# BMAT 13A02 - Quantitative and mathematical methods for social Sciences - Intermediate level

Type d'enseignement : Seminar

Semester : Autumn 2018-2019

Number of hours : 24

Language of tuition : English

## Pre-requisite

aucun

## 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

- MANAK, Tarlochan (Professeur)
- PEGLIASCO, Laurent (Professeur de mathématiques)

## Pedagogical format

Sessions 1 and 2: Basic operations and functions - Fractions, indices, rates, percentages - Development, factorization - Order of magnitude, relative and absolute values, exact and approached values - The concept of variable/parameter/constant - Basic functions (absolute value, linear/non-linear, inverse, power, exponential, logarithm, etc.): characteristics and graphic representations Sessions 3 and 4: 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 - Second order derivative, convexity, concavity - Partial derivatives - Returns to scale, logarithmic derivative, elasticities Sessions 5 and 6: Equations and inequalities - Linear equations with 1/2 variables - Inequalities Sessions 7 and 8: Constrained optimizations - Constrained and unconstrained Optimization: with one variable, or multiple variables (only looking for critical points) Session 9: Integration - Calculation of simple areas (triangle, trapezoid etc.) - Single variable integrals on a segment - Search for evident primitives Sessions 10 and 11: Real sequences - Monotony, convergence (graphical method using step curves) - Sum indices - Arithmetic and geometric sequences/sums Session 12: Final exam

## Course validation

Continuous examination and final exam