icy0001 logic and discrete mathematicsicy0001 logic and discrete mathematics margarita spit²akova...
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ICY0001 Logic and Discrete Mathematics
Margarita Spit²akova
Department of Software Science
Tallinn University of Technology
2019/20 Fall semester
[email protected] Introduction 1 / 14
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Next section
1 About this courseGoals and learning outcomesTopics to be coveredLiterature
2 Arrangement
3 Finally ...
[email protected] Introduction 2 / 14
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Next subsection
1 About this courseGoals and learning outcomesTopics to be coveredLiterature
2 Arrangement
3 Finally ...
[email protected] Introduction 3 / 14
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Course objectives
The main objective of the to give you knowledge and skills that wouldenable to use the basic methods of discrete mathematics in subsequentcourses, in the design and analysis of algorithms, computability theory,software engineering, computer systems, and others.
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ioc.pdf
Next subsection
1 About this courseGoals and learning outcomesTopics to be coveredLiterature
2 Arrangement
3 Finally ...
[email protected] Introduction 5 / 14
ioc.pdf
Topics to be covered
Elementary set theory (basic de�nitions and set operations, the power set and Cartesianproducts);
Basic connectives in propositional logic and their properties with emphasis on some of themethods of proving mathematical results;
Quanti�ers in predicate logic and in in�nitely large domain sets;
Mathematical induction;
Binary relations and, in particular, the equivalence relation; partial order relations;
Basic counting techniques, combinations, permutations;
Binomial coe�cients, Pascal's triangle;
Graphs, vertices, edges, paths, cycles;
Eulerian and Hamiltonian graphs, travelling-salesman problem;
Basic de�nitions and properties of trees;
Planar graphs, graph colouring.
[email protected] Introduction 6 / 14
ioc.pdf
Topics to be covered
Elementary set theory (basic de�nitions and set operations, the power set and Cartesianproducts);
Basic connectives in propositional logic and their properties with emphasis on some of themethods of proving mathematical results;
Quanti�ers in predicate logic and in in�nitely large domain sets;
Mathematical induction;
Binary relations and, in particular, the equivalence relation; partial order relations;
Basic counting techniques, combinations, permutations;
Binomial coe�cients, Pascal's triangle;
Graphs, vertices, edges, paths, cycles;
Eulerian and Hamiltonian graphs, travelling-salesman problem;
Basic de�nitions and properties of trees;
Planar graphs, graph colouring.
[email protected] Introduction 6 / 14
ioc.pdf
Topics to be covered
Elementary set theory (basic de�nitions and set operations, the power set and Cartesianproducts);
Basic connectives in propositional logic and their properties with emphasis on some of themethods of proving mathematical results;
Quanti�ers in predicate logic and in in�nitely large domain sets;
Mathematical induction;
Binary relations and, in particular, the equivalence relation; partial order relations;
Basic counting techniques, combinations, permutations;
Binomial coe�cients, Pascal's triangle;
Graphs, vertices, edges, paths, cycles;
Eulerian and Hamiltonian graphs, travelling-salesman problem;
Basic de�nitions and properties of trees;
Planar graphs, graph colouring.
[email protected] Introduction 6 / 14
ioc.pdf
Topics to be covered
Elementary set theory (basic de�nitions and set operations, the power set and Cartesianproducts);
Basic connectives in propositional logic and their properties with emphasis on some of themethods of proving mathematical results;
Quanti�ers in predicate logic and in in�nitely large domain sets;
Mathematical induction;
Binary relations and, in particular, the equivalence relation; partial order relations;
Basic counting techniques, combinations, permutations;
Binomial coe�cients, Pascal's triangle;
Graphs, vertices, edges, paths, cycles;
Eulerian and Hamiltonian graphs, travelling-salesman problem;
Basic de�nitions and properties of trees;
Planar graphs, graph colouring.
