Announcements:

• The final exam is on December 8, 8:30 AM, in SWNG 222.
• Office hours during the exam period: Mondays and Wednesdays, 1-2 pm, in MATH 200. These are for both of my classes, but on Dec. 5 and 7, priority will be given to Math 320 students.
• For practice, here is a final exam from 2015. Solutions are posted here. The last two questions concern differentiation which was not covered in this year's class, so you can skip these.
• Here is a list of the topics we covered. You will be responsible for all of them on the final exam:
  • Chapter 1: all of it except for the Appendix, pp. 17-21.
  • Chapter 2: everything except "Perfect sets", pp. 41-42
  • Chapter 3: we skipped the proofs of Theorems 3.31 and 3.32 (the theorems are useful to know but you don't need to remember the proofs). Theorem 3.37 clarifies the relationship between the root test and the ratio test, but will not be required on the exam. You do not need to remember the summation by parts formula in Theorem 3.41. We skipped the last part of Chapter 3, starting with page 72. ("Absolute convergence" is still required, "Addition and multiplication of series" and "Rearrangements" (pp. 72-78) are not.)
  • Chapter 4: we skipped Theorem 4.20. "Infinite limits" (pp. 97-98) was not discussed in class. This is a very easy extension of the concept of limits and you should read it on your own.
• All past homework assignments and solutions are posted here.
• Midterm solutions are here.
• Midterm 1 was on Friday Oct. 21, in class. It covered all material up to and including open and closed sets in metric spaces (ending on p. 35).
• Practice midterm solutions are here.
• A practice midterm is posted here. Solutions will be posted on Wednesday. Update, Oct. 4: In #5(a) and (b), we will expect proofs from the definition. In #5 (c), you may use theorems from the textbook, including the limits in "Some special sequences", pp. 57-58. This material will be covered on Friday, Oct. 7. In #1, we expect you to provide a function that establishes the equality of cardinal numbers, and a proof that this function is a bijection. A picture is not sufficient.
• We are covering Chapters 2 and 3 of Rudin according to the following schedule:
  • Chapter 2: "Finite, countable, and uncountable sets", pp. 24-30
  • Chapter 3: "Convergent Sequences", pp. 47-51, but for sequences in R instead of general metric spaces.
  • Monotone sequences, 3.13-3.14, p. 55
  • Subsequences, Def, 3.13, p. 51
  • Every bounded sequence in R has a monotone subsequence (not in Rudin), therefore a bounded sequence has a convergent sequence (this corresponds to 3.6 in Rudin, but with a different proof)
  • Cauchy sequences and completeness of R, pp. 52-54.
  • "Some special sequences", p. 57, needed for homework
  • Chapter 2: Metric spaces, pp. 30-43
  • Chapter 3: "Upper and lower limits", pp. 55-57
  • Chapter 3: "Series" and the rest of the chapter, pp. 58-78. Some topics may be omitted.

Mathematics 320 (Real Variables I), Fall 2016

• Instructor contact information: Math Bldg 200, (604) 822 4457, ilaba@math.ubc.ca
• Office hours: Mon 1-2, Wed 10-11, Fri 12-1
• The best way to contact the instructor is by email. Please note that email received on evenings and weekends will be answered on the next business day. If you cannot attend regular office hours due to schedule conflict, please make an appointment in advance. Drop-ins and same-day requests for appointments cannot always be accommodated.

• Section 101: http://www.math.ubc.ca/~perkins/teaching.html (page maintained by Prof. E. Perkins)
• Section 102: http://www.math.ubc.ca/~ilaba/teaching/math320_F2016 (page maintained by Prof. I. Laba)

• Please read the UBC policy on Student Conduct and Discipline.
• Mathematics Learning Centre: The Math Learning Centre (or MLC for short) is a space for undergraduate students to study math together, with support from tutors, who are graduate and undergraduate students in the math department. Please note that while students are encouraged to seek help with homework, the MLC is not a place to check answers or receive solutions, rather, our aim is to aid students in becoming better learners and to develop critical thinking in a mathematical setting. The MLC is located in Rooms 301 and 302 in the Leonard S. Klinck (LSK) Building, and is open Monday through Friday, 11:00am to 6:00pm. Check the website above for any changes to hours and announcements.
• Past final exam database
• UBC Math Club, located in Math Annex 1119, sells math exam packages (old exams together with solution sets) for a nominal price before each final exam session.