Jen Paulhus, Ph.D.

Elementary Number Theory

email: paulhus@math.grinnell.edu     pgp key
Office Hours: Monday 11:00-11:30, Tuesday 1:30-2:30, Wednesday 11:00-11:30, Thursday 2:00-3:00, or by appointment
Office: 2519 Noyce Science Center

Text: Explorations in Number Theory, Jeanne Agnew
Material Covered: Chapters 1-4, 7

The primary goal of this course is to prepare students for the 300 level mathematics courses and beyond. We use number theory as a backdrop to discuss how to think about mathematics, how to read mathematical writings, and how to write good mathematics.

Syllabus

Homework

Daily Topics

Class Date Section Pages Other Notes
Aug. 26 1.1 v-vi, 1-5
Aug. 29 1.2, how to read mathematics 7-9 Reading Report 1 (due night before)
Aug. 31 1.3 11-12, 15
Sep. 2 1.3, 1.4 13-15, 16-17 Reading Report 2 (due night before)
Sep. 5 1.4, 1.5 17-18, 22-25 Questions?
Sep. 7 1.5, 1.6 25, 27-30 Reading Report 3 (due night before)
Sep. 9 1.6,1.7 31, 32-34 Questions?
Sep. 12 1.7, 1.8, homework tips 34-35, 37-39 Reading Report 4 (due night before)
Sep. 14 1.10 45-49 Questions?
Sep. 16 basic counting, how to prepare for exams Reading Report 5 (due night before)
Sep. 19 1.9 41-43 Questions?
Sep. 21 1.11 51-54 Reading Report 6 (due night before)
Sep. 23 Exam 1 1.1-1.8, 1.10, induction, basic counting
Sep. 26 σ(n) and equivalence relations 53-54 (again), 63-65 Questions?
Sep. 28 2.1, 2.2 66-71 Reading Report 7 (due night before)
Sep. 30 math cultural norms, more counting see PWeb "Daily Topics and Homework" Questions?
Oct. 3 binomial theorem, 2.2, 2.3 72-74, 76-77 Reading Report 8 (due night before)
Oct. 5 should you take more math classes?, 2.4 What it feels like to be bad at math , 79-81 Questions?
Oct. 7 2.3 76-77 Reading Report 9 (due night before)
Oct. 10 2.3, 2.4 78-82 Questions?
Oct. 12 2.4, 2.6 82-83, 90-91 Reading Report 10 (due night before)
Oct. 14 2.6 91-93 Questions?
Oct. 24 Jen and Isidora Try to Solve Number Theory Problems no reading Questions?
Oct. 26 Exam 2 1.9, 1.11, 2.1- 2.4, binomial theorem, combinations ("n choose k") and related counting problems, equivalence relations
Oct. 28 Inclusion/Exclusion Morris section 10.2 Questions?
Oct. 31 more inc/exc, 3.1 104-105 Questions?
Nov. 2 Nov. 4 3.1,3.2 106-110 Reading Report 11 (due night before)
Nov. 7 3.2, 3.3 110, 112-114 Questions?
Nov. 9 3.4 118-121 Reading Report 12 (due night before)
Nov. 11 3.6, 128-129 Questions?
Nov. 14 3.6, 3.8 130-132, 142 (Theorem 3.8.1 statement only) Questions?
Nov. 16 2.5 84-88 Reading Report 13 (due night before)
Nov. 18 7.1 227-231 Questions?
Nov. 21 Exam 3 2.6, 3.1- 3.4, 3.6, 3.8, inclusion-exclusion
Nov. 23 7,2 233-238 (especially convolution) Reading Report 14 (due night before)
Nov. 28 4.1, 4.3 145-148, 157-159 Questions?
Nov. 30 4.3, 1.4 161-162 (part (1) and (2) of proof), 19-21 (greatest integer function) Reading Report 15 (due night before)
Dec. 2 4.3 162-163 Questions?
Dec. 5 4.3 164-166 Reading Report 16 (due night before)
Dec. 7 infinity
Dec. 9 RSA public key cryptosystem

Homework Assignments

Make sure you are familiar with the Grading Policies and Rubric for the class. Homework solutions will be posted on Pweb. Homework is due by 9:45 AM, unless you LaTeX the solutions and are in class the day the homework is due. Then it should be submitted on PWeb by 7 PM that day.

HW Due Date Problems
# 1 Aug. 31 [pdf]
# 2 Sep. 5 [pdf]
# 3 Sep. 9 [pdf]
# 4 Sep. 14 [pdf]
# 5 Sep. 19 [pdf]
# 6 Sep. 26 [pdf]
# 7 Sep. 30 [pdf] and reflection 1
# 8 Oct. 5 [pdf]
# 9 Oct. 10 [pdf]
# 10 Oct. 14 [pdf]
# 11 Oct. 31 [pdf]
# 12 Nov. 4 Nov. 7 [pdf]
# 13 Nov. 11 [pdf]
# 14 Nov. 18 [pdf]
# 15 Nov. 28 [pdf]
# 16 Dec. 2 [pdf]
# 17 Dec. 9 TBA

   * Some extra induction problems.