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Théorie des nombres

Cours associés (32)

This course introduces the basics of cryptography. We review several types of cryptographic primitives, when it is safe to use them and how to select the appropriate security parameters. We detail how

CS-101: Advanced information, computation, communication I

Discrete mathematics is a discipline with applications to almost all areas of study. It provides a set of indispensable tools to computer science in particular. This course reviews (familiar) topics a

MATH-313: Number theory I.b - Analytic number theory

The aim of this course is to present the basic techniques of analytic number theory.

MATH-489: Number theory II.c - Cryptography

The goal of the course is to introduce basic notions from public key cryptography (PKC) as well as basic number-theoretic methods and algorithms for cryptanalysis of protocols and schemes based on PKC

MATH-410: Riemann surfaces

This course is an introduction to the theory of Riemann surfaces. Riemann surfaces naturally appear is mathematics in many different ways: as a result of analytic continuation, as quotients of complex

MATH-521: Advanced analytic number theory

We will present the work of James Maynard (MF 2022) on the existence of bounded gaps between primes

MATH-511: Number theory II.a - Modular forms

In this course we will introduce core concepts of the theory of modular forms and consider several applications of this theory to combinatorics, harmonic analysis, and geometric optimization.

MATH-101(g): Analysis I

Étudier les concepts fondamentaux d'analyse et le calcul différentiel et intégral des fonctions réelles d'une variable.

MATH-494: Topics in arithmetic geometry

P-adic numbers are a number theoretic analogue of the real numbers, which interpolate between arithmetics, analysis and geometry. In this course we study their basic properties and give various applic

MATH-101(en): Analysis I (English)

We study the fundamental concepts of analysis, calculus and the integral of real-valued functions of a real variable.

MATH-200: Analysis III - complex analysis and vector fields

Apprendre les bases de l'analyse vectorielle et de l'analyse complexe.

MATH-417: Number theory II.b - selected topics

This year's topic is "Additive combinatorics and applications." We will introduce various methods from additive combinatorics, establish the sum-product theorem over finite fields and derive various a

MATH-482: Number theory I.a - Algebraic number theory

Algebraic number theory is the study of the properties of solutions of polynomial equations with integral coefficients; Starting with concrete problems, we then introduce more general notions like alg

MATH-310: Algebra

This is an introduction to modern algebra: groups, rings and fields.

COM-102: Advanced information, computation, communication II

Text, sound, and images are examples of information sources stored in our computers and/or communicated over the Internet. How do we measure, compress, and protect the informatin they contain?

MATH-205: Analysis IV - Lebesgue measure, Fourier analysis

Learn the basis of Lebesgue integration and Fourier analysis

EE-556: Mathematics of data: from theory to computation

This course provides an overview of key advances in continuous optimization and statistical analysis for machine learning. We review recent learning formulations and models as well as their guarantees

MATH-670: The theta correspondence

In the course we will discuss some introductory aspects of the local/global theta correspondence for automorphic forms/representation for various dual pairs. One of the objectives will be to prove Wal

MATH-305: Introduction to partial differential equations

This is an introductory course on Elliptic Partial Differential Equations. The course will cover the theory of both classical and generalized (weak) solutions of elliptic PDEs.

MATH-351: Advanced numerical analysis II

The student will learn state-of-the-art algorithms for solving differential equations. The analysis and implementation of these algorithms will be discussed in some detail.