BMAT 13A03 - Math Applied to Social Sciences - Advanced level

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.

Tarlochan MANAK

Séminaire

English

Autumn 2024-2025

Continuous examination and in-class final exam (session 12).

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