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.
| Topic | Understanding Analysis Stephen Abbott | An Introduction to Analysis William Wade |
|---|---|---|
| logic, proofs, induction | 1.2 | 1.4 |
| sets, functions | 1.2 | 1.1, 1.5-6 |
| properties of ℝ, completeness | 1.3-4 | 1.2-3 |
| sequences, limits of sequences | 2.2-4 | 2.1-2 |
| subsequences, Cauchy sequences | 2.5-6 | 2.3-4 |
| open and closed sets | 3.2 | 8.3-4* |
| compact sets | 3.3 | 9.2, 9.5* |
| limits of functions | 4.2 | 3.1-2 |
| continuity of functions | 4.3-5 | 3.3 |
| uniform continuity | 4.4 | 3.4 |
| the derivative | 5.2-4 | 4.1-3 |
| sequences of functions | 6.2 | 7.1 |
| uniform convergence | 6.2 | 7.1 |
| Riemann integration | 7.2-5 | 5.1-3 |
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