Mathematics for Economists, 212.214, Spring 2019
Practical message: I will sign the override / cho an ji form after the first lecture. Depending on the demand for this, I may have to limit the numbers to ensure that everyone can fit in the classroom, in which case a first come, first served principle will apply.
Course web page
https://sites.google.com/site/oyvindthomassen/ma19s
Time and place
Tuesday 9.30 - 12.20, Building 83 Room 305
No classes on the following day
7 May (Substitute holiday for Children's Day)
Exam dates
Mid-term exam Tuesday 16 April.
Final exam Tuesday 11 June.
Content / purpose
To teach basic mathematical methods useful in economics: linear algebra, optimization of functions of several variables, analysis on the real line. See lecture notes for more details.
Prerequisites
Familiarity with single-variable calculus, at least the material in chapter 2 of Simon and Blume.
Grading
Mid-term exam 45%, final exam 55%.
Attendance
You are expected and encouraged to come to all lectures, but there will be no attendance check.
Reading
We will follow the order of topics in the lecture notes. The lecture notes refers to the relevant chapters / pages of the textbooks for each topic.
The lecture notes follow the textbooks closely. The lecture notes contain all the material you need for the exams.
You may study only the notes, only the book, or both - depending on what you find most helpful. They are alternative presentations of the same material. In any case you will probably want to solve some of the problems in the textbooks. Both textbooks have the answers to some problems in the back of the book. In addition, there is a solutions manual for Simon and Blume that you can probably find online by googling 'simon blume solutions' or something similar.
Lecture notes
Simon and Blume (1994): Mathematics for Economists, Norton
Ross (2013): Elementary Analysis. The Theory of Calculus, 2nd ed., Springer
Past exams
Fall 2018 final, solution
Fall 2018 mid-term, solution
Fall 2017 final, solution (there was no mid-term exam)
Spring 2016 final, solution
Spring 2016 mid-term, solution
Spring 2015 final, solution
Spring 2015 mid-term, solution
Lecture plan
Page numbers refer to the lecture notes.
5 March, Lecture 1
p. 7-13 (Systems of linear equations, rank)
12 March, Lecture 2
p. 14-19 (Rank)
19 March, Lecture 3
p. 19-32 (Elementary matrices, square matrices)
26 March, Lecture 4
p. 32-37, 41-50 (LU decomposition, determinant, real numbers, absolute value, least upper bound, sequences)
2 April, Lecture 5
p. 50-57 (Limit theorems for sequences, definition of continuity)
9 April, Lecture 6
p. 57-63 (Continuity, subsequences)
16 April, Mid-term exam
23 April, Lecture 7
p. 64-68 (Bolzano-Weierstrass theorem, Extreme value theorem, Intermediate value theorem)
Note: we will skip the proof of the intermediate value theorem.
30 April, Lecture 8
p. 69-76 (Uniform continuity, pointwise convergence of a sequence of functions, uniform convergence)
7 May, No lecture (Substitute holiday for Children's Day)
14 May, Lecture 9
p. 77-81 (Metric spaces, continuity in metric space)
21 May, Lecture 10
p. 80-92 (Quadratic forms, unconstrained optimization)
28 May, Lecture 11
p. 93-109 (Constrained optimization, envelope theorem)
4 June, Lecture 12
Content will be announced later
11 June, Final exam