Logic and Discrete Mathematics (Spring 2017)

See the course description at kursus.ruc.dk for a brief and formal description of the course. Practical information can be found at the Moodle page of the course (requires login). All day-to-day information will be sent via Moodle to your RUC email account, so please read your RUC email regularly.

 

This page describes the content and structure 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.

During the course three mini projects are carried out, based on a handed out problem formulation. One of the mini-projects involves use of the programming language Prolog (Programming in logic) which will be briefly introduced at the course.

 

All references below 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

 

#

Day

Curriculum

Pages

Assignments

Hand-in

1

Tuesday 14/3

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, 1.1.44, 1.1.49

 

2

Thursday 16/3

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

Tuesday 21/3

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

Thursday 23/3

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

Tuesday 28/3

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, 1.3.12abcd, 1.3.18abc, 1.3.50, 1.3.52, 1.4.52

Mini-projekt 1 start

6

Thursday 30/3

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

7

Tuesday 4/4

2.3

133-142

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

Thursday 6/4

3.1, A-3

167-172

A10-A15

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 1315

9

Tuesday 11/4

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

Mini-projekt 2 and 3 start

No teaching 13/4 (Easter)

10

Tuesday 18/4

3.3 and Prolog intro

193-199

not ex. 5, 6

3.1.14, 3.3.13, 3.3.23, 3.3.27

 

11

Thursday 20/4

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

3.2.6, 3.2.18, 3.3.4, 3.3.12ab

12

Tuesday 25/4

4.3, 4.4 and Prolog intro

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

Mini-projekt 2 to be handed in

13

Thursday 27/4

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)

14

Tuesday 2/5

12.5

827-837

not ex. 2

12.5.1, 12.5.3, 12.5.7, 12.5.11, 12.5.15

Mini-projekt 3 to be handed in

15

Thursday 4/5

No teaching

Intensive

period

Thusday 8/6

Questioning hour 13-14. More info sent via Moodle

 

Tuesday 13/6

Exam. More instructions sent via Moodle

Remember to bring your mini-projects