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01:640:356 - Theory of Numbers

General Information (Catalog Description)

Priorities of the natural numbers, congruences, disophantine equations, and elementary arithmetical functions.

Prerequisite: CALC3.

This prerequisite will be strengthened effective Fall 2009 to Math 300 or permission of the department.
Math 300 (Mathematical Reasoning) or a very good background in mathematical proof is strongly recommended. Students with a strong record in their mathematics courses who have not taken Math 300, but wish to take Number Theory, should request a prerequisite override from the Head Advisor (advisor@math.rutgers.edu).

Suggested Textbook

Instructors in 356 sometimes use a different text and follow a different syllabus than the one shown. Check the textbook list for additional information.

The text, starting in the Summer Semester 2000, is: Kenneth H. Rosen; Elementary Number Theory and Its Applications (sixth edition); Addison Wesley, 2011 (768 pp.); (ISBN: 0-321-50031-8; ISBN13: 9780321500311)

Suggested Syllabus

A suggested syllabus follows. However, anything posted on a page for the current semester supersedes this syllabus.

Lecture NumberSection in TextSuggested Exercises
1 1.2 8, 12, 20, 30.
1.3 6, 8.
2 1.4 4, 8, 20, 22.
3 2.1 2, 6, 12, 28.
4 2.2 4, 6, 12.
2.3 2, 4, 14, 18.
5 3.1 2, 4, 6, 8, 12, 14, 16, 20.
6 3.2 4, 6, 8, 14, 22.
3.3 2, 8, 9, 10, 14, 15.
7 3.4 2, 4, 8, 10, 14, 15, 16.
8 3.6 2, 4, 8, 14.
9 4.1 4, 5, 10, 12, 14, 16, 22, 28.
10 4.2: 2, 6, 8, 10, 16, 18.
11 4.3 2, 4, 6, 8, 34.
12 4.4 2, 4, 6, 8, 10.
4.6 2.
13 exam
optional 5.1 2, 4, 12, 24.
5.2 2, 6.
5.5 2, 6, 8, 12, 14, 16.
14 6.1 2, 6, 8, 10, 14, 20.
6.2 8, 12, 16d.
15 6.3 1(all), 2, 4, 16, 18.
16 7.1 2(all), 4(all), 6, 8, 12, 14, 34.
17 7.2 2(all), 4, 6c, 8, 10, 12.
18 7.3 4, 8, 10, 14.
7.4 2 (all), 6, 8, 10, 13, 14.
19 11.1 2, 4, 5, 11, 12, 14.
20 11.2 1(all), 2, 4.
21 11.3 1(all), 2, 5, 6.
22 9.1 2(all), 4(all), 6, 8, 14.
9.2 1(all), 2(all), 4, 6, 8, 12.
23 9.3 2, 4(all), 6(all), 8(all), 10.
24 12.1 1(all), 6(all), 8, 9, 12.

One midterm exam and a final exam seem appropriate for this course. A selection of the optional topics in the middle of the table may be inserted if the earlier material is completed before an exam can be given. Topics listed for lecture 14 should not be introduced before the midterm exam. This syllabus allows two weeks at the end of the course for additional topics. Such topics should be dictated by the interest of the class.


Sections Taught This Semester:

Theory of Numbers (01: 640: 356, Summer 2017 )

Theory of Numbers (section B6)
Index Number: 00469
Credits: 3
Professor: KARASIEWICZ
Schedule:
  • [L] Wed 6:00PM-8:45PM HLL-425 (BUS)
  • [L] Mon 6:00PM-8:45PM HLL-425 (BUS)
  • [L] Thu 6:00PM-8:45PM HLL-425 (BUS)


Previous Semesters

  • Fall 2016 : Prof. Tunnell
  • Fall 2013 : Doron Zeilberger
  • Summer 2011 : Jerrold Tunnell
  • Fall 2010 : Anders Buch
  • Summer 2010 : Thom Tyrrell
  • Fall 2009 : Prof. Weibel
  • Summer 2009 : L. Medina
  • Fall 2008 : Prof. Munshi
  • Summer 2008 : Michael Weingart
  • Fall 2007 : Prof. Sahi
  • Fall 2006 : Prof. Sills (T Th 1:40-3 PM, SEC-217)
  • Fall 2001 : Prof. Miller
  • Summer 2000 : One section taught by David Nacin. A lecture schedule is available.
  • Fall 1998 : Prof. Bumby (One section.)

Disclaimer: Posted for informational purposes only

This material is posted by the faculty of the Mathematics Department at Rutgers New Brunswick for informational purposes. While we try to maintain it, information may not be current or may not apply to individual sections. The authority for content, textbook, syllabus, and grading policy lies with the current instructor.

Information posted prior to the beginning of the semester is frequently tentative, or based on previous semesters. Textbooks should not be purchased until confirmed with the instructor. For generally reliable textbook information—with the exception of sections with an alphabetic code like H1 or T1, and topics courses (197,395,495)—see the textbook list.

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Department of Mathematics

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