Discrete Mathematics MAA 103 (Year 1) has two main objectives: (i) teach fundamental concepts in discrete mathematics, which are the building blocks of many different areas of science and of advanced mathematics (ii) teach how to write proofs. The cours strarts with elementary logic (e.g. quantifiers, different methods of proof), sets, and functions. The second part of the course introduces students to combinatorics and probability (on finite sets).
The lectures will closely follow the textbook Mathematics: A Discrete Introduction (3rd Edition) by Scheinerman. For a different presentation and broader applications concerning computer science, one may have a look at Discrete Mathematics with Applications by Epp.
Course webpage: http://www.cmap.polytechnique.fr/~kortchemski/dmaths/
Discrete Mathematics (MAA103) begins by introducing students to the central notions needed to pursue advanced mathematics, such as elementary logic (e.g. quantifiers, different methods of proof), sets, and functions. The second part of the course introduces students to combinatorics and probability (on finite sets). Course material is supplemented with examples and applications, such as graphical modeling and generating functions.
The second part is dedicated to the study of ordinary differential equations, mainly first order linear differential equations and linear systems of ODEs, with a special focus on linear differential equations with constant coefficients.
The third part is devoted to the study of plane parametric curves. We will see their fundamental properties and how to sketch a plane curve. We will cover parametric curves in Cartesian coordinates and in polar coordinates.
The aim of Introduction to Numerical Analysis (MAA 106) is to provide the students with practical knowledge of basic mathematical algorithms and computer programming.
The course is divided into 4 cycles and covers several notions such as the representation of numbers, the complexity of algorithms, interpolation of functions, numerical integration and solving equations. Mathematics are used to study the notions of error, convergence, order of convergence... We also focus on the practical implementation of the methods, using in particular Python notebooks which enable to test easily the algorithms with multiple parameters for instance.
The last three weeks of the course are devoted to a more personal project that will allow the student to understand deeper a notion seen in class. The grading of the course includes the project, a test and homeworks.