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Midterm 1 review - Review sheet for Midterm 1 MAT 319...

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Review sheet for Midterm 1, MAT 319, Foundations of Analysis, Spring 2013 1. Mathematical induction. You need to be able to clearly state the princi- ple of mathematical induction and do a induction-based proof. Sample problems: 1.2, 1.5, 1.6, 1.9. 2. Fields, properties of Q and R . I will not give any problems directly on this. Don’t bother memorizing the axioms in Paragraph 3, this is something ”you already know”. However, make sure you are confident with inequalities, absolute value, and the triangle inequality. 3. The completeness axiom. Definitions you need to know: maximum, minimum, upper bound, lower bound, least upper bound, greatest lower bound (make sure you know exactly what the difference between these is). You need to be able to state the Completeness Axiom (4.4), the Archimedean axiom (4.6) and the denseness of Q (4.7). Sample prob- lems: 4.1-4.4 (try to do these in your head), 4.5, 4.6, 4.9, 4.15. 4. Infinity. You need to know the conventions about using the symbols + and -∞ (page 27). 5. Dedekind cuts. You need to know the definitions (i)-(iii) in Paragraph
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