
Spectroscopie atomique et moléculaire Option A
Description quantique de l’atome. Bases quantiques de la spectroscopie. Termes spectroscopiques. Notions de théorie des groupes. Règle d'or de Fermi. Application à la spectroscopie atomique et aux spectroscopies moléculaires micro ondes, IR et UV.
Teaching language FRANÇAIS / FRENCH | 6 | 24h | 24h | 10h |
|
Automatisme Option B
Etude des systèmes continus linéaires invariants
Teaching language FRANÇAIS / FRENCH | 6 | 24h | 24h | 12h |
|
Dynamique des fluides Option A
Lois de comportement des fluides newtoniens. Equations de continuité et de Navier-Stokes. Théorème de Bernoulli généralisé. Théorème d'Euler.
Teaching language FRANÇAIS / FRENCH | 4 | 16h | 16h | 8h |
|
Stage Option B
Teaching language FRANÇAIS / FRENCH | 2 |