Math 105 (Basic Number Theory)

Contact information

• Instructor: Aaron Pollack; apollack@ucsd.edu
• TA: Finley McGlade fmcglade@ucsd.edu

Office hours

• Pollack: Thursdays 11am-1pm
• McGlade: Fridays 2pm-4pm

Syllabus

Lecture Topics

Recorded lectures can be found on Canvas

• Monday 3 January: Introduction to course (Chapter 1.1, 1.2) Lecture 1
• Wednesday 5 Janurary: Introduction to course; the Euclidean algorithm (Chapter 2.1) Lecture 2
• Friday 7 Janurary: Euclidean algorithm and gcds(Chapter 2.1) Lecture 3
• Monday 10 Janurary: Gcds and unique factorization (Chapter 2.1, Chapter 2.2) Lecture 4
• Wednesday 12 Janurary: Applications of unique factorization; multiplicative functions (Chapter 2.3, 2.4) Lecture 5
• Friday 14 Janurary: Multiplicative functions; linear diophantine equations (Chapter 2.4, 2.5) Lecture 6
• Monday 17 Janurary: No lecture (MLK day)
• Wednesday 19 Janurary: linear diophantine equations, congruences (Chapter 2.5, 3.1, 3.2) Lecture 7
• Friday 21 Janurary: congruences (Chapter 3.2) Lecture 8
• Monday 24 Janurary: congruences; linear congruence equations (Chapter 3.2, 3.3) Lecture 9
• Wednesday 26 Janurary: linear congruence equations (Chapter 3.3) Lecture 10
• Friday 28 Janurary: No lecture (Exam 1)
• Monday 31 Janurary: Reduced residue systems and Euler's totient function (Chapter 3.4) Lecture 11
• Wednesday 2 February: More on Euler's totient function and polynomial congruences (Chapter 3.5, 3.6) Lecture 12
• Friday 4 February: polynomial congruences (Chapter 3.6) Lecture 13
• Monday 7 February: polynomial congruences and primitive roots (Chapter 3.6, 3.7) Lecture 14
• Wednesday 9 February: primitive roots (Chapter 3.7) Lecture 15
• Friday 11 February: primitive roots, Diophantine equations (Chapter 3.7, 5.1) Lecture 16
• Monday 14 February: Diophantine equations via congruences; Pythagorean triples (Chapter 5.2, 5.3) Lecture 17
• Wednesday 16 February: The technique we applied to Pythagorean triples (Chapter 5.3) Lecture 18
• Friday 18 February: Techniques for Diophantine equations (Chapter 5.3) Lecture 19
• Monday 21 February: No lecture (Presidents Day)
• Wednesday 23 February: Fermat's method of descent (and ascent) (Chapter 5.4) Lecture 20
• Friday 25 February: No lecture (Exam 2)
• Monday 28 February: The decimal expansion of rational numbers (Chapter 6.1) Lecture 21
• Wednesday 2 March: Irrational and transcendental numbers (Chapter 6.2, 6.3) Lecture 22
• Friday 4 March: transcendental numbers, magic squares, the uniform step method (Chapter 6.3, 4.1) Lecture 23
• Monday 7 March: the uniform step method, filled squares (Chapter 4.1, 4.2) Lecture 24
• Wednesday 9 March: magic rows and columns (Chapter 4.2) Lecture 25
• Friday 11 March: Sums of two squares Lecture 26

Homework Assignments

Homework is due by 10:00pm Pacific time on Gradescope on the days listed below

• Friday January 14th Homework 1
• Friday January 21st Homework 2
• Friday January 28th Homework 3
• Friday February 4th Homework 4
• Friday February 11th Homework 5
• Friday February 18th Homework 6
• Friday February 25rd Homework 7
• Friday March 4th Homework 8
• Friday March 11th: There is not a HW 9

Exams

• Exam 1: Friday January 28th Review Problems
• Exam 2: Friday February 25th Review Problems
• Final Exam: Friday March 18th Review Problems, Hints and solutions