MA 109 Autumn 2022

Slides and solutions would be posted here.

Please find the tutorial booklet here.

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Tutorial One

To be held in LT-105 on Wednesday, November 9. The recap session will start at 1:45 PM. Report by 1:40 PM for the same. The tutorial will be from 2-3PM.

The general \(\epsilon-N\) proof method was taught through the example of \(a_n:=1/n \to 0\). Problems that were discussed – From the first tutorial sheet,

  • Q2: i,ii,vi
  • Q3: i,ii
  • Q5: ii
Recap Slides: With Pauses   Without Pauses

Extra session for tutorial one

To be held in Room 113 in the Department of Mathematics on Sunday, November 13 from 3-4PM. Problems that were discussed (from the first tutorial sheet)

  • Q5: iii
  • Q6,7,8,9,10

Further, some additional problems were given, and a proof of divergence of \(a_n := (-1)^n\) was given. Recap Slides: With Pauses | Without Pauses

Tutorial Two

To be held in Room 113 in the Department of Mathematics on Wednesday, November 16. The recap session will start at 1:45 PM. Report by 1:40 PM for the same. The tutorial will be from 2-3PM.

A proof of the Dirichlet Function being continuous nowhere was given. Questions 1,2,4,8 (from the second tutorial sheet) were discussed. An (out of syllabus) extra question about comparing the cardinality of \(\mathbb{Q}\) and \(\mathbb{R}/\mathbb{Q}\) was asked.

Recap Slides: With Pauses Without Pauses

Tutorial Three

To be held in Room 113 in the Department of Mathematics on Sunday, November 20. We will start at 3:15 PM. Please turn in the (optional) practice assignment one if you wish to do so.

Quiz (23 Nov)

Quiz Solutions

Tutorial Five

To be held in Room 105 in the Department of Mathematics on Wednesday, December 7 from 2PM. Questions to be discussed include Q7 from the fourth sheet, and Q1-(ii), Q5, Q6, Q9 from the fifth sheet.

Recap slides: With Pauses

Tutorial Six

Held in Room 105 in the Department of Mathematics on Sunday, December 11 from 5PM. Questions that were discussed – Q3,5,6,8,9(i),10 from the sixth sheet.

Recap slides: With Pauses Without Pauses

Tutorial Seven

Held in Room 216 in the Department of Mathematics on Sunday, December 12 from 7PM. Questions that were discussed – Q1,4,5,9 from the seventh sheet.

Recap slides: With Pauses Without Pauses

TSC Slides

Endsem (14 Dec)

Endsem Solutions

Extra Material

  1. We talked about finite sets, and briefly about the cardinality of infinite sets. We defined countable sets using bijection with \(\mathbb{N}\). We left the discussion with the claim that there exists no bijection between \((0,1)\) and \(\mathbb{N}\). This is shown using Cantor’s Argument. One can read this document to learn more.
  2. Practice Assignment One. Here is the solution.