# Preparatory Math Course for the Intake 2013

Guest Instructor:
Anton Velinov
Christopher Boortz
Time I:
Monday, 09:00am to 04:00pm
Venue I:
HU Berlin, Hegelplatz 1, Seminargebäude, Room 1.403
Description:

Starting Date: October 7

Preliminary Outline:

--> Logic and Sets:
 Logic: methods of proof
-Constructive proof
-Contrapositive proof
 De Morgan's laws
 Convexity

--> Functions:
 Mappings: surjective, injective, bijective
 correspondence: Upper and lower hemicontinuity
 Continuity and dierentiability
 Integration
 Concavity and convexity (for multidimensional functions)
 Quasiconcavity
 Taylor's Theorem
 Implicit Function Theorem
 Homogeneous functions and Euler's formula

--> Sequences:
 Metric and normed spaces
 Convergence of sequences in metric spaces
 Bounded and Compact sets
 Limits of functions
 Contraction Mapping Theorem
 Extreme Value Theorem
 Separating Hyperplane Theorem
 Fixed Point Theorems

--> Matrix Algebra:
 Trace, determinant, rank
 Inversion
 Positive deniteness
 Eigenvalues, Eigenvectors
 Diagonalization, Jordan decomposition, Choleski decomposition
 Matrix dierentiation, Kronecker products, vectorization

--> Complex numbers:
 sin, cos functions
 De Moivre's Theorem