# BMAT 13A01 - Quantitative and mathematical methods for social Sciences - Introductory level

Type d'enseignement : Seminar

Semester : Autumn 2018-2019

Number of hours : 24

Language of tuition : English

## Pre-requisite

Continuous examination and final exam

## Course Description

A 12-session mathematics course with three levels (introductory, intermediate, advanced) Taught over 12 sessions, this course aims at providing students with the mathematical foundations needed to support notions taught in the first-year introduction to economics course, and more generally, quantitative methods in social sciences. This course places emphasis on practice, with progressive exercises and case studies, so that students can gain autonomy quickly with the taught themes. Breakdown of the students (unless a derogation is made): Terminale L or international equivalent (no mathematics in last year of high school) for the introductory class Terminale ES or international equivalent (mathematics, but not in a scientific field) for the intermediate class Terminale S or international equivalent (scientific field) for the advanced class. Foreign students will self-select their level, after reading the syllabus below.

## Teachers

PEGLIASCO, Laurent (Professeur de mathématiques)

## Pedagogical format

Sessions 1 and 2: Basic operations - Multiplication, division, mental arithmetic, order of magnitude - Fractions, indices, rates, percentages - Development, factorization, sum and product indices - Order of magnitude, relative and absolute values, exact and approached values - The concept of variable/parameter/constant Sessions 3, 4 and 5: Functions - Rate of increase / slope, tangent - Graphic representation, relative positions of two curves, curve displacement - Derivative of polynomial, product, quotient and composite functions, and study of variations Sessions 6 and 7: Basic functions - Basic functions (absolute value, linear/non-linear, inverse, power, exponential, logarithm, etc.): characteristics and graphic representations - Computation of simple areas (triangle, trapezoid, etc.) Sessions 8 and 9: Equations and inequalities - Linear equations with 1/2 variables - Inequalities Sessions 10,11: Constrained optimization - Second order derivative, convexity, concavity - Partial derivatives - Returns to scale, logarithmic derivative, elasticities - Constrained and unconstrained Optimization: with one variable, or multiple variables (only looking for critical points) Session 12: Final exam