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Math 104A General Information
Fall 2006



Course Information

This is a first course in elementary number theory. Topics include: properties of integers, prime numbers, Diophantine equations, congruences and quadratic reciprocity. An important emphasis of the course is the coherent writing of mathematical proofs.

  • Class time and Location: MWF 1-1:50 pm at Warren Lecture Hall 2207.
  • Textbook: An Introduction to Number Theory, by Harold Stark.
  • Homework and Exams: see below
  • Instructor: Wee Teck Gan, Office: AP&M 5808, Tel :534-0997, email: wgan@math.ucsd.edu
  • Office Hourse: Wed 11am-12pm. (Office Hours during Final Exam Week: Wed 11am-12pm, Thurs 2-4pm)

  • Sections: A01 Tues 1-1:50pm, A02 Tues 2-2:50pm, HSS 2152
  • Teaching Assistant: Aaron Wong, Office Hrs: Tues: 3-4pm and Fri: 10:30-11:30am at AP&M 6311, email: awong@math.ucsd.edu (Office Hours during Final Exam Week: By Appointments during the priod Wed and Thurs: 1-4pm).


    Exams

    There will be 3 midterms and a final exam.

  • All exams are close-book, close-notes. No calculator is allowed.

  • Final Exam: The final exam will be on Fri 12/8, 11:30am-2:30pm. Here is a Sample Final . (Question 5 is not in our syllabus, so dont worry about it). And here is the solution .
  • Midterms: Will be held during the lecture hour on the following dates. I will take your 2 best midterm scores for the computation of the final grade, so you are allowed to drop one of your midterm scores. Here are the midterm dates and the chapters of the book they cover:

    (i) Oct 18 (Wed): covers Chapter 1 and 2, but excluding Sect 2.4. Here is a Sample Midterm ;

    (ii) Nov 8 (Wed): covers Section 3.1-3.4.

    (iii) Nov 29 (Wed): covers Section 2.4, 3.5, 3.6 and stuff on quadratic recoprocity (which is not in the textbook).

  • Student ID is required to take the exams. Students without ID will not be allowed to take the exams.
  • (Absolutely) NO make-up exams.


  • Homework

    There will be weekly homework assignments, which you can find below. Homework is due in class on Wednesdays.

  • Late homework will not be accepted.
  • I will pick your 5 best homework scores for the computation of your final grade.

  • It is very important that you attempt all the homework, since it is almost impossible to learn the subject matter without doing many problems.
  • We encourage you to work together on the exercises. Any assignment, though, should represent your own work (i.e. you should write it up yourself).
  • Here are the homeworks:
    HW1 (Due 10/4): Problems ; Selected Solutions ;

    HW2 (Due 10/11): Problems ; Selected Solutions ;

    HW3 (Due 10/18): Problems ; Selected Solutions ;

    HW4 (Due 10/25): Problems ; Selected Solutions ;

    HW5 (Due 11/1): Problems ; Selected Solutions ;

    HW6 (Due 11/8): Problems Selected Solutions ;

    HW7 (Due 11/15): Problems ; Selected Solutions ;

    HW8 (Due 11/27, Mon): Problems ; Selected Solutions ;



    Rough Schedule

  • Here's an approximate week-by-week schedule:
    Week 1: Divisibility and prime numbers

    Week 2: Greatest common divisor and Euclid's algorithm, Fundamental theorem of arithmetic (unique factorization)

    Week 3: Irrationality, Linear Diophantine equations, Pythagorean triples

    Week 4: Fermat's infinite descent, Midterm I, Multiplicative functions

    Week 5: Introduction to Congruences: basic properties, linear congruence equations

    Week 6: Chinese remainder theorem, Fermat's little theorem, Wilson's theorem

    Week 7: Reduced residue system and Euler's theorem, Midterm II

    Week 8: Orders and Primitive roots

    Week 9-10: Legendre symbols and Quadratic reciprocity, Midterm III


    Grades

    Grades will be based on the following percentages.


    Homework 20%
    Midterms 30%
    Final 50%