ma18
Mathematics for Economists, 212.214, Fall 2018
Practical message: it will not be possible to sign up for this course with the override / cho an ji form. Because of the large number of emails I have received about this issue, I have not been able to reply to everyone.
Course web page
https://sites.google.com/site/oyvindthomassen/ma18
Time and place
Monday 14:00~16:50, Building 83 Room 501
No classes on the following days
24 September (Chuseok), 15 October (SNU Anniversary)
Exam dates
Mid-term exam Monday 22 October
Final exam Monday 10 December.
2.00 pm - 4.00 pm. Please make sure you arrive at 1.55 pm at the latest so the exam can start on time.
IMPORTANT: half of the class will be in the usual classroom (building 83, room 501); the other half will be in building 64, room 301. Check here to see which room you are in.
For those of you who are in building 64 make sure you check in advance where the building is, so you know were to go at the time of the exam.
The exam will mainly be about material covered after the mid-term exam, but there may be a question or two about topics covered before the mid-term.
Topics that are in the lecture notes but were not discussed during the lectures are not likely to be on the exam. The more time we spent on something in lectures, the more important it is.
No notes, books, etc. is permitted. You may use a simple calculator, but not your phone. (In any case a calculator will probably not be needed).
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 40%, final exam 60%.
Reading
We will follow the order of topics in the lecture notes. The lecture notes refers to the relevant chapters of the textbooks.
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
Previous exams
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.
3 September, Lecture 1
p. 7-15 (Systems of linear equations, rank)
10 September, Lecture 2
p. 16-29 (Rank, elementary matrices)
17 September, Lecture 3
p. 29-37 (Square matrices, LU decomposition, determinant)
24 September No lecture
1 October, Lecture 4
p. 41-50 (Real numbers, absolute value, least upper bound, sequences)
8 October, Lecture 5
p. 50-57 (Limit theorems for sequences, definition of continuity)
15 October No lecture
22 October Mid-term exam
29 October, Lecture 6
p. 57-65 (Continuity, subsequences, Bolzano-Weierstrass theorem)
5 November, Lecture 7
p. 65-69 (Extreme value theorem, Intermediate value theorem, uniform continuity)
12 November, Lecture 8
p. 70-77 (Pointwise convergence of a sequence of functions, uniform convergence, definition of metric space)
19 November, Lecture 9
p. 77-81 (Metric spaces, continuity in metric space)
26 November, Lecture 10
p. 80-92 (Quadratic forms, unconstrained optimization)
3 December, Lecture 11
p. 93-109 (Constrained optimization, envelope theorem)
10 December Final exam