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 11:00 am - 12:30 pm, in PMA 5.118
Attending classes is mandatory.
Lecture notes will be posted below 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.
Students are encouraged to ask questions, including homework-related questions.
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
- Tue Jan 10: (course details,) integers; 1.1 in the notes.
- Thu Jan 12: mathematical induction, divisibility; 1.3 and 1.5 in the notes.
- Tue Jan 17: greatest common divisor and linear combinations, Euclidean algorithm; 3.3 and 3.4 in the notes.
- Thu Jan 19: linear Diophantine equations; 3.5 in the notes.
- Tue Jan 24: prime factorization; 3.6 in the notes.
- Thu Jan 26: prime factorization, introduction to congruences; 3.6 and 4.1 in the notes.
- Tue Jan 31: classes cancelled.
- Thu Feb 2: classes cancelled.
- Tue Feb 7: introduction to congruences; 4.1 in the notes.
- Thu Feb 9: midterm exam 1.
- Tue Feb 14: linear congruences; 4.2 in the notes.
- Thu Feb 16: the Chinese remainder theorem, some simple divisibility tests; 4.3 and 4.4 in the notes.
- Tue Feb 21: some simple divisibility tests, Wilson's theorem; 4.4 and 5.1 in the notes.
- Thu Feb 23: theorems by Fermat and Euler; 5.3 in the notes.
- Tue Feb 28: the RSA cryptosystem, Mersenne primes; 6.1 and 6.2 in the notes.
- Thu Mar 2: pseudoprimes; 6.3 in the notes.
- Tue Mar 7: arithmetic functions, the Euler φ function; 7.0 and 7.1 in the notes.
- Thu Mar 9: the Euler φ function, the number and sum of divisors; 7.1 and 7.2 in the notes.
- Tue Mar 21: the number and sum of divisors, Möbius inversion; 7.2 and 7.4 in the notes.
- Thu Mar 23: midterm exam 2.
- Tue Mar 28: Möbius inversion, the order of an integer and primitive roots; 7.4 and 9.1 in the notes.
- Thu Mar 30: the order of an integer and primitive roots; 9.1 in the notes.
- Tue Apr 4: primitive roots for primes; 9.2 in the notes.
- Thu Apr 6: existence of primitive roots; 9.3 in the notes.
- Tue Apr 11: index arithmetic; 9.4 in the notes.
- Thu Apr 13: qadratic (non)residues; 11.1 in the notes.
- Tue Apr 18: quadratic reciprocity; 11.2 in the notes.
- Thu Apr 20: finite continued fractions; 12.1 in the notes.