Home   About me   Education   Experience   Teaching   Publications   Supervision   Contact   Miscellaneous

MA21201/MA31005 - Real Analysis

Topics covered

Lectures Contents
Lecture 1 Course introduction, finite and infinite sets
Lecture 2 Finite and infinite sets
Lecture 3 and 4 Finite and infinite sets
Lecture 5 Finite and infinite sets
Lecture 6 Algebraic and order properties of R
Lecture 7 and 8 Algebraic and order properties of R, bounded and unbounded sets
Lecture 9 Suprema and infima, Completeness property of R.
Lecture 10Archimedean Property, Density of Q in R.
Lecture 11 and 12 Intervals, Nested interval property, Uncountability of R.
Lecture 13 Sequences: Definition and examples, convergent and divergent sequences.
Lecture 14Tail of a sequence, bounded sequences, squeeze theorem.
Lecture 15 and 16 Cauchy's limit theorems, Monotone convergence theorem.
Lecture 17 Subsequences.
Lecture 18 and 19 Monotone subsequence theorem, Bolzano-Weierstrass theorem, Cauchy's sequence.
Lecture 20 Series: Examples and properties of convergent series.
Lecture 21 and 22 Comparsion test, Absolute convergence.
Lecture 23 Tests for (Absolute) convergence.
  • Problem sheets (To be updated)