Math 220, May-June 2018

• Instructor: Rachel Ollivier Email: ollivier@math.ubc.ca
• TA: Bowen Tian. btian02 at math.ubc.ca
                      
  
  
                    
  
  
  
• Time and Location: Tu-Th-F: 10am-12pm and W: 10am-11am
  in MATX 1100
  
• Office hours: W 11am-12pm  and F 12pm-1pm.
  
  Regular office hours will take place in the classroom
  For a meeting in my office (Math 235), please make an appointment.
  

• Book:  Book of Proof (2nd edition), by R. Hammack.
  You may purchase a physical copy of this book at the bookstore, or you may access and download
  the book for free at the author's web page. The sections we will cover can be found in
  the syllabus link below.
  
  
  
  
  

• Syllabus, grading (ie weight of the homework and tests in your grade): please check here.
  
• Past exams
  
  
• Midterm #1:  in class on Wednesday May 30h.  Solution.
  Practice Midterm 1 (Except for Questions 1.c and 5 which involve respectively "partition" and "proof by contrapositive"...we will do this later)
  Practice Midterm 2 (Except for Question 1.d on "partition")
  Midterm 1 Topics
  
  
• Midterm #2:  in class on Thursday June 14th. Solution
  (Non exhaustive) summary  of Week 3
  Practice midterms: #1 and #2. You can ignore the questions about "relations", "equivalence classes", "equivalence relation" (we will cover this in early week 5).
  
  
• Final Exam: Tuesday June 26 at 12:00 in Buchanan A104.
  Practice exams: #1 and #2. Ignore questions on supremums,minimums, and convergence of sequences.
  To help you review: see Problem set 5 and examples of problems from the book below.
  
• Homework will be due in class on Fridays. The problemsets (with due date) will be posted here.
  There will  be one assignment posted per week (unless otherwise specified), each due on the following week.
  Questions about the HW may be addressed to either your instructor or to the course TA. This class is about learning the language of mathematics, so to earn full marks you will need to write your answers in a logical sequence that is easy to follow and confirm. Your proofs will probably contain more words than mathematical symbols.
  
  
  1. Problem set 1 due Friday May 25th (+ a preview a  problem which will be due Friday June 1st + the proof of Euclidean Division Theorem which we did together in class). Here are some hints and explanations (see also drawing on the last page).
     
     
  2. Problem set 2 due Friday June 1st.  Hints and explanations.
     
  3. Problem set 3 due Friday June 8th. Hints
     
  4. Problem set 4 due Friday June 15th. Hints
     
  5. Last problem set on functions, equivalence relations + review Some hints.
     
  6. Sample problems from the book:
     Chapter 1: 1.3: A and C 1.4: 1,3,4  1.5: 3  1.8: 3,4,8,9,11 12
     Chapter 2: Practice with negations (section 2.10)+see HWs, Midterm 1, course notes, "midterm 1 topics link "above
     Chapter 4: Direct proofs. your course notes contain many examples. See also problems 10,11,26,27,28.
     Chapter 5: Proof by contrapositive, pick your favorite ones in that list of problems...
     Chapter 6: Contradiction. 6,7,10,11,17,18
     Chapter 7: 8,9,10,11,22,23
     Chapter 8: Proofs involving sets. 1,2,19,21,22,23,24,27,28
     Chapter 9: Prove or disprove. 1,2,13,14,18,19,21,30
     Chapter 10: Induction. 1,3,6,10,11,12,16,22,25--28 + Problem set4 and your coursenotes for double induction.
     Chapter 11:  11.2: 7,8,9 + examples from coursenotes and problemset 5 11.4 all problems should feel fairly easy.
     Chapter 12: 12.2 (injection, surjection) and 12.4 (composition):pick your favorite problems
                          12.5 computing inverses 1,2,7,8,9 12.6 image, preimage 6--14 and problem set 5
     Chapter 13: see problemset 5.