Description and Syllabus

Math 470 is a capstone course for math majors with a secondary education emphasis. It aims to be a course in mathematics, as opposed to a course in a topic of mathematics. What is meant by this is that the course is one where the central topics of mathematics - geometry, algebra and analysis - come together in a historically coherent and unifying narrative.
• We will meet on MWF from 2.30-3.20 in Roop 213.
• Office hours are MWF 9.35-9.55, 1.50-2.15 in Roop 323. I will also come to Roop 213 15 minutes before the start of class at 2.15.
• A syllabus is here.
• Some tips on how to write mathematics.

Homework

All assignments refer to "Mathematics for Secondary Teachers" text unless indicated otherwise by [G] for Gems or [O] for Origins.

• For 1/14: Reading: Sections 1.1 and 1.2. "Thales" in [G]. Do all exercises in these sections.
• For 1/16: Reading: Sections 1.3 and 1.4. "Pythagoras" in [G].
  • 1.3: 1,2,6,8,9,10.
  • 1.4: 1,3,5,8,9,12,14.
• For 1/19 and 1/21: Reading: Sections 1.5, 1.6 and 1.7. "Democritus" and "Euclid" in [G].
  • 1.5: 1,2,3,9,10,11,12,14.
  • 1.6: 1,2,4,8,10,11,13,15-19.
  • 1.7: 2-5, 10,12,13,18.
• For 1/23: Reading: Sections 2.1 and 2.2. "Archimedes" in [G].
  • All: Flesh out details of part (c) of 10 in 1.5.
  • 2.1: 1,2,5.
  • 2.2: 2,3,7,10,12-14,16-18.
• For 1/26: Reading: Sections 2.3 and 2.4. Next bio in [G].
  • All (from last class): Flesh out details of 17 in 2.2, especially the graphical interpretation of the inverse function of the line, looking again at 1.6.
  • 2.3: (1,2), 4,5, 6,7. (the notation (a,b,c,..) means a,b,c,.. are v. short and grouped as one question)
  • 2.4: (1,2),(3,4),6,7,10, 17+18 (17+18 shared between no.s 11,12,13).
• For 1/30: Reading: Sections 2.3 and 2.4 again. Discussion on ALL Bios from [G], read thus far.
  • Same as last day, tying up the loose ends.
  • Prepare three discussion points on each biography from [G].
• For 2/2: Reading: Sections 2.5 and 2.6. Next Bio from [G].
  • 2.5: (4,5), (6,10),(11,15), 14, (17,20), 18,19, 23.
  • 2.6: 1,2,4,5,6.
• For 2/4: Reading: Section 2.6. Next Bio from [G].
  • 2.6: 1,2,4,5,6.
• For 2/6: Reading: Sections 2.8 and 3.1. Next Bio from [G].
  • 2.8: (everyone) All samples.
  • 3.1: All questions, assigned in order
• For 2/9: Reading: Section 3.2.
  • 3.2: All six questions, two people responsible for each question.
• For 2/11: Reading: Section 3.3.
  • Take Home Exam assigned today. Due Monday (in LaTeX)
  • 3.3: 5,6,7,9,14,(15,16),18,19,20,21,23,24,26.
• For 2/13: LaTeX Day.
  • SAMPLE FILES POSTED HERE SOON.
• For 2/16: (moved to 2/18 because of snow) Biographies from Caluclus Gems Day
• For 2/20: Reading: Section 3.5. Section 3.4 of [O], that is, Origins.
  • 3.5: Your turn 18,19,20. All ten questions that follow.
• For 2/23: Reading: Sections 3.2,3.3,3.4 of [O], that is, Origins.
  • Questions from 3.5 of [O]: Q.3.1, Q.3.3, Q.3.4.
• For 2/25: (We'll come to Origins again later)
  Reading: Sections 4.1, and 4.2.1 and 4.2.2 only of 4.2.
  • 4.1: (1,2),(3,4),(5,6),(7,8),9,10,11,12,13.
  • 4.2: (1,2),(3,4),(5,6),(7,8).
• For 2/27: Reading: Remainder of 4.2 plus all of 4.3. Pick your three favourite questions, ones that you'd like to share emost with a future high school student.
• For 3/2: Reading: Section 4.4. Pick your three favourite questions, ones that you'd like to share emost with a future high school student.
• For 3/4: Reading: Section 4.5. Pick your three favourite questions, ones that you'd like to share emost with a future high school student.
• For 3/6: Reading: Section 4.6. Pick your three favourite questions, ones that you'd like to share emost with a future high school student.
• For 3/16: Reading: Sections 4.7 and 4.8. Pick your three favourite questions, ones that you'd like to share emost with a future high school student.
• For 3/18: Reading: Section 10.1 and all the problems.
• For 3/20: Reading: Section 10.2 and all the problems.
• For 3/23: Reading: Section 10.2 and all the problems (again) and sections 5.1,5.2 and 5.3 from Origins.
• For 3/25: Test is now due on Monday, 3/30.
  Reading: Sections 5.1,5.2 and 5.3 (again) from Origins, as well as Section 5.4.
  • Origins 5.5 Questions 1, 2, and 3. Read 4 and 5 as a complement to Section 10.1 of the main text.
• For 3/27: No class.
• For 4/1: Reading: Section 10.3 and all the problems.
• For 4/3: Reading: Section 10.4 and all the problems.
• For 4/6: Reading: Sections 2.1 and 2.3 of Origins. Be ready to present 2.1 and 2.3 to each other in groups in class.
  • Exercises (from Section 2.5) 2.3 and 2.4. How did you justify Exercise 2.4 before this class? Hop does the claimed result help you compute the area underneath (and between the x-axis) the power functions?
• For 4/8: Reading: Section 2.4 (the approximation of pi) from Origins. It's a careful, slow read. The results of 2.1 and 2.3 both make star turns.
• For 4/10: Reading: Sections 6.1 and 6.2. On Page 78, why can we think of "we can find the rectangle DEGH having area equal to that of DEFB" as a sort of mean value theorem? Also, Eqn 6.1 should read 'horizontal AD'
  • Exercises 6.2 (a,b only). Exercise 6.5 (a,b,c only).
• For 4/13: Reading: Sections 6.3 of Origins. Do problem 6.6 (a,b,c,d only) of Origins.
  • Draw a lot of pictures in color for understanding the transmutation theorem. By starting to look at the HW due for Friday, try to get a feel for the boundary of how far the translutation theorem can get you. For example, section 6.4 says it's great for circles, but what about for power functions? for exponentials? etc.
• For 4/15: Reading: Sections 6.4 of Origins and B.13 of Gems. Contrast and compare the classical and slightly more modern notation in each respective presentation.
  HW, sent my email, is also due in class.