Responsible Instructor 

Contact Hours / Week x/x/x/x 
4/0/0/0 hc; 2/0/0/0 wc

Education Period 

Start Education 

Exam Period 

Course Language 

Required for 
Every course in which exact reasoning is required e.g. to prove a theorem or reasoning from the assumption that a theorem is true. Examples: * Logicbased AI * Probability and Statistics * Calculus * Linear Algebra * Algorithm Design * Automata, Languages and Computability * Complexity Theory

Course Contents 
It is often useful or even essential to know if a certain statement is true, e.g. Pythagoras' famous a^2 + b^2 = c^2 theorem about rightangled triangles. Knowledge gathered from these statements or theorems can be broadly used to solve more complicated problems. This way of working, i.e. deriving more complex theorems from simpler ones, is useful in many fields, in particular also in computer science. An argument or reasoning is a set of premisses or assumptions, followed by a conclusion. To be certain of the truth of an argument, the conclusion has to be a logical consequence of the assumptions. To prove this, the conclusion is being derived from the premisses. The derivation shows us that once all premisses are true, the conclusion is true as well. The course Reasoning and Logic is about proving the logical validity of arguments. What is a valid argument? When is an argument logically valid and when is it not? How can we determine whether an argument is logically valid? How can we derive a logically valid conclusion from the premisses? Or how can we prove that a conclusion is not a logical consequence of the premisses? In this course we will first explain a number of basic proof techniques, such as proof by contradiction, proof by mathematical induction, proof by division into cases, and the use of invariants. The application of these techniques will be practiced by proving and rejecting simple mathematical theorems. These proof techniques can only lead to a valid argument when the formulation of the premisses and the conclusion is sufficiently exact. To do this, multiple artificial languages exist of which we will learn two: propositional calculus and predicate logic. For both languages we look at the syntax and semantics and study how to translate expressions from a natural language to the more exact languages. Furthermore we will look at how to establish the logical validity of a reasoning in both languages. Moreover, to be able to assign truth values to formulas in predicate logic and because of the importance of this subject in every exact science, in this course we will also pay attention to elementary set theory.

Study Goals 
The student: * Has knowledge of the elementary concepts in set theory, propositional and predicate logic. * Can identify the logical structure of mathematically exact propositions. * Has knowledge of the basic concepts of theoretical computer science such as graphs, algorithms and relational databases. * Is able to deliver proofs for simple theorems using proofs by contradiction, proofs by (mathematical) induction and proofs by division into cases. * Can determine the logical validity of a simple argument by using a truth table. * Knows the elementary notations and operations of set theory. * Can prove simple theorems of set theory.

Education Method 
Every week has two lectures, during which questions about the material will be answered. There will also be small interactive exercises to help the students to evaluate their understanding of the material.
During the course 6 homework assignments have to be made in pairs. The first 5 assignments have to be approved by a teaching assistant who will test the students' knowledge on the material. Every week there will be a practical session where questions can be asked and students can sign up to let their assignments being evaluated.

Literature and Study Materials 
Discrete Mathematics with Applications, Fourth edition, International edition, Susanna S. Epp, Cencage Learning, 2011. The material covered by the course consists of most parts in Chapters 1 up to and including 8. Furthermore, additional material will be posted online throughout the course.

Assessment 
To pass the course, two passing criteria have to be met. Firstly, the averaged grade of both exams (the midterm and the endterm) has to be at least a 6. Seccondly, all homework assignments have to be approved in time. If one of these two conditions has not been met during the academic year, the two exams as well as all homework have to be completely redone during the next year or later.
More information about the logistics regarding the homework assignments is to be provided in the student manual which will be made available on the course web page at the beginning of the course.

Permitted Materials during Tests 
None

Judgement 
The course consists of two exams; the midterm (week 1.5) and the endterm (week 1.9). Both exams cover all prior material and consist of open and multiple choice questions.
During the second quarter a separate resit can be done for both exams. The final grade will be the average of the highest grades for both the midterm and the endterm. There is no minimal grade for the separated exams, the averaged will be rounded and has to be at least a 6.
Missing one of the homework assignments will provide you with an inadequate grade for the homework assignments and requires you to retake the entire course. You will get a bonus for each homework assignment that you hand in the first possible week (and so not later than that). The entire bonus adds up to at most 1 point to the final grade of the course.
More information about the logistics regarding the homework assignments is to be provided in the student manual which will be made available on the course web page at the beginning of the course.

Coinstructor 
