|kconrad at math dot uconn dot edu. (When you send an email message, please identify yourself at the end.)|
|Office hours||MSB  318; W Th 12:30—1:30|
|Text||A Concrete Introduction to Higher Algebra, 3rd ed. (paperback), by Lindsay Childs. The author's website here has a link to an errata page for the latest edition of the book.|
An online calculator is available here
and you will need to use it during the course.
It was written by Joe Silverman for a number theory course he teaches
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 anyone with an interest in further study of number theory should definitely download PARI and play around with it.
Squares mod p, parts I , II, and III.
Square Applications, parts I and II.
Squares Modulo Primes, Table IV.
Squares Modulo Primes, Table III.
Squares Modulo Primes, Table II.
The original RSA paper.
Chinese remainder theorem.
Examples of induction for those who need a review.
Fermat's Compositeness Test
Primes and Congruence Conditions
Squares Modulo Primes
Moduli with a Generator for the Units
Universal Divisibility Test
Analogies with Polynomials
Divisibility and Greatest Common Divisors
The division theorem for integers and polynomials. (Note carefully the analogies in the two proofs.)
Homework groups and Homework rules
9/16: Some homework groups have changed and the new list is posted in place of the old list.
8/31: The semester begins!
Syllabus: We plan to cover the following topics, most of which are related to chapter headings in the textbook. (In some cases, there will be handouts to supplement the textbook.)
Prerequisites: Math 2710. In particular, you are expected to know something about writing proofs, although the course itself will provide a lot of further practice.
Homework: Homework assignments will be posted on the bottom of this web page. No late homeworks will be accepted.
Exams: There will be one midterm and a final.
- An integral part of each homework is the assigned reading from the text (or handout) 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.
- Each student's lowest homework grade is going to be dropped.
- You are encouraged to discuss homework problems with the instructor during office hours.
- 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.
- There are no makeup exams. If you miss the midterm, the grade is 0.
- You might be asked to bring UConn photo ID to the exams.
- If you need exam 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.
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 Appendix A of the Student Code.
|Due Week of||Homework Assignment|
|1. Aug. 31||
|2. Sept. 7
|3. Sept. 14
|4. Sept. 21
|5. Sept. 28
|6. Oct. 5
|7. Oct. 12
|8. Oct. 19|
|9. Oct. 26
|10. Nov. 2
|11. Nov. 9
|12. Nov. 16
|13. Nov. 23||
|14. Nov. 30
|15. Dec. 7
|16. Dec. 14||
Final Exam Week