Analysis (MATH10011) 1st half 2018-2019

This is the webpage for the first half of the University of Bristol Analysis unit (MATH10011). Lectures for this unit will be in Tyndall Lecture Theatre (Physics Building) on Tuesday at 1pm and Thursday at 4pm. There will be a problems class in the same room at Friday at 11am. You will have fortnightly tutorials (in even weeks) and homeworks will be set on the Friday of odd weeks. My ofice hour (office 4.12 Howard house) is on Tuesdays at 4pm or by appointment. There will be an exam dropin session from 10-12 on Monday 14th january in the 4th floor seminar room in howard house.

Lecture notes

  • Parts 1 and 2 of the notes.
  • Parts 3 and 4 of the notes
  • Parts 5 and 6 of the notes
  • Part 7 of the notes (a couple of corrections have been made in the proof of Theorem 7.7 from the printed version, in a couple of places in the printed notes f(a) should be y)
  • Homework

    Note that the 3rd and 5th homeworks will be assessed and will be realeased on the Fridays of week 5 (Nov 2nd) and week 9 (Nov 30th). The other homework questions will be set from this booklet.

    Assigned homework

  • Friday October 5th: Questions 1,2,1.4,1.5 and 1.6 from the question booklet. (Solutions to part 1 exercises).
  • Friday October 19th: Questions 2.4, 2.5 (parts (a) and (c)), 2.7, 3.1 and 3.4(parts (b) and (d)) from the question booklet. (Solutions to part 2 exercises, solutions to part 3 exercises and solutions to part 4 exercises)
  • Friday November 16th: Questions 5.8,5.9,6.2 and 6.3 from the question booklet. (Solutions to part 5 exercises, solutions to part 6 exercises and solutions to part 7 exercises).
  • Friday December 14th: Questions 8.7,8.9,9.3, 9.4 (c)and 9.5 from the question booklet. (Solutions to part 8 exercises and solutions to part 9 exercises).

    Assessed homework

    First assessed homework (solutions)

    You should hand in your work along with a completed cover sheet to the labelled cabinet on the ground floor of the School of mathematics. The deadline is noon on Monday 12th November. Your work should be stapled together with the cover page at the front. Cover sheets are available from the ground floor of the mathematics building, the unit website and blackboard. Solutions will be released online on the 14th November.

    Second assessed homework (solutions)

    You should hand in your work along with a completed cover sheet to the labelled cabinet on the ground floor of the School of mathematics. The deadline is noon on Monday 10th December. Your work should be stapled together with the cover page at the front. Cover sheets are available from the ground floor of the mathematics building, the unit website and blackboard. Solutions will be released online on the 12th December.

    Additional exercises

  • Some challenging questions
  • Additional exercises on rational and irrationals
  • Additional exercises on inequalities and induction
  • Additional exercises on suprema and infima
  • Additional exercises on sequences and limits
  • Additional exercises on divergent and convergent sequences
  • Additional exercises on monotone convergence and subsequences
  • Additional exercises on Cauchy sequences
  • Additional exercises on series
  • Additional exercises on limits and continuity
  • Additional exercises on the intermediate and extremal value theorems
  • Extras

  • Irrational Adventures by Charles Cox. More on the proof of the irrationality of the square root of 2 written by Charles Cox.