Advanced Mathematics for Economics (HS25)
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).
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.
Organsational Matters
There are exercises and a written exam.
You do not have to solve the exercises. If you hand in solutions to all the exercises, they will be marked. These marks are averaged together to give the 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 solutions to the exercises, your examination mark will be your final mark.
There is no compulsory attendance at all.
Examination
When? Saturday, October 18, 2025, from 9:00 to 10:30 a.m.
Where? S15 (WWZ)
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.
Exercises
Please solve the following problems and hand (handwritten and directly or by email) in your solutions of the marked questions by 19.09.2025 at the latest.
Timetable
Mo, 01.09.25, 09:15-12:00 (Juristische Fakultät, Seminarraum S6 HG.52)
1. Part Theoretical foundations (presentation of the handout): vector, matrix, linear maps and matrices, eigenvalue, eigenvector
2. Part Self-study (of the handout), questions and work on the exercises
Tue, 02.09.25, 09:15-12:00 (Juristische Fakultät, Seminarraum S6 HG.52)
1. Part Theoretical foundations (presentation of the handout): diagonalization, spectral theorem for symmetric matrices
2. Part Self-study (of the handout), questions and work on the exercises
We, 03.09.25, 09:15-12:00 (Juristische Fakultät, Seminarraum S6 HG.52)
1. Part Theoretical foundations (presentation of the handout): quadratic forms
2. Part Self-study (of the handout), questions and work on the exercises
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.
Exercises
Please solve the following problems and hand (handwritten and directly or by email) in your solutions of the marked questions by 19.09.2025 at the latest.
Timetable
Thu, 04.09.25, 09:15-12:00 (Juristische Fakultät, Seminarraum S6 HG.52)
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), questions and work on the exercises
Fri, 05.09.25, 09:15-12:00 (Juristische Fakultät, Seminarraum S6 HG.52)
1. Part Theoretical foundations (presentation of the handout): Taylor formula, concave and convex functions
2. Part Self-study (of the handout), questions and work on the exercises
Mo, 08.09.25, 09:15-12:00 (Juristische Fakultät, Seminarraum S6 HG.52)
1. Part Theoretical foundations (presentation of the handout): unconstrained optimization
2. Part Self-study (of the handout), questions and work on the exercises
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.
Exercises
Please solve the following problems and hand in (handwritten and directly or by email) your solutions of the marked questions by 19.09.2025 at the latest.
Timetable
Tue, 09.09.25, 09:15-12:00 (Juristische Fakultät, Seminarraum S6 HG.52)
1. Part Theoretical foundations (presentation of the handout): local and global extremal points, unconstrained optimization, constrained optimization, Lagrange method
2. Part Self-study (of the handout), questions and work on the exercises
Wed, 10.09.25, 09:15-12:00 (Juristische Fakultät, Seminarraum S6 HG.52)
1. Part Theoretical foundations (presentation of the handout): Karush-Kuhn-Tucker method
2. Part Self-study (of the handout), questions and work on the exercises
Thu, 11.09.25, 09:15-12:00 (Juristische Fakultät, Seminarraum S6 HG.52)
Only Self-study (of the handout), questions and work on the exercises
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