### Fall 2017

### Handouts

- Syllabus
- Day 1
- How to solve problems?
- How to write correct proof by Chris Heil
- An Intuitive Development of the Real Numbers

**Outline of sections and homework sets**

- Appendix A:
- A set of logic review reviewing part of MATH 180 is posted on Blackboard. Please submit your solutions for this quiz by September 13, 2017
- outline and homework
- Appendix A (solutions)

- Section 1.2 Mathematical induction
- Section 2.1 Algebraic and order properties of R
- Homework Section 2.1
- solutions

- Section 2.2 Absolute Value
- Homework Section 2.2
- solutions

- Section 2.3 The completeness property of R
- Homework section 2.3
- solutions

- Section 2.4 Application of the supremum property
- Section 2.5 Intervals
- Section 3.1 Sequences and their limits
- Section 3.2 Limits theorems
- Section 3.3 Monotone sequences
- Section 3.4 Subsequences and the B-W Theorem
- Section 3.5 The Cauchy Criterion
- Section 3.6 Properly divergent sequences
- Section 4.1 Limits of functions
- Section 4.2 Limit theorems
- Section 5.1 Continuous functions
- Section 5.2 Combination of continuous functions
- Section 5.3 Continuous functions on intervals
- Section 5.4 Uniform continuity

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