Agenda, Semester Week 2

Sets and Functions

This week dives into the foundations of set theory as well as general proporties of functions. We will study the inverse functions and compositions of functions, and will pay special attention to so-called recursively-defined functions.

Key Terms

Sets and set relations. Set union \(\cup\), set intersection \(\cap\), and set difference \(\setminus\). The classical sets of numbers: \(\,\mathbb N,\, \mathbb Z,\, \mathbb Q,\, \mathbb R\,\). Functions and functional expressions. The domain, co-domain, and image set/range. Composite functions \(\circ\), inverse functions, and recursively-defined functions. Summation notation \(\sum\).

Preparation and Syllabus

This week will cover Chapter 2 until and including Example 2.3.2 as well as Sections 3.1 and 3.2 in Chapter 3 in [the textbook].

Exercises

Exercises for Long Day.

Exercises for Short Day.