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Syllabus for

Academic year
TMV200 - Discrete mathematics
Diskret matematik
 
Syllabus adopted 2021-02-26 by Head of Programme (or corresponding)
Owner: TKITE
7,5 Credits
Grading: TH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Education cycle: First-cycle
Main field of study: Mathematics
Department: 11 - MATHEMATICAL SCIENCES


Teaching language: Swedish
Application code: 52137
Open for exchange students: No
Maximum participants: 150
Only students with the course round in the programme plan

Module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0104 Examination 7,5 c Grading: TH   7,5 c   14 Jan 2022 pm J,  12 Apr 2022 pm J,  26 Aug 2022 pm J

In programs

TKELT ELECTRICAL ENGINEERING, Year 3 (compulsory elective)
TKITE SOFTWARE ENGINEERING, Year 1 (compulsory)

Examiner:

Christian Johansson

  Go to Course Homepage


Eligibility

General entry requirements for bachelor's level (first cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Specific entry requirements

The same as for the programme that owns the course.
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Aim

This course is the first mathematics course and is a transition between gymnasium and university mathematics. The material is essential and central to computer science and information technology. The overall aim is to put mathematics in the right perspective and as an integrated part in the students' curriculum.

Learning outcomes (after completion of the course the student should be able to)


  • communicate mathematics, orally and in writing,
  • describe the structure of mathematics with axioms, definitions and theorems,
  • construct simple proofs and do mathematical reasoning,
  • formulate arguments in terms of the language of logic,
  • formulate mathematical relationships in terms of functions, relations and graphs,
  • use induction in proofs and to describe sets,
  • explain the elementary multiplicative structure of integers,
  • solve linear Diophantine equations and perform computations with congruences,
  • explain RSA cryptography, code and decode messages using this technique,
  • solve simple combinatorial problems,
  • use graphs to formulate and solve mathematical problems.

Content

The course consists of three main themes. Within each theme some relevant mathematical concepts will be studied. One and the same concept, such as proof for instance, may be dealt with in several different themes. The themes that are studied in the course are:Logic, functions and relations, and proof
  • Elementary number theory and the RSA algorithm
  • Combinatorics and graphs
Some basic concepts such as sets and functions appear in the introduction course which precedes this one, but play an important role when they are studied in more depth in this course.

Organisation

The teaching is built around themes. Each theme includes a Theme lecture by an invited speaker on a concrete application where mathematics is essential. Involved mathematics is presented briefly and then studied more deeply within the rest of the course activities comprising:
  • Scheduled tutorials in groups aimed to reflect on the mathematical theory.
  • Lectures highlighting and explaining the mathematical theory.
  • Classes where problems connected with the theory are solved individually and in groups.
  • Student presentations of selected problems.

Literature

Johan Jonasson and Stefan Lemurell: Algebra och diskret matematik, 2nd edition Studentlitteratur, Lund, 2013.

Examination including compulsory elements

Written exam. During the course students can gain bonus points by presenting solutions of the weekly exercises.



The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers on educational support due to disability.


Page manager Published: Thu 03 Nov 2022.