Note:
Access to document files (lecture notes, exams, homework)
is restricted to
hosts from
.utexas.edu
or to user class with the appropriate password.
Lectures are Tue Thu 11:00-12:30
They are held online via interactive Zoom sessions.
The Meeting ID will be posted ahead of time on
Canvas.
(Most likely Canvas sends out automatic announcements as well.)
Login via your UT Account as
described here.
Guest logins will not be allowed.
The lectures will be recorded and made available afterwards
on Canvas.
(Active speaker with shared screen, participants' names.)
Class recordings are reserved only for students in this class
for educational purposes and are protected under FERPA.
The recordings should not be shared outside the class in any form.
Violation of this restriction by a student could lead to Student Misconduct proceedings.
The online lectures follow the lecture notes,
on a somewhat more basic level than the notes,
including summaries, previews, extra context, etc.
There is time for answering questions, including homework-related questions.
There may be some "poll" questions during lectures
to test basic understanding.
Updated lecture notes (and a syllabus) are posted here.
Students are strongly encouraged to read them before the lecture.
Lecture notes
Remarks:
The notes are cumulative.
The latest set should be considered work in progress,
so the numbers assigned to theorems, equations, and examples may change.
The indicated date is something like a "target date",
by which the version is meant to be stable.
The sections and subsections in the notes
correspond mostly to those in the textbook.
But the theorems, equations, examples,
and their numbers can differ from the textbook.
Syllabus
- Thu Aug 27: (course details,) integers; 1.1 in the notes.
- Tue Sep 1: mathematical induction; 1.3 in the notes.
- Thu Sep 3: divisibility, greatest common divisor and linear combinations; 1.5 and 3.3 in the notes.
- Tue Sep 8: the Euclidean algorithm, linear Diophantine equations; 3.4 and 3.5 in the notes.
- Thu Sep 10: linear Diophantine equations, primes; 3.5 and 3.6 in the notes.
- Tue Sep 15: prime factorization; 3.6 in the notes.
- Thu Sep 17: prime factorization, introduction to congruences; 3.6 and 4.1 in the notes.
- Tue Sep 22: introduction to congruences; 4.1 in the notes.
- Thu Sep 24: linear congruences; 4.2 in the notes.
- Tue Sep 29: midterm Exam 1.
- Thu Oct 1: the Chinese remainder theorem; 4.3 in the notes.
- Tue Oct 6: some divisibility tests, Wilson's theorem; 4.4 and 5.1 in the notes.
- Thu Oct 8: Wilson's theorem, theorems by Fermat and Euler; 5.1 and 5.3 in the notes.
- Tue Oct 13: theorems by Fermat and Euler, the RSA cryptosystem; 5.3 and 6.1 in the notes.
- Thu Oct 15: Mersenne primes, pseudoprimes; 6.2 and 6.3 in the notes.
- Tue Oct 20: pseudoprimes, Pollard's p-1 method; 6.3 and 6.4 in the notes.
- Thu Oct 22: arithmetic functions, the Euler φ function; 7.0 and 7.1 in the notes.
- Tue Oct 27: the Euler φ function, the number and sum of divisors; 7.1 and 7.2 in the notes.
- Thu Oct 29: midterm Exam 2.
- Tue Nov 3: Möbius inversion; 7.4 in the notes.
- Thu Nov 5: the order of an integer and primitive roots; 9.1 in the notes.
- Tue Nov 10: primitive roots, primitive roots for primes; 9.1 and 9.2 in the notes.
- Thu Nov 12: primitive roots for primes, existence of primitive roots; 9.2 and 9.3 in the notes.
- Tue Nov 17: existence of primitive roots, index arithmetic; 9.3 and 9.4 in the notes.
- Thu Nov 19: index arithmetic, quadratic (non)residues; 9.4 and 11.1 in the notes.
- Tue Nov 24: quadratic (non)residues, quadratic reciprocity; 11.1 and 11.2 in the notes.
- Tue Dec 1: quadratic reciprocity; 11.2 in the notes.
- Tue Nov 3: finite continued fractions; 12.1 in the notes.