[email protected] Introduction 6 / 14
ioc.pdf
Topics to be covered
Elementary set theory (basic de�nitions and set operations, the power set and Cartesianproducts);
Basic connectives in propositional logic and their properties with emphasis on some of themethods of proving mathematical results;
Quanti�ers in predicate logic and in in�nitely large domain sets;
Mathematical induction;
Binary relations and, in particular, the equivalence relation; partial order relations;
Basic counting techniques, combinations, permutations;
Binomial coe�cients, Pascal's triangle;
Graphs, vertices, edges, paths, cycles;
Eulerian and Hamiltonian graphs, travelling-salesman problem;
Basic de�nitions and properties of trees;
Planar graphs, graph colouring.
[email protected] Introduction 6 / 14
ioc.pdf
Topics to be covered
Elementary set theory (basic de�nitions and set operations, the power set and Cartesianproducts);
Basic connectives in propositional logic and their properties with emphasis on some of themethods of proving mathematical results;
Quanti�ers in predicate logic and in in�nitely large domain sets;
Mathematical induction;
Binary relations and, in particular, the equivalence relation; partial order relations;
Basic counting techniques, combinations, permutations;
Binomial coe�cients, Pascal's triangle;
Graphs, vertices, edges, paths, cycles;
Eulerian and Hamiltonian graphs, travelling-salesman problem;
Basic de�nitions and properties of trees;
Planar graphs, graph colouring.
[email protected] Introduction 6 / 14
ioc.pdf
Topics to be covered
Elementary set theory (basic de�nitions and set operations, the power set and Cartesianproducts);
Basic connectives in propositional logic and their properties with emphasis on some of themethods of proving mathematical results;
Quanti�ers in predicate logic and in in�nitely large domain sets;
Mathematical induction;
Binary relations and, in particular, the equivalence relation; partial order relations;
Basic counting techniques, combinations, permutations;
Binomial coe�cients, Pascal's triangle;
Graphs, vertices, edges, paths, cycles;
Eulerian and Hamiltonian graphs, travelling-salesman problem;
Basic de�nitions and properties of trees;
Planar graphs, graph colouring.
[email protected] Introduction 6 / 14
ioc.pdf
Topics to be covered
Elementary set theory (basic de�nitions and set operations, the power set and Cartesianproducts);
Basic connectives in propositional logic and their properties with emphasis on some of themethods of proving mathematical results;
Quanti�ers in predicate logic and in in�nitely large domain sets;
Mathematical induction;
Binary relations and, in particular, the equivalence relation; partial order relations;
Basic counting techniques, combinations, permutations;
Binomial coe�cients, Pascal's triangle;
Graphs, vertices, edges, paths, cycles;
Eulerian and Hamiltonian graphs, travelling-salesman problem;
Basic de�nitions and properties of trees;
Planar graphs, graph colouring.
[email protected] Introduction 6 / 14
ioc.pdf
Topics to be covered
Elementary set theory (basic de�nitions and set operations, the power set and Cartesianproducts);
Basic connectives in propositional logic and their properties with emphasis on some of themethods of proving mathematical results;
Quanti�ers in predicate logic and in in�nitely large domain sets;
Mathematical induction;
Binary relations and, in particular, the equivalence relation; partial order relations;
Basic counting techniques, combinations, permutations;
Binomial coe�cients, Pascal's triangle;
Graphs, vertices, edges, paths, cycles;
Eulerian and Hamiltonian graphs, travelling-salesman problem;
Basic de�nitions and properties of trees;
Planar graphs, graph colouring.
[email protected] Introduction 6 / 14
ioc.pdf
Topics to be covered
Elementary set theory (basic de�nitions and set operations, the power set and Cartesianproducts);
Basic connectives in propositional logic and their properties with emphasis on some of themethods of proving mathematical results;
Quanti�ers in predicate logic and in in�nitely large domain sets;
Mathematical induction;
Binary relations and, in particular, the equivalence relation; partial order relations;
Basic counting techniques, combinations, permutations;
Binomial coe�cients, Pascal's triangle;
Graphs, vertices, edges, paths, cycles;
Eulerian and Hamiltonian graphs, travelling-salesman problem;
Basic de�nitions and properties of trees;
Planar graphs, graph colouring.
