Course - Analysis I MT22
The first course in a three part series to serve as an introduction to “real analysis”. Real analysis is about putting the idea of things like convergence, limits, continuity, and differentation on a rigorous footing (in the context of real numbers).
This course dealt specifically with results about sequences and series of real numbers, such as the Bolzano-Weierstrass theorem: if you write down a sequence of real numbers that doesn’t shoot off to plus or minus infinity, then you can always find a subsequence of that sequence and a real number such that the subsequence gets infinitely close to that real number.
Out of all the maths courses in [[Courses MT22]]U, this felt like the most different from A-level. Since I was still getting into the groove of taking notes at uni, a lot of the notes for this course are organised chronologically in the Lectures section, rather than by concept in the Notes section.
- Course Website
- Lecture Notes
- Other analysis courses:
- [[Course - Analysis II HT23]]U
- [[Course - Analysis III TT23]]U
- …and in [[Part A]]U, the theme continues with:
- [[Course - Metric Spaces MT23]]U
- [[Course - Complex Analysis MT23]]U
- Other courses this term: [[Courses MT22]]U
Notes
- [[Notes - Analysis I MT22, Rationals and irrationals]]U
- [[Notes - Analysis I MT22, Infimums and supremums]]U
- [[Notes - Analysis I MT22, Triangle inequality]]U
- [[Notes - Analysis I MT22, Approximation property]]U
- [[Notes - Analysis I MT22, Algebra of limits]]U
- [[Notes - Analysis I MT22, Limit inequality theorem]]U
- [[Notes - Analysis I MT22, Convergent implies bounded]]U
- [[Notes - Analysis I MT22, Limits are unique]]U
- [[Notes - Analysis I MT22, Monotone sequence theorem]]U
- [[Notes - Analysis I MT22, Scenic viewpoint theorem]]U
- [[Notes - Analysis I MT22, Cauchy sequences]]U
- [[Notes - Analysis I MT22, Alternating series test]]U
- [[Notes - Analysis I MT22, Integral test]]U
- [[Notes - Analysis I MT22, Power series]]U
- [[Notes - Analysis I MT22, Misc]]U
Lectures
- [[Lecture - Analysis MT22, I]]U
- [[Lecture - Analysis MT22, II]]U
- [[Lecture - Analysis MT22, III]]U
- [[Lecture - Analysis MT22, IV]]U
- [[Lecture - Analysis MT22, V]]U
- [[Lecture - Analysis MT22, VI]]U
- [[Lecture - Analysis MT22, VII]]U
- [[Lecture - Analysis MT22, VIII]]U
- [[Lecture - Analysis MT22, IX]]U
- [[Lecture - Analysis MT22, X]]U
- [[Lecture - Analysis MT22, XI]]U
- [[Lecture - Analysis MT22, XII]]U
- [[Lecture - Analysis MT22, XIII]]U
- [[Lecture - Analysis MT22, XIV]]U
- [[Lecture - Analysis MT22, XV]]U