Mathematics 220 - Term 2 2011-2012
"Mathematical Proof"

Lecture details

Lecture time and location

• Section 201 is taught by Andrew Rechnitzer
  • Tuesday and Thursday 11:00am - 12:30pm in LSK Room 200
• Section 102 is taught by Rajiv Gupta
  • Tuesday and Thursday 2:00pm - 3:30pm in LSK Room 460

Lecturer: Andrew Rechnitzer (section 101)

• Mathematics Building Room 215
• Email: andrewr@math.ubc.ca
  • Please put "MATH220" in the subject line of your email.
• Phone: 604-822-4516
• Office hours - Mondays and Tuesdays 2pm-3:30pm.
• You can also make an appointment by email.

Lecturer: Rajiv Gupta (section 102)

• Mathematics Annex Room 1104
• Email: gupta at math dot ubc dot ca
  • Please put "MATH220" in the subject line of your email.
• Phone: 604-822-5645
• Office hours - see here.
• You can also make an appointment by email.

Drop-in tutorial hours

• Drop-in tutoring is available (see here for general details)

Announcements

• The sixth homework set is up (sorry for the delay). See below.
• The third workshop problems, their solutions, and the quizzes are all posted below.
• The solutions to the fifth homework set are up (sorry for the delay). See below.
• The first midterm will be on Feb 14th and the second midterm will be in mid March (date to be determined soon)..

Course description

• The main aim of the course is to learn how write clear and correct mathematical proofs. It provides the gateway to more advanced mathematics.
• A little more precisely (though this is provisional)
  • Sets - definitions, set operations (chapter 1)
  • Logic - logical connectives, quantifiers (chapter 2)
  • Proofs - direct and contrapositive. (chapters 3 and 4)
  • Equivalence realtions (chapter 8)
  • Functions - injective, surjective, bijective, inverses and compositions (chapter 9)
  • Proofs - existence and contradiction (chapter 5)
  • Cardinality of sets - finite sets and different types of infinite sets (chapter 10)
  • Induction (chapter 6)
  • Elementary real analysis - limits of sequences and series (chapter 12). Also supplement this with extra material on supremums.
  The chapters refer to the textbook - see below.

The learning goals for this course are detailed here.

Prerequisites

• You must have either
  • a score of 64% or higher in one of MATH 101, MATH 103, MATH 105, SCIE 001, or
  • one of MATH 121, MATH 200, MATH 217, MATH 253, MATH 263.

Textbook

• Gary Chartrand, Albert D. Polimeni and Ping Zhang: Mathematical Proofs - A Transition to Advanced Mathematics (Second Edition). Pearson / Addison Wesley, 2008. ISBN 978-0321390530
• The course will (mostly) follow the text and the homework will also be assigned from it.
• We will mostly cover material in the same order as the text.

Assessment and Grading scheme

• The assessment for this course will consist of
  • Final exam
  • Two midterms
  • Weekly homework assignments
  • Short quizzes
• Your final grade will be computed by the following formula
  • Homework = 10%, Quizzes=10%, Midterms = 30%, Exam = 50%
• If a homework or quiz is missed for a documented medical or other reason, it will be ignored.
  Note that, original written documentation, for example a doctor's note or letter from a coach, is required; otherwise, a score of 0 will be given for the missed homework or midterm.
  Permission to write a makeup midterm or reweighting of other course components may be granted in the following two circumstances:
  • (a) prior notice of a valid, documented absence (e.g. out-of-town varsity athletic commitment) on the scheduled date; or
  • (b) notification to the instructor within 72 hours of absence due to medical condition.
• Please do not eat leftover sushi before your midterms or exam. It is surprising how many students become ill because of this.

Midterm and Exam

• The midterms will be in class - Tuesday February 14th and mid March (we will determine the date of the second midterm in the near future).
• We will put up more information about the midterms and exam here as it becomes available.
• Calculators, notes and books are not allowed in the midterms or the final exam.
• Some exams from previous years can be found here. Note that the material covered in 220 does change from term to term, and so there may be questions on previous exam on material we have not studied.
• You should use the learning goals to help your exam and midterm prepartion.
• The Math Club will (hopefully) be selling Exam Packages during the last week of term. We will put more details here when we get them.

Quizzes and workshops

• This term we will have workshops every second Thursday.
• The workshops will be at the same time and in the same place as your usual lecture.
• During the workshop you will be given a short list of problems to work on in small groups.
• At the end of each workshop there will be a short quiz consisting of a problem similar to those you have just worked on.
• These quizzes will make up 10% of your final mark.
• We will put up more information about the workshops soon.

Homework

• Homework will be assigned week-by-week.
• Homework will be due in the last lecture each week and we will try to return it to you within 1 week.
• Solutions will be posted immediately after the homework is to be handed in.
• You should also attempt other questions from the text as we cover each topic.
• Please read these notes on plagiarism and academic integrity.
• We will not accept late homework.

Extra notes

• From time to time we might put some extra notes up here.