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Analysis Diagnostic Topics

Texts:
Understanding Analysis, by Stephen Abbott
An Introduction to Analysis, by William Wade
Math 341 Lecture Notes, by Michael Frazier

The following table shows the basic topics covered on the Analysis Diagnostic Exam in Column 1. Column 2 shows the sections where this topic can be found in Abbot’s Understanding Analysis. The third column shows where this material can be found in Wade’s An Introduction to Analysis.

TopicUnderstanding Analysis
Stephen Abbott
An Introduction to Analysis
William Wade
logic, proofs, induction1.21.4
sets, functions1.21.1, 1.5-6
properties of ℝ, completeness1.3-41.2-3
sequences, limits of sequences2.2-42.1-2
subsequences, Cauchy sequences2.5-62.3-4
open and closed sets3.28.3-4*
compact sets3.39.2, 9.5*
limits of functions4.23.1-2
continuity of functions4.3-53.3
uniform continuity4.43.4
the derivative5.2-44.1-3
sequences of functions6.27.1
uniform convergence6.27.1
Riemann integration7.2-55.1-3

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last updated: October 2021

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