Note:
Access to document files (lecture notes, exams, homework)
is restricted to
hosts from
.utexas.edu
or to user class with the appropriate password
(posted on Canvas).
Lectures (Tue Thu 11:00am - 12:15pm)
Lectures will be in-person,
except when the UT Administration decides to switch
in-person lectures to online lectures, for safety reasons.
But there may be a few other exceptions.
Any switch between in-person and online mode
will be communicated to the students via Canvas announcements.
In order to improve safety during the first 3 weeks,
I recommend that students whose last name starts with A,B,...,Me
only attend the in-person lectures on Tuesdays
(and watch the recordings of the Thursday lectures),
while students whose last name starts with Mi,...,N,...,Z
only attend the in-person lectures on Thursdays
(and watch the recordings of the Tuesday lectures).
Attending the lectures or viewing the recordings is mandatory.
Detailed lecture notes will be posted HERE one week in advance,
together with a list of topics for the upcoming two lectures.
The class lectures follow the lecture notes,
on a somewhat more basic level than the notes,
including summaries, previews, extra context, etc.
You are encouraged to ask questions, including homework-related questions.
In-person lectures in JGB 2.202 are recorded (voice and document camera)
during the time period when, as recommended above, half of the class attends
only the Tuesday lectures and the other half only the Thursday lectures.
These recordings are made available in Canvas.
Access is via the "Lectures Online" tab.
For Zoom lectures, the Meeting ID (the same for all lectures)
is posted on Canvas.
Login via your UT Account. Guest logins will not be allowed.
The lectures will be recorded and made available afterwards on Canvas.
(Active speaker with shared screen, participants' names.)
Access is via the "Zoom" tab, and from there "Cloud recordings".
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.
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 26: (course details,) integers; 1.1 in the notes.
- Tue Aug 31: mathematical induction, divisibility; 1.3 and 1.5 in the notes.
- Thu Sep 2: divisibility, greatest common divisor and linear combinations; 1.5 and 3.3 in the notes.
- Tue Sep 7: linear Diophantine equations; 3.5 in the notes.
- Thu Sep 9: prime factorization; 3.6 in the notes.
- Tue Sep 14: prime factorization, introduction to congruences; 3.6 and 4.1 in the notes.
- Thu Sep 16: introduction to congruences; 4.1 in the notes.
- Tue Sep 21: linear congruences; 4.2 in the notes.
- Thu Sep 23: the Chinese remainder theorem, some simple divisibility tests; 4.3 and 4.4 in the notes.
- Tue Sep 28: Midterm Exam 1.
- Thu Sep 30: some simple divisibility tests, Wilson's theorem; 4.4 and 5.1 in the notes.
- Tue Oct 5: theorems by Fermat and Euler; 5.3 in the notes.
- Thu Oct 7: The RSA cryptosystem, Mersenne primes; 6.1 and 6.2 in the notes.
- Tue Oct 12: Mersenne primes, Pseudoprimes; 6.2 and 6.3 in the notes.
- Thu Oct 14: Arithmetic functions, the Euler φ function; 7.0 and 7.1 in the notes.
- Tue Oct 19: the Euler φ function, the number and sum of divisors; 7.1 and 7.2 in the notes.
- Thu Oct 21: the number and sum of divisors, Möbius inversion; 7.2 and 7.4 in the notes.
- Tue Oct 26: Möbius inversion, the order of an integer and primitive roots; 7.4 and 9.1 in the notes.
- Thu Oct 28: Midterm Exam 2.
- Tue Nov 2: the order of an integer and primitive roots; 9.1 in the notes.
- Thu Nov 4: primitive roots for primes; 9.3 in the notes.
- Tue Nov 9: existence of primitive roots, index arithmetic; 9.3 and 9.4 in the notes.
- Thu Nov 11: index arithmetic; 9.4 in the notes.
- Tue Nov 16: qadratic (non)residues; 11.1 in the notes.
- Thu Nov 18: qadratic (non)residues, quadratic reciprocity; 11.1 and 11.2 in the notes.
- Tue Nov 23: quadratic reciprocity; 11.2 in the notes.
- Tue Nov 30: finite continued fractions; 12.1 in the notes.
- Thu Dec 2: infinite continued fractions; 12.3 in the notes.