[email protected] Introduction 6 / 14
ioc.pdf
Topics to be covered
Elementary set theory (basic de�nitions and set operations, the power set and Cartesianproducts);
Basic connectives in propositional logic and their properties with emphasis on some of themethods of proving mathematical results;
Quanti�ers in predicate logic and in in�nitely large domain sets;
Mathematical induction;
Binary relations and, in particular, the equivalence relation; partial order relations;
Basic counting techniques, combinations, permutations;
Binomial coe�cients, Pascal's triangle;
Graphs, vertices, edges, paths, cycles;
Eulerian and Hamiltonian graphs, travelling-salesman problem;
Basic de�nitions and properties of trees;
Planar graphs, graph colouring.
[email protected] Introduction 6 / 14
ioc.pdf
Next subsection
1 About this courseGoals and learning outcomesTopics to be coveredLiterature
2 Arrangement
3 Finally ...
[email protected] Introduction 7 / 14
ioc.pdf
Study material
Primary material:
S.Lipschutz and M.Lipson.Schaum's Outline of Discrete Mathematics, McGraw Hill 2007, Revised 3rd editionISBN-13: 978-0071615860, ISBN-10: 0071615865.
K. H. Rosen.Discrete Mathematics and Its Applications, WCB/McGraw Hill, 7th editionISBN-10: 0073383090, ISBN-13: 978-0073383095.
[email protected] Introduction 8 / 14
ioc.pdf
Study material
Primary material:
S.Lipschutz and M.Lipson.Schaum's Outline of Discrete Mathematics, McGraw Hill 2007, Revised 3rd editionISBN-13: 978-0071615860, ISBN-10: 0071615865.
K. H. Rosen.Discrete Mathematics and Its Applications, WCB/McGraw Hill, 7th editionISBN-10: 0073383090, ISBN-13: 978-0073383095.
Additional material:
L. Lovász, J. Pelikan, and K. Vesztergombi.Discrete Mathematics: Elementary and Beyond, Springer, 2003.CALL no in TTU Library: 519/L-94
Web page of the coursehttp://www.cs.ioc.ee/ITKDM/
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Next section
1 About this courseGoals and learning outcomesTopics to be coveredLiterature
2 Arrangement
3 Finally ...
[email protected] Introduction 9 / 14
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Timetable
The class consists of
one weekly (standard) lecture, Thursdays 10:00�11:30
one recitation session (o�cially called �practicum�, Thursdays11:45�13:15) in which students solve problems related to the lectures.
Recitation classes include:
Discussions of the solutions of homework problems (weeklyapproximately 3 problems related to the lectures will be announced tosolve; students will be asked to present his/her individual solutions atblack/whiteboard and discussed with participation of the audience.)
Quizzes on the topics of prior to that week.
There will be midterm test on 24.10.19 (with one make-up test, if needed)and a �nal test by the end of the semester 28.11.19.
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GradingThe 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 ofquizzes, tests and exam (maximum sum of points is 100) and the �nal grade will be as follows:
�0� - less than 51 points
�1� - 51�60 points
�2� - 61�70 points
�3� - 71�80 points
�4� - 81�90 points
�5� - 91 and more points
[email protected] Introduction 11 / 14
ioc.pdf
GradingThe 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 ofquizzes, tests and exam (maximum sum of points is 100) and the �nal grade will be as follows:
�0� - less than 51 points
�1� - 51�60 points
�2� - 61�70 points
�3� - 71�80 points
�4� - 81�90 points
�5� - 91 and more points
[email protected] Introduction 11 / 14
ioc.pdf
GradingThe 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 ofquizzes, tests and exam (maximum sum of points is 100) and the �nal grade will be as follows:
�0� - less than 51 points
�1� - 51�60 points
�2� - 61�70 points
�3� - 71�80 points
�4� - 81�90 points
�5� - 91 and more points
[email protected] Introduction 11 / 14
ioc.pdf
Next section
1 About this courseGoals and learning outcomesTopics to be coveredLiterature
2 Arrangement
3 Finally ...
[email protected] Introduction 12 / 14
ioc.pdf
Changes
When appropriate, the rules may be changed during the semester.
Such changes will be announced in advance in the lectures and on thecourse web site.
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Contact
Instructor: Margarita Spit²akova
e-mail: [email protected]
Course web site:
http://www.cs.ioc.ee/ITKDM/
Slack:
http://itkdm.slack.com/
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