t.BA.ITM.DM.19HS (Discrete Mathematics)
Module: Discrete Mathematics
This information was generated on: 21 June 2024
No.
t.BA.ITM.DM.19HS
Title
Discrete Mathematics
Organised by
T IAMP
Credits
4

### Description

Version: 3.0 start 01 February 2020
•

#### Short description

Introduction to discrete mathematics and foundations of mathematics for computer science.

#### Module coordinator

Full Name (ZHAW username)

#### Learning objectives (competencies)

 Objective competence Taxonomy level Students understand the basic terminology of mathematics. Students meet the field’s standards in preciseness and rigor in expressing mathematical statements. F,M K2, K3 Students are able to prove simple mathematical statements and evaluate proofs for their level of correctness and rigor. M K3, K4 Students understand the difference between syntax and semantics of a formal system. They know the syntax and semantics of propositional logic. F K1, K2 Students are able to formalize colloquial mathematical statements in terms of first order logic. Students understand statements denoted in first order logic F,M K3, K4 Students understand the basics of set theory (union, intersection, relative complements and power set). Students know the sets ℕ, ℤ, ℚ and ℝ. F,M K1, K2, K3 Students know how sets are compared in terms of cardinalities and they know the notion of (un-) countability. Students are able to prove that the sets ℤ and ℚ are countable and that ℝ is uncountable. F K2, K3, K4 Students know the notions of equivalence- and ordering relations and their basic properties and notations. F K1, K2 Students are able to apply the principle of mathematical induction and they understand the relationship between induction and recursion. F,M K2, K3 Students apply the Euclidean algorithm to compute gcd and lcm as well as to solve systems of linear congruencies. F,M K2, K3 Students are familiar with the basics of modular arithmetic. Students know the Chinese remainder Theorem. F,M K2, K3 Students are familiar with prime numbers and factorization. F,M K2,K3

#### Module contents

Logic:
• Propositions, predicates and quantifiers
• Syntax and semantics of propositional logic
Set theory:
• The notion of sets, set-unions, set-intersections, powersets and set-products.
• The basic sets ℕ, ℤ, ℚ and ℝ.
• Cardinalities: countable and uncountable sets
• First- and second diagonal argument
Relations:
• Equivalence relations, equivalence classes and partitions
• Quotient sets and classes of representatives
• Ordering relations
• Graphs, topological ordering
Natural numbers:
• Peano arithmetic, induction and recursion
• Algebraic properties of the natural numbers
• Order theoretic properties of the natural numbers and well-orderings.
Basic number theory
• Divisibility and Euclidean division
• gcd, lcm and Euclidean algorithm and Bézout's lemma
• Prime numbers and integer factorization
• Chinese remainder Theorem and modular arithmetic
• Solving Systems of linear congruencies.
• Fermat’s little theorem

Script, Slides

#### Supplementary literature

• title = "Diskrete Strukturen -- kurz gefasst"
series = "Spektrum--Hochschultaschenbuch"
author = "Ulrich Knauer"
year = "2011"
publisher = "Spektrum Akademischer Verlag"

• title = "Mathematik für Informatiker -- ein praxisbezogenes Lehrbuch"
series = "Mathematik/Informatik"
author = "Peter Hartmann"
year = "2004"
publisher = "Vieweg"
edition = "3"

• title = "Diskrete Mathematik für Informatiker"
author = "Rod Haggarty"
year = "2007"
publisher = "Pearson Studium"

• title = "Lineare Algebra für Informatiker"
author = "Bodo Pareigis"
year = "2000"
publisher = "Springer"

• title = "Grundbegriffe der Mathematik​"
author = "Martin Huber, Claudia Albertini"
year = "2015"
publisher = "EAGLE-STARTHILFE"

none

#### Teaching language

(X) German ( ) English

( ) Yes (X) No

#### Module structure

Type 2b
For more details please click on this link: T_CL_Modulauspraegungen_SM2025

#### Exams

 Description Type Form Scope Grade Weighting Graded assignments during the teaching semester regular tests written Each test max. 45 minutes Grade 20%, only if the tests positively affect the final grade. End-of-semester exam Exam written 90 Min. Grade min. 80%

#### Remarks

In the first week of the semester, the exact number and duration of tests will be communicated for all instances of the module.

#### Legal basis

The module description is part of the legal basis in addition to the general academic regulations. It is binding. During the first week of the semester, a written and communicated supplement can specify the module description in more detail.

### Note

Course: Diskrete Mathematik - Vorlesung
No.
t.BA.ITM.DM.19HS.V
Title
Diskrete Mathematik - Vorlesung

### Note

• No module description is available in the system for the cut-off date of 01 August 2099.