Topic outline

  • General

    The aim of the course is to provide students with a thorough understanding of the main mathematical concepts and tools used in Economics. We will study:
    - linear algebra: we will focus on how to solve systems of linear equations;
    - calculus of several variables: we will analyze functions of several variables and learn how to apply differential calculus to them
    - optimization: we will learn how to find the points in the domain of a function that maximize or minimize the function’s value, with or without constraints;

    Waiver exam
    It is possible to waive the first half of the course (part on linear algebra) by taking a waiver exam. Passing the waiver exam requires 60 % of points, and after that the course grade will be based on second half only. Topics covered in the exam: vectors and matrices, determinant, inverse, Cramer's rule, Gauss-Jordan elimination, eigenvalues and eigenvectors (book chapters 6--1, 23)


    Schedule (preliminary)

    First period

    - Lecture 1: Sets and Functions
    - Lectures 2-4: Sequences, Series, Differentiation
    - Lecture 5: Integration 
    - Lecture 6: Linear Algebra: Gauss-Jordan elimination
    - Lecture 7: Vectors
    - Lecture 8: Matrices
    - Lecture 9: Determinant
    - Lecture 10: Linear Equations: Rank, Inversion
    - Lecture 11: Eigenvectors and eigenvalues

    Second period
    - Lecture 12: Multivariate functions, injection, surjection, bijection, partial derivatives
    - Lecture 13: Multivariate calculus; Jacobian, chain rule, Hessian
    - Lecture 14: Quadratic Forms
    - Lecture 15: Implicit function theorem
    - Lecture 16: First Order Conditions in Unconstrained Optimization
    - Lecture 17: Second Order Conditions in Unconstrained Optimization
    - Lecture 18 (13.11.): Convex and Concave Functions
    - Lecture 19 (14.11) : Constrained Optimization I
    TA session (17.11), Problem Set 6 DL (22.11)
    - Lecture 20 (20.11.): Optimization with Equality Constraints
    - Lecture 21 (21.11.): Optimization with Inequality Constraints
    TA session (17.11.), Problem Set 7 DL (29.11.)
    - Lecture 22 (27.11.): Sufficient Optimality Conditions, Review
    TA session (1.12.), Problem Set 8 DL (7.12.)

    Textbook

    Carl P. Simon and Lawrence Blume, Mathematics for Economists, Norton, 1994

    Grading

    74 % exam/partial exams

    20 % problem sets

    6 % exercises in lectures

    Grade point limits
    1: 40-49
    2: 50-59
    3: 60-74
    4: 75-84
    5: 85-100

    Exams
    midterm (Oct. 18th) + final exam (Dec. 14th) or an exam (Feb. 5th) that covers entire material

    About the midterm:
    October 18th, 13:00-15:00, lecture hall D (undergraduate center)
    calculators are not needed, but you are allowed to use scientific calculators.

    December 14th, 13:00-15:00, lecture hall U4 (U142)
    calculators are not needed, but you are allowed to use scientific calculators.
    Arrangements due to transportation strike https://mycourses.aalto.fi/mod/forum/discuss.php?d=377879

    Retakes:
    January 22nd for those who passed the waiver: 2nd part material, results
    February 5th: full material, results
    March 25th: full material, results


    Zulip