Logic and Discrete Mathematics

Transcription

1 ICY0001 Logic and Discrete Mathematics Margarita Spit²akova Department of Software Science Tallinn University of Technology 2018/19 Fall semester Introduction 1 / 14

2 Next section 1 About this course Goals and learning outcomes Literature 2 Arrangement 3 Finally... margarita.spitsakova@ttu.ee Introduction 2 / 14

3 Next subsection 1 About this course Goals and learning outcomes Literature 2 Arrangement 3 Finally... margarita.spitsakova@ttu.ee Introduction 3 / 14

4 Course objectives The main objective of the to give you knowledge and skills that would enable to use the basic methods of discrete mathematics in subsequent courses, in the design and analysis of algorithms, computability theory, software engineering, computer systems, and others. Introduction 4 / 14

5 Next subsection 1 About this course Goals and learning outcomes Literature 2 Arrangement 3 Finally... margarita.spitsakova@ttu.ee Introduction 5 / 14

6 Elementary set theory (basic denitions and set operations, the power set and Cartesian products); Basic connectives in propositional logic and their properties with emphasis on some of the methods of proving mathematical results; Quantiers in predicate logic and in innitely large domain sets; Mathematical induction; Binary relations and, in particular, the equivalence relation; partial order relations; Basic counting techniques, combinations, permutations; Binomial coecients, Pascal's triangle; Graphs, vertices, edges, paths, cycles; Eulerian and Hamiltonian graphs, travelling-salesman problem; Basic denitions and properties of trees; Planar graphs, graph colouring. Introduction 6 / 14

7 Elementary set theory (basic denitions and set operations, the power set and Cartesian products); Basic connectives in propositional logic and their properties with emphasis on some of the methods of proving mathematical results; Quantiers in predicate logic and in innitely large domain sets; Mathematical induction; Binary relations and, in particular, the equivalence relation; partial order relations; Basic counting techniques, combinations, permutations; Binomial coecients, Pascal's triangle; Graphs, vertices, edges, paths, cycles; Eulerian and Hamiltonian graphs, travelling-salesman problem; Basic denitions and properties of trees; Planar graphs, graph colouring. Introduction 6 / 14

8 Elementary set theory (basic denitions and set operations, the power set and Cartesian products); Basic connectives in propositional logic and their properties with emphasis on some of the methods of proving mathematical results; Quantiers in predicate logic and in innitely large domain sets; Mathematical induction; Binary relations and, in particular, the equivalence relation; partial order relations; Basic counting techniques, combinations, permutations; Binomial coecients, Pascal's triangle; Graphs, vertices, edges, paths, cycles; Eulerian and Hamiltonian graphs, travelling-salesman problem; Basic denitions and properties of trees; Planar graphs, graph colouring. Introduction 6 / 14

9 Elementary set theory (basic denitions and set operations, the power set and Cartesian products); Basic connectives in propositional logic and their properties with emphasis on some of the methods of proving mathematical results; Quantiers in predicate logic and in innitely large domain sets; Mathematical induction; Binary relations and, in particular, the equivalence relation; partial order relations; Basic counting techniques, combinations, permutations; Binomial coecients, Pascal's triangle; Graphs, vertices, edges, paths, cycles; Eulerian and Hamiltonian graphs, travelling-salesman problem; Basic denitions and properties of trees; Planar graphs, graph colouring. Introduction 6 / 14

10 Elementary set theory (basic denitions and set operations, the power set and Cartesian products); Basic connectives in propositional logic and their properties with emphasis on some of the methods of proving mathematical results; Quantiers in predicate logic and in innitely large domain sets; Mathematical induction; Binary relations and, in particular, the equivalence relation; partial order relations; Basic counting techniques, combinations, permutations; Binomial coecients, Pascal's triangle; Graphs, vertices, edges, paths, cycles; Eulerian and Hamiltonian graphs, travelling-salesman problem; Basic denitions and properties of trees; Planar graphs, graph colouring. Introduction 6 / 14

11 Elementary set theory (basic denitions and set operations, the power set and Cartesian products); Basic connectives in propositional logic and their properties with emphasis on some of the methods of proving mathematical results; Quantiers in predicate logic and in innitely large domain sets; Mathematical induction; Binary relations and, in particular, the equivalence relation; partial order relations; Basic counting techniques, combinations, permutations; Binomial coecients, Pascal's triangle; Graphs, vertices, edges, paths, cycles; Eulerian and Hamiltonian graphs, travelling-salesman problem; Basic denitions and properties of trees; Planar graphs, graph colouring. Introduction 6 / 14

12 Elementary set theory (basic denitions and set operations, the power set and Cartesian products); Basic connectives in propositional logic and their properties with emphasis on some of the methods of proving mathematical results; Quantiers in predicate logic and in innitely large domain sets; Mathematical induction; Binary relations and, in particular, the equivalence relation; partial order relations; Basic counting techniques, combinations, permutations; Binomial coecients, Pascal's triangle; Graphs, vertices, edges, paths, cycles; Eulerian and Hamiltonian graphs, travelling-salesman problem; Basic denitions and properties of trees; Planar graphs, graph colouring. Introduction 6 / 14

13 Elementary set theory (basic denitions and set operations, the power set and Cartesian products); Basic connectives in propositional logic and their properties with emphasis on some of the methods of proving mathematical results; Quantiers in predicate logic and in innitely large domain sets; Mathematical induction; Binary relations and, in particular, the equivalence relation; partial order relations; Basic counting techniques, combinations, permutations; Binomial coecients, Pascal's triangle; Graphs, vertices, edges, paths, cycles; Eulerian and Hamiltonian graphs, travelling-salesman problem; Basic denitions and properties of trees; Planar graphs, graph colouring. Introduction 6 / 14

