Prerequisites: MAA101, MAA102
Mathematical Modeling (MAA107) introduces some basic mathematical models that find applications in mechanics, physics (for example mechanical systems), biology (population dynamics) and economics (pricing, contract theory). In particular, this course introduces some techniques such as Markov chains and ordinary differential equations with a hands-on approach.
The purpose of MAA205 is to use computer science and programming to solve problems in discrete mathematics, and vice versa. Topics include: graphs and their matrices, combinatorics and generating functions, elementary probability, sorting algorithms. The course consists of lectures and practical labs in python.
Linear algebra (FMA_1F001_EP, formerly MAA101) is a fast-paced course which provides students with an overview of the most useful techniques of linear algebra. Upon completion of this course, students will fully understand the fundamental concepts of vector spaces, dimension, linear systems, matrices and determinants, and how they apply to problems in other elds of the Bachelor program.
Euclidean and Hermitian Spaces continues the study of linear maps between vector spaces, started in MAA101. The goal is to obtain simple and efficient models for these applications up to suitable changes of coordinates. The concept of duality is initially introduced in the general context of mere vector spaces. Then, the focus is put on vector spaces enjoying a richer structure, namely prehilbert spaces, which is available in most applications (e.g. in solid mechanics or in quantum mechanics). The geometry of these spaces, as well as their important transformations (e.g. normal or unitary maps) is also discussed.
Algebra (MAA 206) is a continuation of Algebra (MAA 201) and covers objects in bilinear algebra. These objects, mainly quadratic forms, have fundamental applications (e.g. in Number Theory and Mechanics), and also lead to the study of algebraic objects; for instance, some special groups of matrices, whose applications in mathematics and physics are fundamental, from Number Theory and geometry to the classification of particles.
Prerequisites: MAA101, MAA103, MAA201, MAA206
MAA303 focuses on groups, rings and fields.
The first part of the course will be dedicated to group theory, and we will cover all the basic notions and tools that one uses to study groups: normal subgroups, quotient groups, simple groups, group actions...
The second part of the course will focus on rings. We will introduce the basic notions related to them, such as ideals, principal ideal domains, prime and maximal ideals, ring quotients..., with a particular emphasis on polynomial rings.
In the last part of the course, we will focus on fields. We will introduce field extensions and study their basic properties. At the very end of the course, we will see how groups, rings and fields are deeply related through the study of algebraic equations and Galois theory.
This course provides an overview of the classical differential geometry of curves and surfaces.
More precisely, we will study the local theory of (regular, parametrized) curves (curvature, torsion), regular surfaces, and the local theory (first and second fundamental forms) and intrinsic geometry (Theorema Egregium and Gauss-Bonnet theorem) of the latter.
Weekly exercise sessions form an integral part of the course.
The instructor will provide lecture notes covering the material seen in class.
Prerequisites: some basic linear algebra, as seen is any undergraduate class (such as MAA101 and 201), and familiarity with multivariable calculus (differential of functions from ℝ^n to ℝ^2, as seen for example in MAA202). The most important notions will be briefly reviewed during the first lecture.
Algebra (MAA101) is a fast-paced course which provides students with an overview of the most useful techniques of linear algebra. Upon completion of this course, students will fully understand the fundamental concepts of vector spaces, dimension, linear systems, matrices and determinants, and how they apply to problems in other elds of the Bachelor program.
Prerequisites: MAA101, MAA102
Mathematical Modeling (MAA107) introduces some basic mathematical models that find applications in mechanics, physics (for example mechanical systems), biology (population dynamics) and economics (pricing, contract theory). In particular, this course introduces some techniques such as Markov chains and ordinary differential equations with a hands-on approach.
The purpose of MAA205 is to use computer science and programming to solve problems in discrete mathematics, and vice versa. Topics include: graphs and their matrices, combinatorics and generating functions, elementary probability, sorting algorithms. The course consists of lectures and practical labs in python.
Euclidean and Hermitian Spaces continues the study of linear maps between vector spaces, started in MAA101. The goal is to obtain simple and efficient models for these applications up to suitable changes of coordinates. The concept of duality is initially introduced in the general context of mere vector spaces. Then, the focus is put on vector spaces enjoying a richer structure, namely prehilbert spaces, which is available in most applications (e.g. in solid mechanics or in quantum mechanics). The geometry of these spaces, as well as their important transformations (e.g. normal or unitary maps) is also discussed.
Algebra (MAA 206) is a continuation of Algebra (MAA 201) and covers objects in bilinear algebra. These objects, mainly quadratic forms, have fundamental applications (e.g. in Number Theory and Mechanics), and also lead to the study of algebraic objects; for instance, some special groups of matrices, whose applications in mathematics and physics are fundamental, from Number Theory and geometry to the classification of particles.
Prerequisites: MAA101, MAA103, MAA201, MAA206
MAA303 focuses on groups, rings and fields.
The first part of the course will be dedicated to group theory, and we will cover all the basic notions and tools that one uses to study groups: normal subgroups, quotient groups, simple groups, group actions...
The second part of the course will focus on rings. We will introduce the basic notions related to them, such as ideals, principal ideal domains, prime and maximal ideals, ring quotients..., with a particular emphasis on polynomial rings.
In the last part of the course, we will focus on fields. We will introduce field extensions and study their basic properties. At the very end of the course, we will see how groups, rings and fields are deeply related through the study of algebraic equations and Galois theory.
This course provides an overview of the classical differential geometry of curves and surfaces.
More precisely, we will study the local theory of (regular, parametrized) curves (curvature, torsion), topological and regular surfaces, and the local theory (first and second fundamental forms) and intrinsic geometry (Theorema Egregium and Gauss-Bonnet theorem) of the latter.
Weekly exercise sessions form an integral part of the course.
The instructor will provide lecture notes covering the material seen in class.
Prerequisites: some basic linear algebra, as seen is any undergraduate class (such as MAA101 and 201), and familiarity with multivariable calculus (differential of functions from ℝ^n to ℝ^2, as seen for example in MAA202). The most important notions will be briefly reviewed during the first lecture.
