Head Start ... for new MMS-EDU students


Introduction to analysis: a review guide

Basically, review the concepts of continuity and differentiability in R. The basic ideas of convergence of sequences and series would be very very helpful.

You can use your favorite text. I use here for illustration the text for the analysis course held at the University of Pittsburgh.

  1. Recall what are the real numbers and their basic properties - Chapter 1. If this is your first encounter with the definition of real numbers, you may want to read here first.

  2. Sequences: from Chapter 2 Section 2.1

    Exercises on p. 51: 2.1.1 up to 2.1.10

    Section 2.2.1, 2.2.2, 2.2.4

    Know the statement of Theorem 2.3.8 (page 67)

    Section 2.4 Exercises 2.4.1, 2.4.2 on p 73

    Series: 2.5 Exercises 2.5.1 up to 2.5.4 on p 83

    The number e: Section 2.6

    Sec 2.7.1

Exercises 2.7.1 p 92

  1. Continuous functions Chapter 3

    Note: the term cluster point used here is more often named limit point.

    Please review also Uniform continuity, Sec. 3.4

    Exercise 3.1.1 a,b,c on p. 101

    Exercise 3.2.4, 3.2.5, 3.2.10 on p.107

  2. The derivative- Chapter 4.