|keith.conrad at uconn dot edu. (When you send an email message, please identify yourself at the end.)|
|Office hours||1:30-3:00 PM T/Th in Mont 234 or by appointment.|
|Reading||We will use course handouts throughout the semester, not a textbook.|
1) Wolfram Alpha
lets you do a number of useful number theory calculations. A
list of some basic commands is here.
2) A standard computer algebra package for number theory computations is PARI. It can be downloaded (for free) at the PARI website here. An online page describing PARI commands is here. A reference card with PARI commands, suitable for printing out, can be downloaded here. You are not required to use PARI for this course, but it is fun to play around with it if you are interested.
Primes and Congruence Conditions
Squares Modulo Primes
Fermat's Little Theorem
Patterns in primes
The Infinitude of the Primes
Universal Divisibility Test (optional)
Analogies with Polynomials (updated)
Counting Roots of Polynomials
Unique Factorization in Z and F[T]
Divisibility and Greatest Common Divisors
The division algorithm in Z and F[T] (updated 2/4/2020)
Pell's Equation, I
Decimal Data (for homework 1)
Wolfram Alpha commands
Induction on the number of terms (updated 1/30/2020)
2/16: Office hours during week of 2/16 are T 2:30-3:30 and Th 1:00-3:00.
2/13: Second problem set due date changed to Feb. 22.
2/4: Handout on division algorithm updated.
1/30: Handouts on induction and division algorithm modified and reposted.
1/21: The semester begins.
Syllabus: We plan to cover the following topics.
Prerequisites: Math 2710. You are expected to know something about writing proofs, although the course itself will provide a lot of further practice. If you did not develop in Math 2710 some skill with expressing mathematical ideas well and writing proofs, then you need to focus some serious efforts in that direction early on.
Course grade: This will be based on the following weighting: homework (20%), quizzes (10%), first and second midterms (15% each), and final exam (40%). The lowest homework and quiz grade will be dropped. This includes a grade of 0 for a homework or quiz that is not submitted. Your lowest midterm exam score will be replaced with the average of the original score on that exam and your final exam score if it is higher (i.e., if it benefits you).
Homework: Homework assignments will be posted on the bottom of this web page, and are due at the time and place indicated on the assignment. No late homeworks will be accepted. Read the homework guidelines here and pay close attention to the rules about submissions. In particular, all homework must be prepared in LaTeX. Students will be provided with a LaTeX template file for each problem set. Information about LaTeX preparation is in the last homework bullet point below.
Quizzes and Exams: In weeks when homework is not due, there will be a quiz at the start of one class, usually on Thursdays. The purpose of quizzes is to provide you some feedback about how well you are following the basic ideas of the course. During the semester there will be two midterms (dates are at the top of this page).
- An integral part of each homework is the assigned reading from the handouts and the re-reading of your lecture notes. Focus on both explanations and examples.
- Homework will be done in student groups. The procedure will be discussed during class in the first week.
- It is a mistake to skip homework, because no skills (in mathematics, foreign language, athletics, and so on) can be learned by passive involvement, but only by regular practice. Moreover, many skills are learned over time, so do not expect to understand everything perfectly right away. You should find your understanding of basic topics improving gradually from one week to the next.
- Proofs on homeworks should not be simply a string of logical and mathematical symbols, but include complete sentences in English. The role of English is to explain the strategy of your proof and the details as well. There will not be partial credit based on having misunderstood a question.
- LaTeX preparation: If you want to download LaTeX for your laptop, a good LaTeX package for PCs (using Windows) is MiKTeX version 2.9, which can be downloaded here; download and run `miktex basic installer' (it takes a while to install). In the start menu of MiKTeX 2.9 you want to look for TeXworks and use that as your TeX interface. (An introductory TeXworks website is here, explaining a bit about it.) When typsetting a document with MiKTeX 2.9 for the first time, be sure to set pdftex to pdflatex. As a front-end for MiKTeX you can use TeXnicCenter.
Students in a homework group of more than one person can use the website Overleaf for collaborative LaTeX writing.Some resources for learning LaTeX are a short document by the instructor here and a longer document prepared by former UConn math major John Pawlina here. Both documents have hyperlinks in them, so if you don't see them try another browser.
- The quizzes will be short.
- You are not allowed to use any aids during the quizzes or exams.
- You might be asked to bring UConn photo ID to the quizzes or exams.
- There are no makeup quizzes or exams. If you miss a quiz or exam without a properly documented reason, your grade on it is 0.
- If you need accommodations based on a documented disability, you need to speak with both the Center for Student Disabilities and the course instructor within the first two weeks of the semester.
Attendance: Since you will be working in groups, your
workmates can get frustrated if you regularly skip class and
then cannot meaningfully contribute to the homework.
The best way to begin to learn the material is to
come to class without exception, see examples and
techniques discussed in real time, and
ask lots of questions. The way you should think about the material
will develop from the way it is presented in class.
To respect everyone's right to a productive learning
environment, please refrain from disruptive activities during
class. This includes using
Please turn off all other electronic gadgets before
entering the classroom (unless you take notes electronically). On a positive note, do feel free to ask
Academic integrity: Students are expected to avoid academic misconduct. Your integrity is not worth losing (and the course not worth failing) by falsely presenting yourself in any aspect of this course. For further information on academic integrity, see the Student Code.
|Due Week of||Homework Assignment|
|1. Jan. 19||
|2. Jan. 26
|3. Feb. 2||
|4. Feb. 9
|5. Feb. 16
|6. Feb. 23
|7. Mar. 1
|8. Mar. 8
|9. Mar. 15
||None (it's Spring Break).|
|10. Mar. 22
|11. Mar. 29
|12. Apr. 5
|13. Apr. 12
|14. Apr. 19
|15. Apr. 26