### Math 356: Theory of Numbers , Summer 2011

Mathematics is the queen of the sciences and number theory is the queen of mathematics.
Carl Friedrich Gauss

Text: Kenneth H. Rosen; Elementary Number Theory and Its Applications (sixth edition); Addison Wesley, 2005 (744 pp.); (ISBN: 0-321-23707-2; ISBN13: 9780321237071)

Lecture: Lucy Stone Hall Room B110, MWTh 6-8:45 PM
New classroom effective 6/6/11: Hill Center 705 MWTh 6-8:45 PM
Office Hours: Mondays and Wednesdays 2-3 pm, Hill 305, and by appointment.

Course Syllabus We will cover chapters 1,3,4,6,7,9, and 11, with parts of 5, 8, 10, and 13.

Class attendance: Students must attend a majority of class meetings since the prior exam in order to take the next exam.
• 20% Homework
• 20% Midterm 1
• 20% Midterm 2
• 40% Final

Homework: There will be five written homework assignments, each due at the beginning of lecture on Wednesdays. Late homework will not be accepted. You may discuss your homework with other classmates, but the work you hand in must be your own.

• Assignment #5 - Turn in the problems in parentheses. The other problems are suggested for practice.
• 9.2 #1,3ace,(5),8,9,(10)
• 9.3 #2,(4b),16
• 9.4 #1,(2a),4,(8),18
• 11.1 #1,(4),6,(8),11,27
• 11.2 #1,(2),4,10,11,13

• Assignment #4 - Turn in the problems in parentheses. The other problems are suggested for practice.
• 7.1 #1,(2abcd),4,8,(12),15,(20),25,32
• 7.2 #(1abcd),(2abcd),8,9,12,20-24
• 7.3 #1,3,5,18
• 7.4 #(1abcd),10,(15),16,22,23,24,30,(31)
• 9.1 #(1),2,5,6,(8),(10),11,12,18

• Assignment #3 - Turn in the problems in parentheses. The other problems are suggested for practice.
• 4.3 #1,4,(4b),(10),15,17,(18),(22),36
• 6.1 #1,(3),5,9,(10),16,18,21,(24),31,33,42
• 6.2 #1,(2),3,16ab
• 6.3 #1,2,3,(7),8,11,(17),19

• Assignment #2 (revised 6/10/11 - Write up and turn in the problems in parentheses (). Work through the other problems, but only those in parentheses are to be turned in.)
• 3.3 #2-6,9,(12),16,17,19,(24)
• 3.4 #(2),(4),5
• 3.5 #1,(6),7,(10),30,32,33,35,37,38,39,42,56,63
• 3.5 #17-21 describe a number system in which unique factorization fails. Try them if you're curious.
• 3.7 2,4,10
• 4.1 #2,(4),(6bcde),(14),30,32,33,35,36,41
• 4.2 #(2abc),5,6,(9),10,12,(18)

• Assignment #1
• 1.3 #7,(8),13,(14),19,20,24,25,32
• 1.4 #(4),5,8,10,14,(16),45
• 1.5 #(5a),6,(7),(8),9-12 14,16,19 ,20 ,21 ,26 ,28
• 3.1 #(3),5,(6),7,(8),12,(16c),24
• 3.2 #7,10,12