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Sequences and series of numbers and functions · GRE Mathematics Subject Test · Courselo

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Introductory real analysis and topology

Sequences and series of numbers and functions

Introductory real analysis and topology · Lesson 1 of 4

Lesson 1 of 4

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Unit 7

Introductory real analysis and topology

4 lessons · 4 h 45 min of study

Sequences and series of numbers and functionsReading · 0%
Continuity, differentiability and integrability1 h 20 min of study
Topology of the real line, Euclidean space and metric spaces1 h 10 min of study
General (point-set) topology1 h of study

This unit is ≈10% of the GRE Math, across 4 lessons. Full syllabus

Lesson 1 of 4 · Introductory real analysis and topology

Sequences and series of numbers and functions

3 quick checks≈3% of the testStretch: Stretch: harder material that separates the top grades

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By the end you’ll be able to

Use the completeness axiom, supremum and infimum, and apply the monotone convergence and Bolzano–Weierstrass theorems
Determine convergence of sequences, including recursively defined sequences, using subsequences, Cauchy sequences, limsup and liminf
Distinguish absolute from conditional convergence and state the effect of rearranging a conditionally convergent series

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Adaptive questions on sequences and series of numbers and functions.

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Distinguish pointwise from uniform convergence of sequences and series of functions, apply the Weierstrass M-test and state what uniform convergence preserves (continuity, integrals)

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