Homework assignments, Foundations of Adv. Math

Section 1 (Janeba), Fall 2009

Links of general interest.  Class handouts.

• Sept. 2:
• Write a 2-3 page STIX II strategy guide.  Submit to turnitin.com and bring hardcopy to class.
• Read syllabus for Friday quiz
• Read handout (through section 1.1, i.e. the whole handout)
  
• Sept. 4:  Read section 1.2 (handout), do 1.1 #1-6
  

• Sept. 9:
• STIX II paper returned today, rewrite and resubmit by Friday, both to turnitin.com and in hardcopy to class.
• Read section 1.3 (class handout)
  
• Do 1.1 #7, 1.2 #1, 1.3 #1
  
• Sept. 11: Do 1.3 #2a,b,c,d,3,5a,c,e,f, read 1.4 (handout)
  

• Sept. 14: Do 1.4 #1-3,4a-g,5,7,8a
  
• Journals collected today
  
• Sept. 16:  Read 1.5, do 1.4 #8bc,9,10 and 1.5 #1,3,4a-d,5
  
• Turn in 1.1#2,4    1.2#1bdefh  1.3 #5ac(and 1.3#2a extra credit if you like)
• Sept. 18: Read 1.6 (handouts), do 1.6#1-7,9-14
  

• Sept. 21: Read 2.1, do 2.1 #1-3,5,6  (copies of the 2.1 handout tacked next to my office door, pick up one)
  
• Sept. 23: Do 2.1 #8ac,10,11,13 and read 2.2
  
• Sept. 25: Quiz today; Do 2.2 #1-3,6,10b,12,14,15

• Sept. 28: Journals collected today; Do 2.2 #17a-d,18; Read 3.1 and do 3.1#1
• Sept. 30: Turn in 1.4#4a-e,5,8a, 1.5#4a,d (skip 4b,4c), 1.6#3-6, and 2.1#2,11; Do 3.1 #1,3,5,13abd
  
• Oct. 2: Read 3.2, skim 3.3.  Do 3.2 #1,2,4,6,7,8
  

• Oct. 5: Do 3.1 #7,10,11,12
• Oct. 7: Exam #1
• Oct. 9: Read 3.3, do 3.3 #1,5,6,7,10,11,16

• Oct. 12: Journals collected today; Do 3.3 #9,13,14 and 3.4 #1,2,4a
• Oct. 14: Do 3.4 #4c,e, read 3.5
• Oct. 16: Prove:  If m and n are positive integers and t = g.c.d.(m,n), then m/t and n/t are integers and are relatively prime.  Also do 3.5 #1-4

• Oct. 19: Write response paper to video The Proof, following the assignment handout.
• Oct. 21:  Read chapter 4 (1 section), do chapter 4 #1,2,4,6 (hint for #6: model on examples 4.3, 4.4)
• Oct. 23: Mid-semester day (no classes)

• Oct. 26: Do chapter 4 #3,7,9,10a,c,d,f,g
• Oct. 28: 
• Oct. 30: Turn in 3.3#6, 3.4#4e, 3.5#3, chapter 4#4. Do Chapter 5.1 #1-3,5-8
  

• Nov. 2: Do Chapter 5.1 #9-12,16,17 (we did a specific case of 17 in class, do note the difference).  Read 5.2, do 5.2 #2
• Nov. 4: Do 5.2 #1(practice only, won't be collected) and #5,7,8,10,17,19
• Nov. 6: [Deadline to withdraw with a W] Read 5.3, do #3,4,5 (the last one may be surprising)

• Nov. 9: Read chapter 5.4, do #1,2a,e
• Nov. 11:
• Nov. 13: Quiz today  Read 6.1, do #1,2,3,5, and show f : given by f(x)=x³ is injective.
  

• Nov. 16: Turn in revised Fermat/Proof paper  Read 6.2, do 6.1#7,8,9, 6.2 #1,2,4,5,12  (I will collect 6.1 #7c and 6.2#12 on Friday)
• Nov. 18:  
• Nov. 20: Exam 2; Turn in 6.1 #7c and 6.2#12

• Nov. 23: Go to the handouts page, and check out the links for TeX downloads.  I recommend installing them on your computer to make homework easier, alternately you can use one of the public computers in Ford.
• In either case, play with TeX a bit, and do at least this much:
• download one of the sample TeX files from the handouts page, make a significant change or two to one or more lines, and print it out.  This will assure that you can run the programs through printing.
• Gut one of the sample files (remove everything from right after \begin{document} to right before \end{document} ) and save it somewhere as your template.  You can keep the first few lines "on the page" if you like.  Then "TeX" a page that includes these lines, and print it out:
• A(BC) = (AB)(AC)
• A(BC) = (AB)(AC)
• If f : ⁺⁺ is given by f(x) = 1/x, then f is a bijection.
  
• Nov. 25:  Some work connected to the Hotel Infinity! story (and, more seriously, Cantor's notions of cardinality):
• We say that a set is countable or countably infinite if there is a bijection between the set and (in either direction).
• Show that the set of all integers (including the negatives and zero) is countably infinite.  Hint: You've already worked with a suitable function from the chapter 6 homework.
• Following the example given in the story (countably many tour busses with countably many people each) and the proof in class that the positive rationals are countable,
  show that A_i is countable if each A_i is countable and no two A_k's share an element (so there's no overlap).  Again, our proof will be verbal rather than giving an explicit formula for your bijection.
• Start to TeX up your two homeworks from last week, that the composition of two injective functions is injective, and the composition of two surjective functions is surjective.

• Nov. 30: Read 6.3, do #1-4,6,9,10, then read 7.1
  
• Dec. 2: Do 7.1 #1a,c,e,f,h,i, 2,3,9(several parts), 10, read 7.2 (distance and neighborhoods)
  
• Dec. 4: Read 7.3 (very lightly) and 7.4 (with care), do 7.2#1abde,3,11   7.3#7ab   7.4 #4ac
  

• Dec. 7: Read 7.5, do 7.4 #4e,5ab and 7.5 #8.  (Turn in 7.4#4c and 7.5#8 on Wednesday)
  
• Dec. 9: Turn in 7.4#4c and 7.5#8.  Do 7.5 #4,5ab,6a,c,e, read 9.1, do 9.1#a,b,d,e,2,4
• Dec. 11: (Last day of class)

• Saturday, Dec. 19th from 8:00 - 11:00 a.m: Final Exam.

Also interesting:

Stuff about Pythagoras and music (did you know he invented the harmonic scale?) Really cool if you have a computer with sound capability.

Prof. Janeba's Home Page | Send comments or questions to: mjanebawillamette.edu