Math 124, Elementary Number Theory
Time and Place: MWF 11:00am in Science Center 310.
Instructor: Nathan Dunfield
- Course Assistant: Lionel Levine
- E-mail: firstname.lastname@example.org.
- Section: Monday at 7pm in SC 101b.
- Office Hour: Thursdays from 4-5 in Loker Commons.
Elementary Number Theory is about properties of the integers
(natural numbers). We will cover most of the text. Topics include:
Factorization and the primes, congruences, quadratic residues and
reciprocity, continued fractions and approximations, Pell's equation,
selected Diophantine equations, theory of integral quadratic forms,
number theory and cryptography.
Davenport: The Higher Arithmetic, 6th ed. The 6th ed is out of
print, but the Coop is selling fancy photocopies. If you manage to
get hold of the 7th ed, that will be fine (though you should
photocopy the problem list from the 6th ed in case they've added
problems and so changed the numbering).
Other useful books
Davenport is the only required text. If you're interested in
additional sources, a couple books that cover similar material are: At
a lower, less rigorous, level than Davenport, there's Joseph
Silverman's A Friendly Introduction to Number Theory. At a
more mathematically sophisticated level, there's Ireland & Rosen's
A Classical Introduction to Modern Number Theory. Both are
published by Springer-Verlag (and are therefore expensive).
Formally, Math 122. In reality, any upper-level proof based math
course should do (e.g. 25, 55, 101, 112, etc.), but if you haven't
taken 122 you should talk to me before signing on. This should
not be your first higher-level math course.
There will a midterm exam on March 17. If people do poorly on the
midterm, there will be a second midterm latter in the semester. The
final exam will a take home exam, and the exact dates will be
announced later. It will probably be either the last week of class or
the first week of reading period. Makeup exams will only be given in
cases of extreme human tragedy.
There will be one HW assignment per week, which will be assigned on
Wednesday and due the next Wednesday. Homework assignments must be
turned in on time -- no late homework will be accepted. However, your
lowest homework grade will be dropped. Homework assignments will be
posted on the course web page.
You are allowed, nay encouraged, to work together on homework
problems. However, you must write up your solutions individually.
Homework will be worth 30% of the final grade, the midterm(s) 30% and
the final 40%.
In addition to the times above, I am available by appointment. For an
appointment, just talk to me before/after class or send me e-mail.
Lionel's office hours and section times are at the top of the page.
There will be open ended problems on the HW for which it will be
useful to do experiments in order to find the correct statement to
prove. (In fact, much of number theory was motivated by experiments).
For this purpose, it's a good idea to have a "lab" to do the
experiments in. The computer program Mathematica is a good
tool, or a scientific calculator that can do modular arithmetic.
(Mathematica is available in the public computer labs, and you
can install it on any computer connected to the university network
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