To be determined from performance in examinations and tutorials. Exact modalities will be announced at the beginning of the module.
4 h lectures
+ 2 h tutorial
= 6 h (weekly)
90 h of classes
+ 180 h private study
= 270 h (= 9 ECTS)
The numbers in parentheses indicate the total number of 2 hour lectures.
DISCRETE MATHEMATICS AND ONE-DIMENSIONAL ANALYSIS
A. Fundamentals of discrete mathematics (8)
1. sets (1)
2. logic (1)
3. methods of mathematical proof, including induction (1)
4. relations (1)
5. maps (2)
- injective, surjective, bijective
- cardinality, countability
- pigeon-hole principle
6. prime numbers and divisors (1)
7. modular arithmetic (1)
B. One-dimensional analysis (22)
B.1 Numbers, sequences and series (8)
8. Axiomatics of real numbers, supremum, infimum (1)
9. complex numbers (1)
10. sequences (1 1/2)
11. big O notation (1/2)
12. series: convergence tests, absolute convergence (2)
13. power series (1/2)
14. representations of numbers (1/2)
15. binomial coefficients and binomial series (1)
B.2 One-dimensional differential calculus (8)
16. continuity (1)
17. elementary functions (1)
18. differentiability (1 1/2)
19. mean-value theorems and L'Hopital's rule (1/2)
20. Taylor's theorem (1)
21. local extrema, convexity, curve sketching (2)
22. numerical differentiation (1)
B.3 One-dimensional integral calculus (6)
23. definite integrals (2)
24. indefinite integrals and the antiderivative (1)
25. improper integrals (1)
26. numerical methods for integration (1)
27. curves and arc length (1)
To be announced before the start of the module on the relevant internet page.
This module is identical in content to the German-language module Mathematik für Informatiker 1.
This module is part of the following study programmes: