JHR's MA378 page
MA378
Number Theory
MTRF 7, G308
John Rickert,
Associate Professor of Mathematics
Office: G-215A, Crapo Hall
Phone: (812) 877-8473
CM: 141
e-mail: john.rickert@rose-hulman.edu
Schedule
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Homework for our next class
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...Today's notes
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The main goal in this class is to have you (the student) perform as an active learner. To do this you will need to do the exercises, raise questions about structures that you are studying, create hypotheses and test these hypotheses.
The textbook for this class is An Introduction to the Theory of Numbers, 5th Ed., by Niven, Zuckerman and Montgomery.
Information about the paper.
Homework
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For Tuesday, March 10: Sec. 1.2 #1,3,5,11,23,31.
Turn in these exercises on Monday, March 16.
Section 1.3 #1,3,4,9,11,16,26,30,32,33,48;
Section 1.4 #1,3,7.
Turn in these exercises on Monday, March 23.
Thursday, March 19: We proved that if p is prime, then
2p == 2 (mod p).
Can you prove that if
2m == 2 (mod m) then m is prime?
Bring a computer or commputing device to class Thursday, March 26.
It will be useful for the worksheet.
Thursday, March 26.
The write-up for the automorphic forms worksheet is due Monday, March 30.
Friday, March 27. There will be no class due to the
Undergraduate Math Conference.
Section 2.1 #1,5,6,9,11,13,14,19,20,23,27,28*,30*,44,45.
* replace the exponent 400 with 4*100400.
Turn in Section 2.1 #5,6,9,13,14,19,20,23,27,28*,30*,44,45
on Thursday, April 1.
Exam #1, Tuesday, April 7.
Do these exercises: Section 2.2 #4,5,14;
Section 2.3 #9,14,37;
Section 2.4 #4,14,15;
Section 2.6 #1,2,9.
Some options for the paper
Turn in Section 2.2 #4,14;
Section 2.3 #9,37;
Section 2.4 #15;
Section 2.6 #9
on Friday, April 24.
Do exercises:
Section 2.7 #2,4,6;
Section 2.8 #6,10,19,23;
Section 2.9 #1,4,5,8.
Turn in Section 2.7 #2,6;
Section 2.8 #23;
Section 2.9 #1,4;
Section 2.10 #7;
Section 2.11 #1,15;
Section 3.1 #7
on Tuesday, May 5.
Do Section 2.10 #1,4,7;
Section 2.11 #1,6,15,16,22;
Section 3.1 #4,7,14,16.
Thursday, May 7: Exam #2.
Section 4.2 #1,5,8,16,20;
Seciotn 4.3 #2,5,8,25;
Section 4.4 #1,5,6,7,25.
Sequences
Monday, March 9: 1,1,1,1,1,1,1,1,1,1,...
1,4,9,16,25,36,49,64,81,100,...
1,3,6,10,15,21,28,36,45,55,...
Tuesday, March 10: 1,1,2,3,5,8,13,21,34,55,89,...
Thursday, March 12:
Friday March 13: 1,1,2,3,5,8,13,21,34,55,91,149,245,...
Monday, March 16: 1,1,2,2,4,2,6,4,6,6,...
Tuesday, March 17: 1,2,5,12,29,70,169,408,987,...
Thursday, March 19: 1,2,2,3,2,4,2,4,3,4...
Friday, March 20: 1,1,1,1,1,1,6,1,1,1, 2,1,6,6,1, ...
Monday, March 23: 3,5,17,257,65537,4294097297,...
Tuesday, March 24: 0,0,0,0,1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,6,...
Thursday, March 26: 1,2,2,1,2,1,1,2,2,1,...
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Questions from class
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Tuesday, March 10:
Conjecture: GCD(Fn,
Fn+k)
= { 1 if k does not divide n}/
{Fk if k|n}.
Find a counter example or proof.
if n > 3, then
1< Fn / Fn+1 < 2.
Can you improve these bounds?
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Random notes
There are 3 in-class exams each worth 15%.
There is a paper worth 10%.
The final exam is worth 30%.
Quizzes and Homework is worth 15%.
There may be two types of quizzes -- announced and unannounced.
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