Advanced Mathematics

Content
The course consists of three parts. In the first part basic conceptual notions of mathematical analysis are developed, such as limits, continuity, differentiation, sequences and series, uniform convergence etc. In the second part these fundamental concepts are blended with linear algebra and extended to the multivariable case resulting in the main theorems of mathematical analysis: Taylors theorem and the implicit function theorem. In the third part we study various applications of the implicit function theorem.
 

Format 
Syllabus and projects
Every week exercises and projects must be handed in. The instructor and his assistants correct and return these to the students for discussion. The exercises serve as an integrated component of the learning process.
In addition to the contact hours, each student is expected to work ten hours a week on the course.
This time should be devoted to:
- reviewing the material of the preceding lecture;
- finishing the exercises started in the preceding problem session;
- preparing exercises to hand in;
- studying the corrections of the previously returned hand-in problems, making sure everything is clear.
 
Software packages
In the course the computer package Mathematica and Matlab can be used as a tool for computations.