Homework for Number Theory
MA 261 Section 001
Spring 2021
Max Kutler
Monday, 1/25: Setting the stage
Actual discussion: What are our goals and exectations for MA 261?
Notes
Wednesday, 1/27: Introduction to proofs
Friday, 1/29: Introduction to proofs; presentations
Reading: Marshall/Odell/Starbird pp. 1-3
Homework due: Please fill out this poll to sign up for
presentations; prove Theorem 1 on the Introduction to proofs handout
Expected discussion: Introduction to proofs, how to give a
presentation
Actual discussion: Introduction to proofs, how to give a
presentation
Notes
Monday, 2/1: Introduction to LaTeX, Divisibility
Reading: Marshall/Odell/Starbird pp. 7-10
Homework: Think about the format of your presentations; complete the
Introduction to proofs handout
Expected discussion: Introduction to LaTeX, how to submit homework
Actual discussion: Introduction to LaTeX, how to submit homework,
congruence modulo n
Notes
Wednesday, 2/3: Divisibility
Reading: Marshall/Odell/Starbird pp. 1-3, 7-10
Homework due: 1.1-1.3, 1.6, 1.7
Presentations: 1.2, 1.6, 1.7
Friday, 2/5: Congruence modulo n
Reading: Marshall/Odell/Starbird pp. 11-12
Homework due: 1.8-1.11
Presentations: 1.9-1.11, equivalence relations
Notes
Monday, 2/8: Congruence modulo n (continued)
Reading: Marshall/Odell/Starbird pp. 12-13
Homework due: 1.12-1.14; please also fill out this poll to sign up for
the next round of presentations
Presentations: 1.12, 1.14
Notes
Wednesday, 2/10: Congruence modulo n (continued), Induction
Reading: Marshall/Odell/Starbird pp. 13-14
Homework due: 1.15-1.17, 1.20
Presentations: 1.17, Induction discussion, 1.20
Notes
Friday, 2/12: Divisibility criteria, axioms
Reading: Marshall/Odell/Starbird p. 14
Homework due: 1.21-1.23
Presentations: 1.21-1.23
Notes
Monday, 2/15: The division algorithm
Reading: Marshall/Odell/Starbird pp. 14-16
Homework due: 1.24-1.26
Presentations: 1.25, 1.26
Notes
Wednesday, 2/17: Exam 1
Friday, 2/19: The division algorithm, common divisors
Reading: Marshall/Odell/Starbird p. 16
Homework due: 1.27-1.30
Presentations: 1.27, 1.28
Notes
Monday, 2/22: Greatest common divisors, Euclidean Algorithm
Reading: Marshall/Odell/Starbird pp. 16-18
Homework due: 1.31-1.35; please also fill out this poll to sign up for
the next round of presentations
Presentations: 1.33-1.34
Notes
Wednesday, 2/24: Induction
Reading: Induction handout
Homework due: Begin your first Portfolio
entries
Presentations: Induction discussion
Notes
Friday, 2/26: Induction
Monday, 3/1: Induction
Wednesday, 3/3: Strong Induction
Friday, 3/5: Linear Diophantine equations
Reading: Marshall/Odell/Starbird pp. 18-19
Homework due: 1.36, 1.37, 1.39
Presentations: 1.37, 1.39
Notes
Monday, 3/8: Linear Diophantine equations
Reading: Marshall/Odell/Starbird pp. 19-20
Homework due: 1.40-1.43; first draft of portfolio entry
Presentations: 1.40, 1.43
Notes
Wednesday, 3/10: Linear Diophantine equations
Reading: Marshall/Odell/Starbird pp. 20-21
Homework due: 1.45, 1.48, 1.51
Presentations: 1.45, 1.48
Notes
Friday, 3/12: Linear Diophantine equations
Reading: Marshall/Odell/Starbird pp. 22-23
Homework due: 1.50, 1.53-1.55
Presentations: 1.53, 1.55
Notes
Monday, 3/15: Least common multiple
Reading: Marshall/Odell/Starbird pp. 23-25
Homework due: 1.56-1.58
Presentations: 1.57, 1.58
Notes
Wednesday, 3/17: Exam 2
Friday, 3/19: Re-assessment
Monday, 3/22: Primes
Reading: Marshall/Odell/Starbird pp. 27-29
Homework due: None
Notes
Wednesday, 3/24: Primes
Reading: Marshall/Odell/Starbird pp. 29-30
Homework due: 2.1, 2.3-2.5; please also fill out this poll to sign up for
the next round of presentations
Presentations: 2.1, 2.3
Notes
Monday, 3/29: Fundamental Theorem of Arithmetic
Reading: Marshall/Odell/Starbird pp. 30-31
Homework due: 2.7-2.9
Presentations: 2.7-2.9
Notes
Wednesday, 3/31: Applications of FTA
Reading: Marshall/Odell/Starbird pp. 31-32
Homework due: 2.10-2.15
Presentations: 2.12-2.15
Notes
Friday, 4/2: Applications of FTA
Reading: Marshall/Odell/Starbird p. 33
Homework due: 2.18-2.20
Presentations: 2.18, 2.19
Notes
Monday, 4/5: Applications of FTA
Reading: Marshall/Odell/Starbird p. 34
Homework due: 2.22, 2.23, 2.26, 2.27
Presentations: 2.26, 2.27
Notes
Wednesday, 4/7: Applications of FTA
Reading: Marshall/Odell/Starbird pp. 34-35
Homework due: 2.28-2.31
Presentations: 2.28, 2.31
Notes
Friday, 4/9: The infinitude of primes
Reading: Marshall/Odell/Starbird pp. 35-36
Homework due: 2.32-2.35
Presentations: 2.32, 2.33
Monday, 4/12: Mersenne and Fermat primes
Reading: Marshall/Odell/Starbird pp. 36-42
Homework due: 2.42-2.44
Presentations: 2.42, 2.43
Wednesday, 4/14: Exam 3
Friday, 4/16: Powers modulo n
Reading: Marshall/Odell/Starbird pp. 43-45
Homework due: 3.1-3.5
Presentations: 3.4, 3.5
Notes
Monday, 4/19: Residue systems
Reading: Marshall/Odell/Starbird pp. 47-48
Homework due: 3.14-3.17
Presentations: 3.14, 3.16, 3.17
Notes
Wednesday, 4/21: Linear Congruences
Reading: Marshall/Odell/Starbird pp. 48-49
Homework due: 3.18-3.20, 3.22
Presentations: 3.19, 3.20, 3.22
Notes
Friday, 4/23: Systems of linear Congruences
Reading: Marshall/Odell/Starbird pp. 49-50
Homework due: 3.24-3.27
Presentations: 3.24, 3.27
Notes
Monday, 4/26: Chinese remainder theorem
Reading: Marshall/Odell/Starbird pp. 51-54
Homework due: 3.28, 3.29, 4.1, 4.2
Presentations: 3.28, 3.29, 4.2
Notes
Wednesday, 4/28: The order of an integer modulo n
Reading: Marshall/Odell/Starbird p. 54
Homework due: 4.3, 4.4, 4.6
Presentations: 4.3, 4.4, 4.6
Notes
Friday, 4/30: Towards Fermat's Little Theorem
Reading: Marshall/Odell/Starbird p. 55-56
Homework due: 4.8-4.11
Presentations: 4.8-4.10
Notes
Monday, 5/3: Fermat's Little Theorem
Reading: Marshall/Odell/Starbird p. 56-58
Homework due: None
Notes