## 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 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

74 % exam/partial exams

20 % problem sets

6 % exercises in lectures

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

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