Math 307: Fundamentals of Advanced Math; Fall 2014.
Time and Location:
MoWeFr 8:50AM - 9:40AM
Crouse 209.
Instructor:
Dr. Stefan Forcey
- Office: CAS 275
- Office Phone: 330 972 6779
- Email is sf34@uakron.edu
(...this is the best way to get a hold of
me)
- Office hours:
- If you can't make my office hours, let me know and we can try to
set up
a time to meet. Here is my schedule
for the spring semester.
Textbook: Required: "Mathematical Proofs: A Transition to Advanced Mathematics", by Chartrand, Polimeni, and Zhang (third edition).
Course Syllabus.
The syllabus will include information about grading
policies, exam schedules and policies, etc. You
should definitely read it.
Here's an approximate schedule of
what we'll be doing this semester. Emphasis on the "approximate".
Homework
There will be homework assigned semi-weekly, and the
assignments will be posted here.
- Homework 1: due Friday 8/29 Surprise
- Homework 2 : Take-home quiz over this on Friday, 9/5(quiz due Monday 9/8).
- Chapter 1: 1, 3, 5, 6, 7, 12, 14, 19, 22, 23
- (2nd Edition.)Chapter 1: 1, 3, 5, 6, 7, 10, 12, 16, 17, 20
- Homework 3 : Take-home quiz over this on Friday 9/12, (quiz due Monday 9/15).
- Chapter 1: 37, 41, 46, 51, 57, 59, 63
- (2nd edition.) Chapter 1: 27, 31, 32, 37, 41, 43, 47
- Homework 4 : Download Take-home quiz over this on Friday, 9/19(quiz due Monday 9/22).
- Chapter 2: 3, 5, 7, 16, 18, 20, 22, 38, 36
- (2nd edition.)Chapter 2: 3, 5, 7, 11, 13, 15, 17, 23, 25
- Homework 5 : Take-home quiz over this on Fri. 9/26 (quiz due Mon 9/29).
- Chapter 2: 36, 38, 39, 47, 49, 52, 54, 67, 71, 75
- (2nd edition.)Chapter 2: 23, 24, 25, 31, 33, 35, 37, 45, 49, 51
- Homework 6 : Take-home quiz over this on Wed 10/1 (quiz due Fri 10/3).
- Chapter 3: 1, 3, 5, 9, 11, 16, 17, 18
- (2nd edition) Chapter 3: 1, 3, 5, 7, 9, 12, 13, 14
- Homework 7 : Take-home quiz over this on Fri 10/17 (quiz due Wed 10/22).
- Chapter 3: 19, 26, 27
- (2nd edition) Chapter 3: 15, 19, 20
and
- Chapter 4: 1, 5, 7, 10, 15, 19, 21
- (2nd edition) Chapter 4: 1, 5, 7, 8, 11, 15, 17
- Homework 7.5 : Take-home quiz over this on Fri 10/24 (quiz due Mon 10/27).
- Chapter 4: 27, 30, 31.
- (2nd ed.) Chapter 4: 20, 23, 24.
and
- Prove: if x>0, then 2x^7 - 7x^2 > -10.
and
- Chapter 5: 1, 3
- (2nd edition) Chapter 5: 1, 3
- Homework 8 : Take-home quiz on Fri 10/31(quiz due Wed 11/5).
- Chapter 5: 13, 14, 19, 31, 34, 40
- (2nd ed.) Chapter 5: 10, 11, 16, 21, 25, 29
- Homework 9 : Take-home quiz over this on Fri. Nov. 7 (quiz due Mon. 11/10).
- Chapter 6: 4, 5, 21, 23, 26, 42, 43 (fixed)
- (2nd ed.) Chapter 6: 4, 5, 18, 19, 20, 33, 34 (fixed)
- Homework 10 : Take-home quiz over this on Fri. Nov. 14 (quiz due Mon. 11/17 or Tues. 11/18).
