Discrete Mathematics

Semester 1 · 76239 · Bachelor in Computer Science · 6CP · EN

The aim of this course is to introduce students to basic topics in discrete mathematics. An overview of proof methods and their relation to logic will be given. The induction principle is introduced in a number of variants, and methods to analyse and describe the main properties of relations, functions, graphs and trees will be studied. We will also introduce the basic principles governing the mathematical definitions of infinite sets and of countability.

Lecturers: Oliver Kutz

Teaching Hours: 40
Lab Hours: 20
Mandatory Attendance: Attendance is not compulsory but recommended. Non-attending students have to contact the lecturer at the start of the course to agree on the modalities of the independent study.

Course Topics
- Elements of logic, propositions and quantifiers, methods of mathematical proof, method of mathematical induction - Numbers and basic number theory - Set Theory, Russell Paradox and Halting Problem - Functions, infinite cardinalities and countability - Relations, orders, equivalence classes - Graphs and trees

Teaching format
The course includes frontal lectures and lab exercises.

Educational objectives
Knowledge and Understanding - D1.1: Have a solid knowledge of mathematical analysis, algebra, numerical calculus, discrete mathematics and elementary notion of logic that are in support of computer science Applying knowledge and understanding - D2.1: Be able to use the tools of mathematics and logic to solve problems. Ability to make judgments - D3.2: Be able to work autonomously according to the own level of knowledge and understanding. Communication skills - D4.1: Be able to use one of the three languages English, Italian and German, and be able to use technical terms and communication appropriately. Learning skills - D5.1: Have developed learning capabilities to pursue further studies with a high degree of autonomy.

Assessment
The written exam includes verification questions, knowledge transfer tasks, and exercises.

Evaluation criteria
Final written exam counting 100% for the evaluation and covering the full program of the course. Written exam questions will be evaluated in terms of correctness, clarity, quality of argumentation, and problem solving ability.

Required readings

Susanna Samuels Epp. Discrete Mathematics with Applications. Cengage Learning, 5th edition, 01 2019. ISBN 978-1337694193. URL: https://www.cengage.com/c/discrete-mathematics-with-applications-5e-epp/9781337694193.

Supplementary readings

K.H. Rosen and K. Krithivasan. Discrete Mathematics and Its Applications: With Combinatorics and Graph Theory. McGraw-Hill Companies, 2012. ISBN 9780070681880.

Further information
If the use of specific software is required, it will be communicated during class by the lecturer.

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Sustainable Development Goals
This teaching activity contributes to the achievement of the following Sustainable Development Goals.