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 |
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 |
|