14 Elementary set theory (basic denitions and set operations, the power set and Cartesian products); Basic connectives in propositional logic and their properties with emphasis on some of the methods of proving mathematical results; Quantiers in predicate logic and in innitely large domain sets; Mathematical induction; Binary relations and, in particular, the equivalence relation; partial order relations; Basic counting techniques, combinations, permutations; Binomial coecients, Pascal's triangle; Graphs, vertices, edges, paths, cycles; Eulerian and Hamiltonian graphs, travelling-salesman problem; Basic denitions and properties of trees; Planar graphs, graph colouring. Introduction 6 / 14

15 Elementary set theory (basic denitions and set operations, the power set and Cartesian products); Basic connectives in propositional logic and their properties with emphasis on some of the methods of proving mathematical results; Quantiers in predicate logic and in innitely large domain sets; Mathematical induction; Binary relations and, in particular, the equivalence relation; partial order relations; Basic counting techniques, combinations, permutations; Binomial coecients, Pascal's triangle; Graphs, vertices, edges, paths, cycles; Eulerian and Hamiltonian graphs, travelling-salesman problem; Basic denitions and properties of trees; Planar graphs, graph colouring. Introduction 6 / 14

16 Elementary set theory (basic denitions and set operations, the power set and Cartesian products); Basic connectives in propositional logic and their properties with emphasis on some of the methods of proving mathematical results; Quantiers in predicate logic and in innitely large domain sets; Mathematical induction; Binary relations and, in particular, the equivalence relation; partial order relations; Basic counting techniques, combinations, permutations; Binomial coecients, Pascal's triangle; Graphs, vertices, edges, paths, cycles; Eulerian and Hamiltonian graphs, travelling-salesman problem; Basic denitions and properties of trees; Planar graphs, graph colouring. Introduction 6 / 14

17 Next subsection 1 About this course Goals and learning outcomes Literature 2 Arrangement 3 Finally... margarita.spitsakova@ttu.ee Introduction 7 / 14

18 Study material Primary material: S.Lipschutz and M.Lipson. Schaum's Outline of Discrete Mathematics, McGraw Hill 2007, Revised 3rd edition ISBN-13: , ISBN-10: K. H. Rosen. Discrete Mathematics and Its Applications, WCB/McGraw Hill, 7th edition ISBN-10: , ISBN-13: Introduction 8 / 14

19 Study material Primary material: S.Lipschutz and M.Lipson. Schaum's Outline of Discrete Mathematics, McGraw Hill 2007, Revised 3rd edition ISBN-13: , ISBN-10: K. H. Rosen. Discrete Mathematics and Its Applications, WCB/McGraw Hill, 7th edition ISBN-10: , ISBN-13: Additional material: L. Lovász, J. Pelikan, and K. Vesztergombi. Discrete Mathematics: Elementary and Beyond, Springer, CALL no in TTU Library: 519/L-94 Web page of the course Introduction 8 / 14

20 Next section 1 About this course Goals and learning outcomes Literature 2 Arrangement 3 Finally... margarita.spitsakova@ttu.ee Introduction 9 / 14

21 Timetable The class consists of one weekly (standard) lecture, Tuesdays 10:1511:45 one recitation session (ocially called praktikum, Tuesdays 12:0013:30) in which students solve problems related to the lectures. Recitation classes include: Discussions of the solutions of homework problems (weekly approximately 3 problems related to the lectures will be announced to solve; students will be asked to present his/her individual solutions at black/whiteboard and discussed with participation of the audience.) Quizzes on the topics of prior to that week. There will be midterm test on (with one make-up test, if needed) and a nal test by the end of the semester margarita.spitsakova@ttu.ee Introduction 10 / 14

22 Grading The grading allocation is designed as follows: Homeworks are not graded, but solving homework problems helps passing quizzes, tests and exam; Quizzes 20% Midterm + nal test 40% Final exam (oral) 40% All quizzes and nal test are closed-book, no notes and no electronic equipment allowed. The nal ranking for the course will turn out by summarising the student's individual results of quizzes, tests and exam (maximum sum of points is 100) and the nal grade will be as follows: less than 51 points points points points points - 91 and more points margarita.spitsakova@ttu.ee Introduction 11 / 14

23 Grading The grading allocation is designed as follows: Homeworks are not graded, but solving homework problems helps passing quizzes, tests and exam; Quizzes 20% Midterm + nal test 40% Final exam (oral) 40% All quizzes and nal test are closed-book, no notes and no electronic equipment allowed. The nal ranking for the course will turn out by summarising the student's individual results of quizzes, tests and exam (maximum sum of points is 100) and the nal grade will be as follows: less than 51 points points points points points - 91 and more points margarita.spitsakova@ttu.ee Introduction 11 / 14

24 Grading The grading allocation is designed as follows: Homeworks are not graded, but solving homework problems helps passing quizzes, tests and exam; Quizzes 20% Midterm + nal test 40% Final exam (oral) 40% All quizzes and nal test are closed-book, no notes and no electronic equipment allowed. The nal ranking for the course will turn out by summarising the student's individual results of quizzes, tests and exam (maximum sum of points is 100) and the nal grade will be as follows: less than 51 points points points points points - 91 and more points margarita.spitsakova@ttu.ee Introduction 11 / 14

25 Next section 1 About this course Goals and learning outcomes Literature 2 Arrangement 3 Finally... margarita.spitsakova@ttu.ee Introduction 12 / 14

26 Changes When appropriate, the rules may be changed during the semester. Such changes will be announced in advance in the lectures and on the course web site. Introduction 13 / 14

27 Contact Instructor: Margarita Spit²akova Course web site: Slack: Introduction 14 / 14