Z-LOG Logika. Logic

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1 MODULE DESCRIPTION Z-LOG-100 Module ode Module name Logika Module name in English Logi Valid from aademi year 2012/201 MODULE PLACEMENT IN THE SYLLABUS Subjet Level of eduation Studies profile Form and method of onduting lasses Speialisation Unit onduting the module Module o-ordinator Logistis 1st degree (1st degree / 2nd degree) General (general / pratial) Full-time (full-time / part-time) All The Department of Mathematis Sylwia Hożejowska, PhD Approved by: MODULE OVERVIEW Type of subjet/group of subjets Module status Language of onduting lasses Module plaement in the syllabus - semester Subjet realisation in the aademi year Initial requirements Examination Number of ECTS redit points Method of onduting lasses Basi (basi / major / speialist subjet / onjoint / other HES) Non-ompulsory (ompulsory / non-ompulsory) Polish rd semester Winter semester (winter / summer) No requirements (module odes / module names) No (yes / no) Per semester Leture Classes Laboratory Projet Other

2 TEACHING RESULTS AND THE METHODS OF ASSESSING TEACHING RESULTS Module target The objetive of the module is to familiarise students with the basis of the lassial propositional alulus, the elements of the funtional alulus, dedutive as well as indutive reasoning, the basis of modular arithmeti, and with the relations and set theories. Effet symbol Teahing results Teahing methods (l//l/p/other) Referene to subjet effets Referene to effets of a field of study A student has elementary knowledge from the field of the lassial propositional alulus and quantifiations, modular arithmeti, and the relations and set theories. A student is able to reate a sentene of a natural language. A student an verify dedutive rules and ondut orret dedution. A student an ondut logially orret reasoning. l/ K_W01 A student is able to hek the properties of relations among the objets and an understand the onsequenes of these properties. A student is apable of making simple modular arithmeti alulations. A student understands the need to improve the aquired skills and knowledge. A student an omprehend the elementary relationship between l/ K_K01 the workload and its effet. A student is familiar with the possibilities of improving the aquired knowledge and skills l/ K_K01 A student is aware of the responsibility for his/her own work and is ready to omply with the rules of team work and to bear the onsequenes of tasks ompleted olletively. K_K0 T1A_W01 T1A_W07 T1A_K01 S1A_K01 S1A_K06 T1A_K01 S1A_K01 S1A_K06 T1A_K0 T1A_K04 S1A_K02 Teahing ontents: Teahing ontents as regards letures Leture number Teahing ontents Irrationality and the risis of the Pythagorean vision of the world. The risis of mathematis in 19th entury. Logiism. Russel s antinomy. Logial onjuntions: onjuntion, alternation, negation, impliation, and equality. Logial value of formulas. The notion of tautology. The methods of formula examination: the zero-one method and the ontradition method. Rules of inferene. Examining inferene orretness. Mathematial indution. Universal and existential quantifiers, reating negations with quantifiers. Permutations and their evenness, omposing permutations. Referene to teahing results for a module

3 The elements of the set theory. The relations among sets. Operations on sets. The laws of set alulus. Analogies between the set alulus and the propositional alulus. Cartesian produt. Relations. The properties of relations. Equivalene, order, and linear order relations. The onept of abstrat lass. Congruenies. The basis of modular arithmeti. Fermat s little theorem. Euler s theorem. Proving Fermat s little theorem with the use of olours. The onept of the RSA enryption algorithm. Teahing ontents as regards lasses Class number Teahing ontents Referene to teahing results for a module 1 Logi riddles, examples of logial reasoning in geometry Building the shemata of sentenes of a natural language. The methods of formula examination: the zero-one method and the ontradition method. The rules of reasoning. Examining inferene orretness. The method of proof by indution. Universal and quantifiers, making sentene ontraditions with quantifiers. Permutations and their evenness, omposing permutations. Relations among sets. Set operations. The laws of set alulus. The properties of relations. Equivalene relations. Abstrat lasses of equivalene relations. Congruenies. The basis of modular arithmeti.

4 8 A test The methods of assessing teahing results Effet symbol Methods of assessing teahing results (assessment method, inluding skills referene to a partiular projet, laboratory assignments, et.) Observing a student s individual work during the lasses; a disussion during letures and lasses. Observing a student s individual work during the lasses; a disussion during letures and lasses. Observing a student s individual work during the lasses; a disussion during letures and lasses. STUDENT S INPUT ECTS redit points Type of student s ativity Student s workload 1 Partiipation in letures 15 2 Partiipation in lasses 15 Partiipation in laboratories 4 Partiipation in tutorials (2- times per semester) 10 5 Partiipation in projet lasses 6 Projet tutorials 7 Partiipation in an examination 8 40 (sum) 9 Number of hours requiring a leturer s assistane Number of ECTS redit points whih are alloated for assisted work Unassisted study of leture subjets Unassisted preparation for lasses 12 1 Unassisted preparation for tests 14 Unassisted preparation for laboratories 15 Preparing reports 16 Preparing for a final laboratory test 17 Preparing a projet or doumentation

5 18 Preparing for an examination 42 (sum) Number of hours of a student s unassisted work 40+42=82 21 Number of ECTS redit points whih a student reeives for unassisted work 22 Total number of hours of a student s work 2 ECTS redit points per module 1 ECTS point=25-0 hours 24 Work input onneted with pratial lasses Total number of hours onneted with pratial lasses 25 Number of ECTS redit points whih a student reeives for pratial lasses =52 1.9