Lectures are TTh 11:00-12:30
Before Spring break: RLM 5.120
After Spring break: online -- see below
Updated lecture notes and a syllabus are posted online -- see below.
The students are expected to read them before the lectures.
The online lectures will concentrate on:
summarizing old and new material,
explaining new concepts, solving extra problems,
answering questions, helping with homework problems, etc.
The online lectures are interactive video conferences using Zoom.
The Meeting ID will be posted ahead of time on
Canvas.
(Most likely Canvas sends out automatic announcements as well.)
Other information or updates are always posted
on the class web site
and (via link) on
Canvas.
Note:
Access to document files (lecture notes, exams, homework)
is restricted to
hosts from
.utexas.edu
or to user class with the appropriate password.
Lecture notes
Remarks:
The notes are cumulative.
The latest set should be considered work in progress,
so item numbers (theorem, equation, example) may change.
The others are "stable".
They are more suited for reference during discussions.
The indicated date is a kind of "target date",
by which the version is meant to be stable.
Content:
The notes start with Section 7 on multiplicative functions.
So the beginning covers roughly a week worth of material
from before the Spring break.
The sections and subsection in the notes
correspond to those in the textbook.
But the item numbers (theorem, equation, example)
differ from those in the textbook.
Syllabus
After induction, divisibility, prime numbers,
fundamental theorem of arithmetic;
congruences, applications,
Chinese remainder theorem, Euler theorem;
arithmetic functions (7.0 in the notes),
we arrived at
- Thu Feb 12: Multiplicative functions; 7.1 in the notes.
- Tue Feb 31: Number and sum of divisors; 7.2 in the notes.
- Thu Apr 2: midterm exam 2
- Tue Apr 7: Mersenne primes, Möbius inversion; 7.3 and 7.4 in the notes.
- Thu Apr 9: Möbius inversion, RSA cryptosystem; 7.4 and 8.4 in the notes.
- Tue Apr 14: The order of an integer and primitive roots; 9.1 in the notes.
- Thu Apr 16: Primitive roots for primes, existence of primitive roots; 9.2 and 9.3 in the notes.
- Tue Apr 21: Index arithmetic; 9.4 in the notes.
- Thu Apr 23: Quadratic (non)residues; 11.1 in the notes.
- Tue Apr 28: Quadratic residues and reciprocity; 11.1 and 11.2 in the notes.
- Thu Apr 30: Quadratic reciprocity, real numbers; 11.2 and 12.0,2 in the notes.
- Tue May 5: Finite continued fractions; 12.1 in the notes.
- Thu May 7: Infinite continued fractions; 12.3 in the notes.