Advanced Mathematics for Economics (HS26)
Content
- In the first part of this course we will give a review of linear algebra.
- In the second part we look at functions and Taylor's formula.
- In the third part we study optimization problems (unconstrained and constrained).
All events
Juristische Fakultät, Seminarraum S6 HG.52
There is no compulsory attendance at all.
Coursework
Coursework
Please submit your coursework to me by 30.09.2026 (either in person or by email).
Complementary literature
Sydsaeter K., Hammond P., Seierstad A., Strom A.: Further Mathematics for Economic Analysis, Prentice Hall.Chiang,
Alpha C.: Fundamental Methods of Mathematical Economics, McGraw-Hill International Editions.
Marking
There are a coursework and a written exam.
You do not have to solve the coursework. If you hand in solutions to all the exercises, they will be marked (preliminary mark).
At the end of the term, there will be an examination.
Your final mark will be the arithmetic mean of your preliminary mark and your examination mark if the arithmetic mean of your preliminary mark and your examination mark is greater than your examination mark. Otherwise, your final mark will be your examination mark.
If you do not hand in the coursework, your examination mark will be your final mark.
Examination
When? In October. The exact date and time will be discussed with the enrolled students.
Where?
Duration? 90 minutes
Allowed electronic means:
simple pocket calculator (einfacher Taschenrechner, according to Merkblatt Hilfsmittel)
Allowed non-electronic means:
open-book
You can download a Mock examination.
Course Arc
1. Linear algebra
Keywords
vector, matrix, eigenvalue, eigenvector, diagonalization, linear transformation, spectral theorem for symmetric matrices, quadratic forms and definitness
Not relevant for examination
generalized eigenvalues
Preparation
Please study the following Handout 1. Start immediately and get (at least) an overview.
Timetable
Mo, 31.08.26, 10:15-12:00
1. Part Theoretical foundations (presentation of the handout): vector, matrix, linear maps and matrices, eigenvalue, eigenvector
2. Part Self-study (of the handout) and questions
Mo, 31.08.26, 13:15-15:00
1. Part Theoretical foundations (presentation of the handout): diagonalization, spectral theorem for symmetric matrices
2. Part Self-study (of the handout) and questions
Tue, 01.09.26, 10:15-12:00
1. Part Theoretical foundations (presentation of the handout): quadratic forms
2. Part Self-study (of the handout) and questions
Tue, 01.09.26, 13:15-15:00
Only Self-study (of the handout) and questions
2. Part: Functions and Taylor's formula
Keywords
gradient, Hesse matrix, differential, directional derivative, chain rule, implicit function theorem and derivative, Taylor formula, concave and convex functions, unconstrained optimization
Not relevant for examination
Quasi-concave and quasi-convex functions
Preparation
Please study the following Handout 2. Start immediately and get (at least) an overview.
Timetable
We, 02.09.26, 10:15-12:00
1. Part Theoretical foundations (presentation of the handout): partial derivative, gradient, Hesse matrix, differential, chain rule, implicit function theorem, directional derivative
2. Part Self-study (of the handout) and questions
We, 02.09.26, 13:15-15:00
1. Part Theoretical foundations (presentation of the handout): Taylor formula, concave and convex functions
2. Part Self-study (of the handout) and questions
Thu, 03.09.26, 10:15-12:00
1. Part Theoretical foundations (presentation of the handout): unconstrained optimization
2. Part Self-study (of the handout) and questions
Thu, 03.09.26, 13:15-15:00
Only Self-study (of the handout) and questions
3. Part: Static Optimization
Keywords
local and global extremal points, unconstrained optimization, constrained optimization, Lagrange method, Karush-Kuhn-Tucker method
Preparation
Please study the following Handout 3. Start immediately and get (at least) an overview.
Timetable
Tue, 08.09.26, 10:15-12:00
1. Part Theoretical foundations (presentation of the handout): local and global extremal points, unconstrained optimization
2. Part Self-study (of the handout) and questions
Tue, 08.09.26, 13:15-15:00
Only Self-study (of the handout) and questions
Wed, 09.09.26, 10:15-12:00
1. Part Theoretical foundations (presentation of the handout): constrained optimization, Lagrange method
2. Part Self-study (of the handout) and questions
Wed, 09.09.26, 13:15-15:00
Only Self-study (of the handout) and questions
Thu, 10.09.26, 10:15-12:00
1. Part Theoretical foundations (presentation of the handout): Karush-Kuhn-Tucker method
2. Part Self-study (of the handout) and questions
Thu, 10.09.26, 13:15-15:00
Only Self-study (of the handout) and questions
Fr, 11.09.26, 10:15-12:00
Only Self-study (of the handout) and questions
Fr, 11.09.26, 13:15-15:00
Only Self-study (of the handout) and questions
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