Math 104A: Number Theory I (Fall 2013)

---

This is first quarter in the MATH 104ABC sequence, the introduction to number theory.

Meeting times:

• Lecture (by Alina Bucur) T/Th 2-3:20pm, AP&M B412
• Discussion section (by Shaunak Das) W 7-8pm, AP&M B402A

Instructor: Alina Bucur Office: AP&M 7131 Email: alina@math.ucsd.edu Office hours: W 1:30-2:30pm                      and by appointment

TA: Shaunak Das Office: AP&M 6434 Email: shdas@ucsd.edu Office hours: W 3-4pm, Th 11am-12pm

Required text: Introduction To Number Theory by Harold Stark. You are expected to read the text BEFORE each lecture.

Homework: Assigned weekly, due Friday 3:30pm in the appropriate box in the basement of APM.

Quiz: Wednesday, October 23, in discussion.

Midterm exam: Thursday, November 7, in class.

Final exam: Thursday, December 12, 3-6pm, APM B412. Please note that by signing up for this course, you are agreeing to sit for the final examination at this date and time. Bring a blue book!

Grading: 20% homework, 10% quiz, 20% midterm, 50% final exam.
               The grading will be done on a curve, the median corresponding to a B-/C+.

No notes, textbooks, calculators are allowed during exams. No make-up exams will be given and no late homework will be accepted. Cheating on an exam results in 0 points for that exam, as well as further disciplinary action. Please familiarize yourselves with the policies of the Academic Integrity Office.

Announcements:

• WELCOME!
• Shaunak will hold special office hours on Friday 10/4 before the first hw is due. Email him for details.
• Shaunak's office hours have changed. See above.
• The lectures on 11/14 and 11/19 will deal with more aspects of congruences, but they are not from the textbook. You will have to rely on your own notes taken in class.
• Here are the four versions of the midterm (no solutions!): 1, 2, 3, 4.
• Special office hours during finals week: Tu 10-11:30am, W 1-2:30pm (Alina).
• Review session: Tu 4-6pm (Shaunak)
• Bring a BLUE BOOK to the final exam.

Reading:

• Th 10/3: 2.1, 2.2, 2.3
• Tu 10/8: 2.4, 2.5
• Th 10/10: 3.1-3.3
• Th 10/31: rest of chapter 3
• Tu 11/26: 5.1 - 5.3
• Th 12/5: rest of chapter 5 and the Fermat primes notes

Homework assignments: You are encouraged to work on these problem sets with a small group of other students in the class, but every student should write up his or her own solutions.
The numbers refer to the textbook.

• HW 1 (due F 10/4)
  • Section 1.2: 1, 4
  • Chapter 1 miscellaneous exercises: 1, 2, 5
  • Section 2.1: 2, 3, 5


• HW 2 (due F 10/11)
  • Section 2.2: 1, 4, 6, 8, 13, 14
  • Section 2.3: 2, 5
  • Section 2.4: 6, 7


• HW 3 (due F 10/18)
  • Section 2.2: 15
  • Section 2.4: 1, 2, 9
  • Section 2.5: 1, 2, 4, 10


• HW 4 (due F 10/25)
  • Chapter 2 miscellaneous exercises: 2, 3
  • Section 3.1: 2-6 , 9, 10
  • Section 3.2: 1, 2, 5, 9, 11, 13


• HW 5 (due F 11/1)
  • Section 3.3: 1, 2, 4, 7, 9, 12, 14, 15, 19, 20, 21
  • Section 3.4: 1, 2, 6, 10


• HW 6 (due F 11/8)
  • Section 3.5: 1 - 4, 7
  • Section 3.6: 1 - 4, 10, 11, 13 - 17
  • Section 3.7: 3, 4, 5, 8, 9, 10, 12


• HW 7 (due F 11/15)
  Find a real life application of modular arithmetic and write it up carefully and prove that it works. Make sure you explain where you found it. The coolest correctly explained example will get 20% extra points on this homework.


• HW 8 (due F 11/22) pdf
  


• HW 9 (due F 12/6, by 12pm)
  part 1: pdf
  part 2: pdf