Course - Analysis MT22

Created: October 17, 2022 | Updated: September 30, 2025 | Read markdown | About these notes | View in context | Study these flashcards

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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 differentiation 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, Lecture 1^U
• Lecture - Analysis MT22, Lecture 2^U
• Lecture - Analysis MT22, III^U
• Lecture - Analysis MT22, IV^U
• Lecture - Analysis MT22, V^U
• Lecture - Analysis VI^U
• Lecture - Analysis 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

Proofs

• Proofs - Analysis I MT22^U

Problem Sheets

• Sheet 1
• Sheet 2
• Sheet 3, Problem Sheet - Analysis I MT22, III^U
• Sheet 4
• Sheet 5
• Sheet 6, Problem Sheet - Analysis MT22, VI^U
• Sheet 7

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• Lecture - Analysis MT22, IV^U

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• Lecture - Analysis MT22, XI^U

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• Lecture - Analysis MT22, XII^U

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• Lecture - Analysis MT22, XV^U

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• Lecture - Analysis MT22, XIV^U

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• Lecture - Analysis MT22, VIII^U

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• Lecture - Analysis MT22, IX^U

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• Lecture - Analysis MT22, III^U

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• Lecture - Analysis MT22, XIII^U

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• Lecture - Analysis MT22, X^U

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• Notes - Analysis I MT22, Rationals and irrationals^U

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• Notes - Analysis I MT22, Cauchy sequences^U

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• Notes - Analysis I MT22, Misc^U

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• Notes - Analysis I MT22, Power series^U

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• Notes - Analysis I MT22, Integral test^U

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• Notes - Analysis I MT22, Infimums and supremums^U

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• Notes - Analysis I MT22, Approximation property^U

  (incoming)
• Notes - Analysis I MT22, Alternating series test^U

  (incoming)
• Notes - Analysis I MT22, Monotone sequence theorem^U

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• Notes - Analysis I MT22, Limits are unique^U

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• Notes - Analysis I MT22, Scenic viewpoint theorem^U

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• Notes - Analysis I MT22, Convergent implies bounded^U

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