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.
·
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
|
# |
Day |
Curriculum |
Pages |
Assignments |
Hand-in |
|
1 |
Tuesday 10/3 |
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 |
Friday 13/3 |
1.2 |
21-27 |
1.1.51, 1.2.5, 1.2.7, 1.2.9, 1.2.11, 1.2.42, 1.2.43, 1.2.56, 1.2.60ab, 1.2.61 |
|
|
3 |
Tuesday 17/3 |
1.3 and slides predicate logic |
30-46 |
1.3.1, 1.3.5, 1.3.7, 1.3.12, 1.3.17, 1.3.25, 1.3.51, 1.3.59 |
1.1.50, 1.2.6, 1.2.22, 1.2.44 |
|
4 |
Friday 20/3 |
1.4 |
50-58 not ex. 8, 16 |
1.4.1, 1.4.9, 1.4.20ab, 1.4.27ab, 1.4.29ab, 1.4.33abc |
|
|
5 |
Tuesday 24/3 |
1.5, 1.6, 1.7 |
63-72, 75-85, 86-94 |
1.5.1, 1.5.3cd, 1.5.5, 1.5.13ab, 1.6.2, 1.6.10, 1.6.15, 1.6.39 |
1.3.18abc, 1.3.50, 1.3.52, 1.4.50, 1.4.52 Mini-projekt 1 start |
|
6 |
Friday 27/3 |
2.1, 2.2 |
111-128 |
2.1.7, 2.1.15, 2.1.17, 2.1.21, 2.1.28ab, 2.2.4, 2.2.16, 2.2.45 |
|
|
No teaching 31/3 and 7/4 |
|||||
|
7 |
Friday
10/4 |
2.3 |
133-146 |
2.3.4a, 2.3.10, 2.3.11, 2.3.19ab, 2.3.25, 2.3.28, 2.3.29, 2.3.35, 2.3.36, 2.3.38, 2.3.76 |
1.5.24,
1.6.16, 2.2.20, 2.2.46 |
|
8 |
Tuesday 14/4 |
3.1, A-3 |
167-172 |
A-3.1, A-3.3,
3.1.1, 3.1.3, 3.1.9, 3.1.13 |
|
|
9 |
Friday 17/4 |
3.2 (A-2 if needed) |
180-190 |
3.2.1abcd, 3.2.3, 3.2.17, 3.2.19ab |
2.3.18ab, 2.3.68, A-3.2, 3.1.6 |
|
10 |
Tuesday 21/4 |
3.3 |
193-199 not ex. 5, 6 |
3.1.14, 3.3.13, 3.3.23, 3.3.27 |
|
|
11 |
Friday 24/4 |
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 Mini-projekt
1 to be handed in 0830 |
|
12 |
Tuesday 28/4 |
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 |
Mini-projekt
2 start |
|
13 |
Tuesday
5/5 |
12.1 |
785-793 |
12.1.5,
12.1.7, 12.1.8, 12.1.13, 12.1.21 |
4.1.6,
4.1.56, 4.2.4, 4.3.24a, 4.4.2, 4.4.10 (compare to algorithm page 169) |
|
14 |
Friday
8/5 |
12.5 |
827-837 not ex. 2 |
12.5.1,
12.5.3, 12.5.7, 12.5.11, 12.5.15 |
Mini-projekt
2 to be handed in 0830 |
|
Intensive period |
|||||
|
|
Tuesday 9/6 |
Questioning hour 13-14 |
|
|
|
|
|
Friday 12/6 |
Exam.
More instructions will be sent by e-mail |
|
Remember to bring your mini-projects and
weekly assignments |
|