Logic and Discrete Mathematics (Spring 2016)

This page describes the content and structure of the course. Day-to-day information can be found at the Moodle page of the course (requires login). See the course description at kursus.ruc.dk for a brief and formal description of the course. In the following, the main subjects of the course are described; a detailed description of the structure of the course can be found further down the page.

·        Logic The first subject of the course is logic, that is, propositional- and predicate logic as well as rules of inference and logic in mathematical proofs. This part of the course comprises the first five course days and covers the first chapter of the textbook.

·        Sets and functions Two course days cover sections 2.1 - 2.3 in the book, which concern sets, set operations (union, intersection, powerset, Cartesian product, ...) and functions between sets (injections, surjections, inverse functions, ...). This is mainly high school material, formulated more rigeously.

·        Algorithms and complexity Three course days covers sections 3.1 - 3.3 as well as Appendix A-3, which concern algorithms, pseudocode, and the computational complexity of algorithms.

·        Induction and recursion Two course days cover sections 4.1 - 4.4 in the book, which concern mathematical induction, structural induction, recursive definitions, and recursive algorithms. The principle of mathematical induction can be used to prove a tremendous variety of results. Understanding how to read and construct proofs by mathematical induction is a key goal of this part of the course.

·        Modeling computation Two course days covers sections 12.1 and 12.5 in the book. Section 12.1 concerns formal languages and different types of grammars, providing models for both natural languages, such as English, and for programming languages, such as Java. Section 12.5 concerns Turing machines, which are general mathematical models of computers, invented by the British mathematician Alan Turing.

All references are to the textbook, which can be bought at Amazon:

Kenneth H. Rosen, Discrete Mathematics and Its Applications, International Version, 6th edition, Mc-Graw Hill.

ISBN-13: 978-0071244749, ISBN-10: 0071244743

 

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Day

Curriculum

Pages

Assignments

Hand-in

1

Friday 4/3

1.1 and slides propositional logic

1-16

1.1.1, 1.1.3, 1.1.5, 1.1.7, 1.1.13, 1.1.25, 1.1.27, 1.1.37, 1.1.44, 1.1.49

 

2

Tuesday 8/3

1.2

21-27

1.1.51, 1.2.5, 1.2.7, 1.2.9, 1.2.11, 1.2.15, 1.2.42, 1.2.43, 1.2.61

 

3

Friday 11/3

1.3 and slides predicate logic

30-46

1.3.1, 1.3.5, 1.3.7, 1.3.17, 1.3.25, 1.3.51, 1.3.59

1.1.50, 1.2.6, 1.2.14, 1.2.44

4

Tuesday 15/3

1.4

50-58

not ex. 8, 16

1.4.1, 1.4.9, 1.4.19ac, 1.4.27ac, 1.4.29ac, 1.4.33abc

5

Friday 18/3

1.5, 1.6, 1.7

63-72,

75-85,

86-94

1.5.1, 1.5.3cd, 1.5.5, 1.5.13ab, 1.6.1, 1.6.15, 1.6.39

1.2.60a, 1.3.12abc, 1.3.18abc, 1.3.50, 1.3.52, 1.4.52

Mini-projekt 1 start

6

Tuesday 22/3

2.1, 2.2

111-128

2.1.7, 2.1.15, 2.1.17, 2.1.21, 2.1.29, 2.2.3, 2.2.13, 2.2.45

No teaching 25/3 (Easter)

7

Tuesday 29/3

2.3

133-146

2.3.4a, 2.3.10, 2.3.19ab, 2.3.25, 2.3.28, 2.3.29, 2.3.35, 2.3.38a, 2.3.76

1.5.24, 1.6.16, 2.2.20, 2.2.46

8

Friday 1/4

3.1, A-3

167-172

A-3.1, A-3.3, 3.1.1, 3.1.3, 3.1.9, 3.1.13

Mini-projekt 1 to be handed in 0830

9

Tuesday 5/4

3.2 (A-2 if needed)

180-190

3.2.1abcd, 3.2.3, 3.2.17, 3.2.19ab

2.3.18ab, A-3.2, 3.1.6, 3.1.24

10

Friday 8/4

3.3

193-199

not ex. 5, 6

3.1.14, 3.3.13, 3.3.23, 3.3.27

11

Tuesday 12/4

4.1,4.2

263-270

278-279

283-288 290-291

4.1.3, 4.1.9 (use ex. 1), 4.1.33, 4.1.47, 4.2.27, 4.2.42

3.1.24, 3.2.6, 3.2.18, 3.3.4, 3.3.12ab

Mini-projekt 2 start

12

Friday 15/4

4.3, 4.4

294-308

311-317

4.3.1ab, 4.3.3ab, 4.3.7ac, 4.3.25a, 4.3.26ac, 4.4.7, 4.4.18, 4.4.21

13

Tuesday 19/4

12.1

785-793

12.1.7, 12.1.8, 12.1.13, 12.1.20, 12.1.21ab

4.1.6, 4.1.56, 4.2.4, 4.3.24a, 4.4.2, 4.4.10 (compare to algorithm page 169)

 

No teaching 22/4

 

 

 

 

14

Tuesday 26/4

12.5

827-837

not ex. 2

12.5.1, 12.5.3, 12.5.7, 12.5.11, 12.5.15

15

Friday 29/4

 

 

 

Mini-projekt 2 to be handed in

Intensive

period

 

Tuesday 7/6

Questioning hour 13-14

 

 

 

Friday 10/6

Exam. More instructions will be sent via Moodle

 

Remember to bring your mini-projects