Math 346: Number Theory

Winter 2020

Professor: Dr. Chiriac Class time: 10:00-11:50 TR in KMC 350
Office: FMH 462N Webpage: web.pdx.edu/~chiriac/346/2020w.html
Office Hrs: Tue 3-4 & Wed 10:30-11:30 Email: mylastname [at] pdx [dot] edu


Course Description:
  • This course is a proof-based introduction to elementary number theory.
  • We will study basic properties of the integers as found in the theory of divisibility, congruences, diophantine equations, and modular arithmetic.
  • Several important applications to computer science and cryptography will also be discussed.


    • Textbook:
  • Number Theory: A lively introduction with proofs, applications and stories by James Pommersheim, Tim Marks and Erica Flapan.
  • Chapters 1-2 offer a quick introduction to the most common methods of proof; I recommend that you read these two chapters on your own.
  • We will cover the core material in Chapters 3-9. Time permitting, we might go over some additional topics from the remaining chapters.

    • Grading:
  • Homework and participation - 40%.
  • Two Midterms and a Final - 20% (each).

    • Grading scale:

    90-100

    85-89

    81-84

    77-80

    73-76

    69-72

    65-68

    61-64

    57-60

    53-56

    49-52

    0-48

    A

    A-

    B+

    B

    B-

    C+

    C

    C-

    D+

    D

    D-

    F

    Exams:
  • All exams are closed-book and closed notes. No calculators are permitted.
  • Midterm I - Thursday, 01/30/20, in class. Sections covered: 2.1, 2.2, 3.1-3.5, 4.1, 4.2, 5.1-5.4, 6.1, 6.2
  • Midterm II - Thursday, 02/27/20, in class. Sections covered: 7.1, 7.2, 7.4, 8.1-8.5, 9.1-9.5
  • Final Exam - Tuesday, 03/17/20, 10:15 am-12:05 pm (it will be administered remotely).
  • Sections covered: 10.1-10.3, 13.1, 13.2, 13.5, 13.6
    • Practice Final (not to be turned in)


    Attendance:
  • Attendance and participation are important ingredients for your success in this course. Frequent absences will be reflected in your grade.
  • If you happen to miss a class, you should try to get the lecture notes from a classmate for that lecture.



    • Homework:
  • Homework will be assigned every Thursday and will be due at the beginning of class the following Thursday.
  • Assignments turned in by the next Tuesday will receive 75% credit. No assignments will be accepted after that.
  • Note that you will need to do the reading to be able to do the homework. If you're stuck, it's ok to consult your classmates or me. However, the work you turn in must be entirely your own, in your own words!
  • All Exercises are from the textbook. Note that "a.b:N" is to be read Exercise N from Section a.b.

    • Problem Set 1 (Due 01/16): 2.2:8 2.3:4 (see the def on page 68) 3.1:19,20,27 3.2:4,14,16 3.3:6,7 (this last exercise is optional)

    Problem Set 2 (Due 01/23): 3.4:3,6,10 3.5:5,7,15,29 4.1:8 4.2:3,4

    Problem Set 3 (Due 01/30): Practice Midterm I

    Problem Set 4 (Due 02/13): 7.1:2,9 7.2:6,7,8 7.4:11 8.2:8,16 8.3:4,5

    Problem Set 5 (Due 02/20): 8.4:1,2 8.5:2 9.1:4,7,10,13 9.2:3,5,18

    Problem Set 6 (Due 02/27): Practice Midterm II

    Problem Set 7 (Due 03/12): 10.1:3,11 10.2:1,5,9 10.3:3 (see Ex 3 on page 439),4,5,15,17(b)




    Access and Inclusion for Students with Disabilities:
    PSU values diversity and inclusion; we are committed to fostering mutual respect and full participation for all students. My goal is to create a learning environment that is equitable, useable, inclusive, and welcoming. If any aspects of instruction or course design result in barriers to your inclusion or learning, please notify me. The Disability Resource Center (DRC) provides reasonable accommodations for students who encounter barriers in the learning environment.

    If you have, or think you may have, a disability that may affect your work in this class and feel you need accommodations, contact the Disability Resource Center to schedule an appointment and initiate a conversation about reasonable accommodations. The DRC is located in 116 Smith Memorial Student Union, 503-725-4150, drc@pdx.edu.

  • If you already have accommodations, please contact me to make sure that I have received a faculty notification letter and discuss your accommodations.
  • Students who need accommodations for tests and quizzes are expected to schedule their tests to overlap with the time the class is taking the test.
  • For information about emergency preparedness, please go to the Fire and Life Safety webpage for information.


    • Title IX Reporting Obligations:
    As an instructor, one of my responsibilities is to help create a safe learning environment for my students and for the campus as a whole. As a member of the university community, I have the responsibility to report any instances of sexual harassment, sexual violence and/or other forms of prohibited discrimination. If you would rather share information about sexual harassment, sexual violence or discrimination to a confidential employee who does not have this reporting responsibility, you can find a list of those individuals. For more information about Title IX please complete the required student module Creating a Safe Campus in your D2L.