M328K Introduction to Number Theory, Adriana Sofer

M328K Introduction to Number Theory

SPRING 2003
UNIQUE# 56085: MWF 9:00-10:00 RLM 6.118
UNIQUE# 56090: MWF 11:00-12:00 RLM 7.114


NEWS
*Office Hours: Thursday 5/22 10am (Adriana)
*Final grades are posted. Your homework grade was computed by
averaging your best 10 scores.
*Participation grade out of 10: at least 2 presentations--10;
1 presentation--5; no presentations--0.

Lecturer: Adriana Sofer, RLM 11.166, Phone: 471-1135
email: asofer@math.utexas.edu
Office Hours: MW 12:30pm or by appointment.

TA: Ariel Pacetti, RLM 9.124, Phone: 475-9134
email: apacetti@math.utexas.edu
Office Hours: Tu 4:00pm.

Text: Kenneth H. Rosen, Elementary Number Theory and its applications,
Fourth Edition, Addison Wesley Longman, 2000.
Syllabus: We will cover material included in Chapters 1-11.


Homework: Homework assignments are posted on this website on a weekly basis.
Selected problems will be graded.

Student presentations: All students are expected to present their homework to
the rest of the class at least two times during the semester.

Tests: There will be two 50 min, in-class tests and a Final comprehensive exam
on the following dates:


Course Grade: The course grade will be computed according to the following:
homework 20%; presentations 10%; two tests, 20% each; final 30%.
An "A" will correspond to a number grade strictly bigger than 89;
a "B", same with 79; a "C", same with 69; a "D", same with 59.

Cumulative list of homework problems from the textbook.
Please see individual assignments to be turned in at the indicated due dates.

Additional problems might be assigned occasionally.

1.1 p.14: 4, 8, 12, 24, 26.

1.2 p.22: 2, 8, 12, 14, 24, 26.

1.4 p.31: 8, 10, 12, 13, 34, 40, 41.

2.1 p.44: 2, 11.

3.1 p.76: 2, 4, 6, 12, 16, 24.

3.2 p.84: 2, 4, 6, 8, 12, 14(a), 16, 22.

3.3 p.93: 2(b)(c), 4(b)(c).

3.4 p.104: 2, 4(a)(b)(c), 6, 10, 32(a)(d), 36, 40, 44(a), 46, 60, 66, 70.

3.6 p.123: 2, 4, 8.

4.1 p.135: 2, 4, 6, 10, 12, 14, 16, 22, 24, 26, 28.

4.2 p.141: 2, 6, 10, 12, 18.

4.3 p.149: 4(a)(b)(c), 8, 10, 12, 15, 17(a), 22, 34.

5.1 p.177: 1(a), 3(a)(b), 5(a), 22, 23.

5.5 p.195: 2, 3(a)(b), 11(a)(b), 12.

6.1 p.202: 10, 12, 16, 18, 22, 24, 28.

6.3 p.218: 1, 2, 4, 6, 10, 16.

7.1 p.227: 2, 4(b)(c), 8, 12, 16, 28.

Recommended additional problems (you don't have to turn these in).

1.1 p.14: 1, 2, 3, 7, 25.

1.2 p.22: 4, 5, 11, 22, 27, 29, 33, 34.

3.1 p.76: 5, 7, 13. Also:
1) Let p, p+r, p+2r be three primes. Show that 6|r if and only if p>3.
2) Show that 3 is the only prime of the form k^4+k^2+1.
3) Given that 71|(7!+1), show that 71|(9!+1).
4) Let S be a subset of {1, 2,..., 2n}; S has n+1 elements. Show
that there are two elements in S that are coprime.

3.2 p.84: 10, 25, 30.

3.3 p.93: 19.

3.4 p.104: 11, 12, 13, 14, 15, 48, 62.

4.1 p.135: 5, 17, 20.

4.2 p.141: 16.

4.3: Show that there are infinitely-many triples of consecutive integers pairwise coprime.
Is the result true for 4 consecutive integers?

5.1 p.177: 17.

6.1 p.202: 30, 33, 39.

Homework assignment. Grades are posted on UT Direct.

Send questions, comments to asofer@math.utexas.edu.
Go to UT Math home page

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