# BMAT 13A03 - Quantitative and mathematical methods for social Sciences - Advanced 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)

## Pedagogical format

Session 1: Basic operations and equations - Fractions, indices, rates, percentages - Development, factorization - Basic functions (absolute value, linear/non-linear, inverse, power, exponential, logarithm, etc.): characteristics and graphic representations - Linear equations of 1st , 2nd and 3rd degree with 1/2/3 variables (and factorizations of the form x-x0), and inequalities - Session 2: 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 3 and 4: Constrained optimization - Constrained and unconstrained optimization: with one variable, or multiple variables (only looking for critical points) - Lagrangian Sessions 5 and 6: Integration - Calculation of simple areas (triangle, trapezoid, etc.) - Single variable integrals on a segment - Search for evident primitives - Integration by parts and substitution of variables Sessions 7 and 8: Real sequences and mathematical induction - Monotony, convergence (graphical method using step curves) - Sum indices - Arithmetic and geometric sequences/sums - Arithmetico-geometric sequences and auxiliary sequences - Convergence theorems (study of bounded monotonic sequences ///of sequences of type f(n) /// of sequences of type u(n+1)=f(u(n)), where f is a contraction mapping) - Mathematical induction Session 9: Vector spaces and linear maps - Vector - Vector space - Linearly independent set, spanning vectors and dimension - Linear maps - Kernel and range, rank-nullity theorem Sessions 10 and 11: Matrices and linear systems solving - Basic calculations - System of equations with n unknowns - Determinant and matrix inversion (Gaussian elimination and adjugate matrix) Session 12: Final Exam

## Course validation

Continuous examination and final exam