Master Year 2 Mathematics of Randomness

Year	Master Year 2
Program	Mathematics of Randomness
ECTS Credits	60
Language	English, French
Orientation	Research (mainly), Industry
Location	Palaiseau Campus, Université Paris-Sud (Orsay)
Course duration	12 months, full time
Course start	September
Degree awarded	Master’s degree

Application dates

WHY ENROLL IN THIS PROGRAM?

Asset n° 1

Open up exciting career opportunities in a variety of sectors through the wide range of courses

Asset n°2

Become familiar with research, choosing between writing a Master’s thesis and completing an internship

Asset n°3

Specialize in probability and statistics or statistics and machine learning

The Mathematics of Randomness Master’s degree is a top-level training program covering diverse fields relating to probability, statistics and machine learning. Largely devoted to fundamental knowledge and skills, the program also considers constraints due to applied considerations. On graduating, most students embark on an academic or industrial PhD, while others directly begin a career in industry.

Courses are split into two specializations:

Probability and statistics with a focus on mathematical research
Statistics and machine learning oriented toward research and job opportunities in private companies

During the second semester, students will deliver a Master’s thesis based on the analysis of several research papers, under the supervision of a professor from the Master’s program. This thesis can be replaced by an internship in a firm or a research laboratory.

Objectives

This program enables students to:

Understand, master and use different modern mathematical tools for modelling randomness and analyzing and treating data
Perform predictions and take decisions

This program equips students to complete a PhD or build a research or industry career in:

Various fields of application where randomness is analyzed, processed and summarized to make predictions and decisions
Sectors such as insurance, banking, pharmaceutical laboratories, energy, climate, transport, aeronautics, communication and signaling

Semester 1

The first semester includes a set of fundamental courses providing the basics of theoretical probabilities and statistics.

Mandatory seminar

Weekly seminar presenting the current research fields in probability and statistics

20h

2.5 ECTS

English

Elective courses (27.5 ECTS)

Students choose their courses (27.5 ECTS total) from the following list. The study program is to be validated afterwards with the Master's coordinator during a personal interview.

Théorie ergodique	37h 7.5 ECTS Français
High dimensional Probability and Statistics	40h 10 ECTS English
Statistical Learning Theory	20h 2.5 ECTS English
Projet Machine Learning pour la prévision	36h 10 ECTS Français
Optimization for Data Science	30h 5 ECTS English
Mouvement brownien et calcul stochastique	48h 7.5 ECTS Français
Modèles graphiques pour l'accès à l'information à grande échelle	20h 2.5 ECTS Français
Hidden Markov chains and sequential Monte-Carlo methods	20h 2.5 ECTS English
Méthodes bayésiennes pour l'apprentissage	20h 2.5 ECTS Français
Graphes aléatoires	37h 7.5 ECTS Français
Generalisation properties of algorithms in ML	20h 2.5 ECTS English
Non paramétric estimation	20h 2.5 ECTS English
Convex analysis and optimisation theory	20h 5 ECTS English
Théorèmes limites et applications	30h 5 ECTS English
Model Selection	20h 5 ECTS English
Concentration of measure	20h 5 ECTS English
Chaîne de Markov : approfondissements	20h 5 ECTS Français
Apprentissage statistique et rééchantillonnage	20h 5 ECTS Français
Reinforcement learning	20h 5 ECTS English

Semester 2

The second semester includes more specialized courses opening on current research topics.
Students choose their courses (16 ECTS total) from the following list.

Sequential learning and optimization	20h 4 ECTS English
Temps locaux et théorie des excursions	20h 4 ECTS Français
Systèmes de particules en intéraction	20h 4 ECTS Français
Statistiques spatiales pour l'environnement	20h 4 ECTS Français
Processus de branchement et populations structurées	20h 4 ECTS Français
Statistics and optimization	20h 4 ECTS Anglais
Modèles solubles en probabilités	20h 4 ECTS English
Matrices aléatoires	20h 4 ECTS Français
Mathematical Introduction to compressed sensing	20h 4 ECTS English
Inférence sur de grandes graphes	20h 4 ECTS Français
Extremes	20h 4 ECTS English
Fiabilité des systèmes	20h 4 ECTS Français
Calcul de Malliavin	20h 4 ECTS Français
Bayésien non paramétrique	20h 4 ECTS Français
Permutations aléatoires et théorie des représentations des groupes symétriques	20h 4 ECTS Français
Analyse topologique des données	20h 4 ECTS Français

Internship or Master's thesis

The internship or master thesis must last between 4 and 6 months and is carried out between April 1st and September 1st. It is compulsory and counts for 14 ECTS

Admission requirements

Academic prerequisites

Completion of a first year of Master in mathematics at Institut Polytechnique de Paris or equivalent in France or abroad.

Language prerequisites

English
French

How to apply

Applications can be submitted exclusively online. You will need to provide the following documents:

Transcript
Two academic references (added online directly by your referees)
CV/resume
Statement of purpose

You will receive an answer in your candidate space within 2 months of the closing date for the application session.

Fees and scholarships

Registration fees are available here

Find out more about scholarships

Please note that fees and scholarships may change for the following year.

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