Jen Paulhus, Ph.D.

Elementary Number Theory

email: paulhus@math.grinnell.edu     pgp key
Office Hours: Mon. 9AM - 9:50AM, Tue. 3:30PM - 4:30PM, Thu. 9AM - 10AM, Fri. 11AM - 12PM
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 our 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
Aug. 30 1.1 1-5
Sep. 2 1.2, how to read mathematics 7-9
Sep. 4 1.3 11-12
Sep. 6 1.3 15
Sep. 9 1.3, 1.4 14, 16-17
Sep. 11 1.4, 1.5 17-18, 23-25
Sep. 13 1.5, 1.6 25, 27-30
Sep. 16 1.6,1.7 31, 32-34
Sep. 18 1.7, 1.8 34-35, 37-39
Sep. 20 1.10 45-49
Sep. 23 basic counting
Sep. 25 1.9 41-44
Sep. 27 1.11 51-55
Sep. 30 equivalence relations 63-65
Oct. 2 Exam 1 1.1-1.10, induction, basic counting
Oct. 4 2.1, 2.2, 1.4 (greatest integer) 63-71, 19-21
Oct. 7 binomial theorem
Oct. 9 2.2, 2.3 71-74, 76-77
Oct. 11 how to fail at math PWeb readings
Oct. 14 2.3, 2.4 78-81
Oct. 16 2.4 82-83
Oct. 18 2.5 84-87
Oct. 28 major, 2.5 87-88
Oct. 30 inclusion-exclusion *
Nov. 1 Exam 2 1.11, 2.1- 2.4, greatest integer function, binomial theorem, combinations ("n choose k") and related counting problems, equivalence relations
Nov. 4 2.6 90-92
Nov. 6 2.6, 7.1 92-93, 227-230
Nov. 8 2.5, 7.1, 7.2 88, 231-236
Nov. 11 7.2, 7.3 236-238, 244
Nov. 11 inc/exc recap
Nov. 15 3.1 103-107
Nov. 18 3.2 108-110
Nov. 20 no class chemicals needed to be evacuated!
Nov. 22 3.3 112-114
Nov. 25 3.4, 3.6 118-121, 128-129
Nov. 27 Exam 3 2.4- 2.6, 3.1- 3.2, inclusion-exclusion, parts of 7.1-7.4
Dec. 2 3.6, 3.8 129-132, 142 (Theorem 3.8.1 statement only)
Dec. 4 4.1 145-150 (Plus small reading)
Dec. 6 4.3 157-162
Dec. 9 4.3 163-164
Dec. 11 4.3 165-166
Dec. 13 infinity
* Notes on Inclusion-Exclusion.

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 the time class starts, unless you LaTeX the solutions and are in class on time the day the homework is due. Then it should be submitted on PWeb by 7 PM that day.

Blue problems below must be done alone.

HW Due Date Problems
# 0 Sep. 2 Email me with answers from class 8/30, and read syllabus
# 1 Sep. 6 [pdf]
# 2 Sep. 11 * [pdf]
# 3 Sep. 16 [pdf]
# 4 Sep. 20 [pdf]
# 5 Sep. 25 [pdf]
# 6 Sep. 30 [pdf]
# 7 Oct. 9 ** [pdf]
# 8 Oct. 14 [pdf]
# 9 Oct. 18 [pdf]
# 10 Oct. 30 [pdf]
#11 Nov. 6 *** [pdf]
#12 Nov. 11 [pdf]
#13 Nov. 15 [pdf]
#14 Nov. 20 [pdf]
#15 Nov. 25 [pdf]
#16 Dec. 6 [pdf]
#17 Dec. 13 [pdf]     (last updated: 12/7)

   * Some extra induction problems.

  ** This will be the last assignment where rewrites will be allowed.

*** Some extra inclusion-exclusion problems.