## Colorado State University, Pueblo; Spring 2012 Math 419 — Number Theory Course Schedule & Homework Assignments

Shortcuts:

• Wiki is a link to the class wiki (which is open only to registered students in the class).
• Syllabus is a link back to the course syllabus/policy page.
In the following all chapters, sections, and page numbers refer to the required course textbook, A Friendly Introduction to Number Theory (3rd edition), by Joseph H. Silverman.

This schedule is will be changing very frequently, please check it at least every class day, and before starting work on any assignment (in case the content of the assignment has changed).

• M:
• W:
• Read: Chapter 3, SCLs are:
• Angela
• Glen
• Content:
1. rational equations versus integral equations
2. working through the proof of Theorem 3.1 quite carefully
3. relationship of the proof to the idea of parameterizing the circle in an unusual way — not by angle, which would be hard to turn into a condition which measures when that point on the circle has rational coordinates, but by drawing a line and seeing where it intersects the circle. This is like the process of stereographic projection, which is used to identify the sphere with the plane.
4. notice a connection between a geometric and a suitably defined number theoretic problem!
• Submit T&Q4 on Chapter 3
• due today:
• SCLs: CCT Chapter 2
• nonSCLs: HW2 = {2.1, 2.2}
• F:
• Read: Chapter 3, SCLs are still
• Angela
• Glen
• Content:
2. discussion of problems 3.1, 3.2 (also 2.7 and 2.8, time permitting; for 2.8, see this page)
• Submit T&Q5 on Chapter 3

• M:
• Read: Chapter 8, SCLs are:
• ...still the huddled masses, yearning to be free...
• Content:
1.
• Submit T&Q14 on Chapter 8
• due today:
• some contribution to CCT Chapter 7 (from everyone since there are no particular SCLs at the moment)
• HW6 = {7.1, 7.2, 7.5} (from everyone)
• W:
• Review for Midterm I
• due today:
• some contribution to CCT Chapter 8 (from everyone!)
• HW7 = {8.1, 8.2} (from everyone)
• F:
• Midterm I, In-class part

• M:
• Midterm I
• going over Midterm I
• W:
• hand in Midterm I revisions, if you like
• Submit T&Q15 on Chapter 9
• F:
• Submit T&Q16 on Chapter 9

• M:
• Submit T&Q17 on Chapter 10
• W:
• due today:
• some contribution to the wiki
• HW8:
1. Give two proofs of the following statement: "If $p$ is prime then $k^p\equiv k\mod{p}\ \forall k\in\ZZ$", as follows
1. A very easy one based on Fermat's Little Theorem.
2. A slighty more computational one, which uses the binomial theorem and a careful analysis of the binomial coefficients $\begin{pmatrix} p\\j\end{pmatrix}$  when $p$ is prime and $1\le j\le p-1$.
2. Prove the statement "$\forall n\in\ZZ$ if $n$ is not a multiple of $17$, then either $n^8+1$ or $n^8-1$ is divisible by $17$."
3. problem 10.1 in the textbook
• Submit T&Q18 on Chapter 11
• please contribution to the wiki!
• F:
• Submit T&Q19 on Chapter 11
• please contribution to the wiki!

• M:
• W:
• Submit T&Q21 on Chapter 13
• please contribution to the wiki!
• F:
• Submit T&Q22 on Chapter 14
• please contribution to the wiki!
• start HW10, which will be due on Monday
• Today [Friday] is the last day to withdraw (with a W) from classes

• Spring Break! No classes, of course.

• M:
• W:
• more review for Midterm II
• please have handed in all outstanding HW assignments and be ready to discuss those (and other) problems
• F:
• Midterm II