På denne siden vil øvingsoppgavene bli lagt ut hver uke. Ta kontakt
med
for spørsmål om
øvingene. Det kreves ikke godkjente øvinger for tilgang til eksamen,
men øvingene er en viktig del av kurset likevel.
De første øvingene er 15. januar og 18. januar.
Det er mange gode oppgaver i læreboka, og dere må gjerne gjøre flere enn de
som står listet opp her!
Dere kan nå levere inn øvingene deres til retting, om
dere ønsker det. Det er satt ut pappbokser merket med fagkode ved
inngangen til Industriell Matematikk, 3. etasje i Nordre Lavblokk. (Gå
opp trappa ved kortsenteret (der man får adgangskort) til andre
etasje. Der finner man en mindre trapp der det står "Lavblokk
Nord".) Dere kan selvsagt også levere direkte til Dagfinn på gruppa.
Oppgavene som legges ut i uke X bør være i boksen i løpet av fredag i uke
X+1. (Øving 1 kan dere levere sammen med øving 2.) Markér besvarelsen
med mandags- eller torsdags-gruppe.
Øving
1 |
Sec. I.2: 12, 13
Sec. I.4: 3, 6, 10 (see Def. 3.7 page 29), 15 (consider
both the general case and the case with the set of all upper
triangular nxn matrices with non-zero determinant), 18, 19, 30,
32, 34, 38
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Øving
2 |
Sec. I.4: 41
Sec. I.5: 5, 6, 11, 13, 22, 23, 26, 33, 41, 45, 46, 51,
53
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Øving
3 |
Sec. I.6: 17, 23, 36, 44, 45, 50, 51, 53
Sec. II.8: 3, 9, 17, 20, 44, 46, 47
Sec. II.9: 1, 9, 11
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Øving
4 |
Sec. II.9: 5, 13, 17, 27 a-b, 29, 34
Sec. II.10: 2, 6, 7, 12, 15, 28, 32, 34
Sec. II.11: 1, 6
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Øving
5 |
Sec. II.10: 39, 40
Sec. II.11: 22, 26, 27*, 39*, 47, 48*
Sec. III.13: 2, 6, 8, 17, 44, 45, 47*, 51*
Sec. III.14: 6, 12
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Øving
6 |
Sec. III.13: 23, 49, 52*
Sec. III.14: 25*, 27, 30*, 31
Sec. III.15: 1, 4, 28, 35, 36, 40*
Also: Show that if ɸ: G → G' is an
isomorphism, and g∈G has order n, then ɸ(g) also
has order n.
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Øving
7 |
Det blir gruppeøvinger også i uke 9, selv om det ikke er
forelesninger.
Sec. III.15: 3, 29
Sec. III.16: 1, 2, 3, 6, 7, 10, 13
Sec. III.17: 2, 3, 5
28. mai 2004: 1
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Midtsemester |
- The midterm exam will be arranged in room S8 in the
Central Building (this is now confirmed) on monday Mars 12,
15.00-17.00.
- The midterm exam counts for 20 percent of the total grade
if you do better on the midterm than on the
final. Otherwise, it does not affect your grade.
You might want to try the previous midterm exams:
When you are preparing for the midterm exam, you should read the
textbook and study the problem sets which have been given during
the semester. There are also some relevant old exam questions
you can take a look at: (Note that the midterm exam will be a
multiple choice test.)
- August 12, 2004: 1a, 3, 4 (corrected from September 1)
- May 28, 2004: 1, 3, 5
- December 7, 2001: 1
- December 5, 2000: 2, 3
- December 2, 1991: 1, 4
You find a pdf-file with the old problems here. (On the front page you
find some newer exams.)
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Øving
8 |
Sec. IV.18: 5, 6, 8, 11, 13, 23*, 28, 34*, 35, 37*, 38, 41*,
46, 49, 54*
Sec. IV.19: 1, 2, 11, 20, 26*, 29
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Øving 9
|
Sec. IV.20: 1, 4, 6*, 8, 9, 10, 24, 27*, 28*
For MA2201: Sec. VII.36: 1, 3, 11*, 12*, 13, 17*, 22*
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Øving
10 |
These problems are for the first week after Easter. They are
only from the syllabus for the MA2201 course.
Sec. VII.36: 5, 14, 16, 18, 19
Sec. VII.37: 7
23. mai 2001: 2
28. mai 2004: 6
Also: Show that if G is a finite abelian group
with n elements, and r divides n, then G has a subgroup with r
elements.
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Øving
11 |
Sec. IV.18: 25, 48, 55
Sec. IV.19: 5, 8, 23, 25
Sec. IV.20: 11, 13, 14, 15
24. august 2000: 1
28. mai 2004: 4
On RSA (see the note on the
Euler phi-function):101 and 113 are prime numbers, and
7467*3=1 mod 11200. Suppose
you post the (RSA-)key (11413,7467) on the web with the
information "space=100, a=101, b=102, etc.". One day you receive
an e-mail with the three numbers 4654, 676 and 2931. What is the
sender trying to say to you? (It's in Norwegian...)
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Øving
12 |
Sec. IV.22: 1, 2, 3, 6, 9, 14, 17, 22, 24
Sec. IV.23: 1, 2, 9, 12, 26, 36
26. november 1999: 2
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Øving
13 |
For all:
- Sec. IV.23: 13, 14, 34
- Sec. V.26: 12, 13, 14, 18, 22, 24, 25, 26, 27
For TMA4150:
- Sec. V.27: 1, 7, 18
- Show that
p(x)=x4+x3+x2+x+1 in the
polynomial ring Z2[x] is irreducible, and
F=Z2[x]/<p(x)>. Find a generator for
the cyclic group F\{0}. (Remember Theorem 10.12 in
Fraleigh.)
- Show that q(x)=x5+x2+1 in Z2[x] is
irreducible, and let E=Z2[x]/<q(x)>. Find a
generator for the cyclic group E\{0}.
- 17. august 2006:: 7
For MA2201:
Also, you should work on some exam problems, especially those
that Idun will present in the lectures. Try them before
you go to these lectures!
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