6 ECTS credits
180 h study time
Offer 1 with catalog number 1010218BNR for all students in the 1st semester at a (B) Bachelor - advanced level.
Construction of the real numbers. Elementary notions and properties concerning metric spaces. Compactness and connectedness for metric spaces and particular results for the real line and the complex plane.
Pointwise and uniform convergence of sequences of functions. Spaces of functions endowed with supnorm. Study of completeness and applications to fix-point theorems.
Theorem of Dini. Derivation and integration of limitfunctions.
Series, convergence and absolute convergence, series with positive terms, series of real and complex numbers.
Series of functions, Taylorseries, powerseries.
Analytical functions. Analytic extension.
Syllabus is available
-The student has basic knowledge of the construction of the real numbers and of basic concepts and properties of metric spaces
- The student has basic knowledge of metric concepts applied to the context of spaces of bounded functions with uniform convergence and recognizes the essential differences with pointwise convergence.
- The student knows the role of compactness in the study of functions.
- The student is able to work with series of numbers, and more generally series of functions and series in normed spaces.
- The student has good understanding of the theory of complex power series and their role with respect to analytic functions.
- The student masters the standard techniques and has the skills to bring calculations to a good end.
- The student has an overall insight in the material, has a deep understanding of new concepts and results and is aware of the connection between de various concepts.
- The student is able to make the link between concepts on one hand and illustrating examples on the other hand.
- The student has insight in the relation to analogous concepts as they were introduced in previous courses.
- The student can analyse proofs and understands the logical reasoning behind them. For a given proposition the student is aware of the role the conditions play in the proof.
- The student can complete easy proofs that are left as an exercise or that are only partially explained in the syllabus or in class. The missing arguments can be filled in independently.
- The student masters the mathematical language and is able to produce correct mathematical formulations and proofs.
- The student can independently solve problems: he/she is able to recognize a problem, to choose an appropriate strategy, to select the most suitable method
The final grade is composed based on the following categories:
Oral Exam determines 60% of the final mark.
Written Exam determines 40% of the final mark.
Within the Oral Exam category, the following assignments need to be completed:
Within the Written Exam category, the following assignments need to be completed:
Written exam: solving problems 40%
Oral exam: theoretical evaluation 60%
Part of the marks for the written exam is based upon points gained for tasks during the semester.
This offer is part of the following study plans:
Bachelor of Physics and Astronomy: Default track (only offered in Dutch)
Bachelor of Mathematics and Data Science: Standaard traject (only offered in Dutch)