- Chapter 6: 42, 43. Chapter 8: 1, 3, 11, 13, 15, 19
- (2nd ed.) Chapter 6: 33, 34. Chapter 8: 1, 3, 5, 7, 9, 13
- Homework 11 : We'll go over some of these in class after break.
- Chapter 8: 39, 44, 45, 47. Chapter 9: 4, 20, 21, 22, 24
- (2nd. ed.)Chapter 8: 24, 28, 29, 31. Ch.9 4, 13, 14, 15, 17
- Given S={-5,-3,1,2,5,7,8,13,17}; Find the equivalence
classes of R on S, where aRb (a related to b) whenever a is congruent to b mod 6.
- On a set S with |S|=n, find a formula for the number of relations that are both reflexive and symmetric.
Recall that the number of reflexive relations is 2^(n^2-n).
Maybe the best way to explain that is in terms of choices. Here’s a simpler problem: If you
have two choices of shirt (red and blue) and two choices of pants (black and tan) but
only one pair of shoes, then how many outfits (one each of shirt, pants, pair of shoes) do you have?
2x2x1=4.
The diagonal pairs (a,a) in a reflexive relation are like the shoes—you have to pick them
every time, so the counting principle turns into multiplying by 1 (only one choice.)
When we use the counting principle to count subsets the power of 2 comes from the
2 choices “in” or “out” for each possible element. The diagonal pairs have to be “in”, so
we could see the formula as actually being 2^(n^2-n)x1x1…x1 where we mutiply by 2 for each non-diagonal pair and by
1 for each of the diagonal pairs.
Alternatively you can say that choosing an outfit is the same as just choosing shirt and pants,
since the shoes are a given. That's how we did the problem in class: just ignore the
diagonal pairs since they are a given!
- Homework 8 : Take-home quiz over this on Fri 3/14 (quiz due Mon 3/17).
- Chapter 5: 1, 3, 5, 9, 10, 11, 16, 21
- Homework 9 : Take-home quiz over this on Wed 3/21 (quiz due Fri 3/21).
- Chapter 6: 4, 5, 18, 19, 20
- Homework 10 : Take-home quiz over this on Fri. 4/4 (quiz due Mon 4/7).
- Chapter 6: 33, 34. Chapter 8: 1, 3, 5, 7, 9, 13
- Homework 11 : Take-home quiz over this on Mon. 4/21 (quiz due Wed 4/23).
- Chapter 8: 15, 17, 18, 31, 39. Chapter 9: 1, 3, 6.
- Homework 12 : Take-home quiz (quiz due Wed 4/30).
- Chapter 9: 11, 13, 14, 15, 17, 21, 22, 34
- Homework 3, due Monday, Feb. 11th.
- Homework 4, due Monday, Feb. 18th.
- Homework 5, due Monday, March 4th.
- Homework 6, due Mon. March 11.
- Homework 7, due Fri. March 15.
- Homework 8, due Fri. March 22.
- Homework 9, due Mon. April 8.
- Homework 10, due Mon. April 22.
- Homework 11, due Friday April 26.
- Homework 12, due Mon. Dec. 3.
Exams
- Exam 1: Wednesday, October 8.
Coverage: up through section 3.3,
Here is a
review sheet for the first exam, and the answers for the review.
- Exam 2: Friday, Nov. 21. Coverage: Chapters 3.4, 4.1-4.3,5.1-5.3,6 (skip 6.3),8.1,8.2, def. of equiv relation.
Here is a
review sheet for the second exam, and the answers for the review. Also study quizzes and hw, 7,7.5,8,9,10.
- Final Exam: 12/12/2014, Friday
7:45AM - 9:45AM
Crouse 211
(two rooms north of our regular classroom).
For review:
Rework the previous two exams, all quizzes, and the online review sheets above.
Also, here is one extra
review sheet just covering the most recent bit of new material.
The final exam is comprehensive, covering the entire class. Here are the
answers for the review.
Resources