MATH-UA 248, Fall 2019: Theory of Numbers


Syllabus

Grading scheme

Assignments20%
Quizzes15%
Midterm25%
Final exam40%

Exam dates

Policies

Assignments

Assignments will usually be given on Wednesdays and due at the beginning of class the next Wednesday. You may also submit your assignment by putting it under the door of my office by 6PM Tuesday evening. If you do so, please let me know by email.

Collaboration is encouraged, but each student must write up their own solutions in their own words. If you work closely with someone else, please identify them on your assignment (e.g., "I worked with __________").

Late assignments will not be accepted except in the case of an emergency. At the end of the semester, your two lowest assignment grades will be dropped from your average. This is meant to accommodate non-emergency absences, so try not to use this unless you have to.

Solving problems is important! Doing exercises and understanding the assignments is the best way to master the material.

Computers

Laptop computers can be helpful for taking notes and doing research, but please be aware of the distraction they may cause to people behind you. If you choose to bring a computer to class, please follow these guidelines:

How to do well in this class


Problem sets


Course outline

09/04 Introduction, Well-Ordering Principle 1.1
09/09, 09/11 Divisibility, GCD 2.2, 2.3
09/16, 09/18 Euclidean Algorithm, \(ax+by=c\) 2.4, 2.5
09/23, 09/25 Primes and prime factorization 3.1-3.3
09/30, 10/02 Congruences and modular arithmetic 4.1-4.3
10/07, 10/09 Linear congruences and systems of congruences 4.4
10/15, 10/16 Fermat's Thm., Wilson's Thm. 5.2-5.3
10/21, 10/23 Number-theoretic functions, perfect numbers 6.1, 11.2
10/28, 10/30 Euler's theorem and the \(\phi\) function 7.2-7.3
11/04, 11/06 The \(\phi\) function, public-key cryptography 7.4, 10.1
11/11, 11/13 Primitive roots 8.1-8.2
11/18, 11/20 Quadratic reciprocity 9.1-9.2
11/25 Quadratic reciprocity 9.3
12/02, 12/04 Continued fractions and rational approximation 15.2-15.3
12/09, 12/11 TBA