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Data, Logic, and Computing: Winter 2025
Counting
One of the first things we learn in mathematics is how to count. Now we want to count large collections of objects quickly, correctly, and precisely. Counting problems include for example:
- How many passwords can you form if they are limited to 5 characters?
- How many anagrams are there of the word "mathematics?
- How many bitstrings of length 16 that start with 1 and end with 00 can you form?
- How many committees of 3 members can you form in a club of 18 menbers?
In this chapter, we cover those counting problems using both a formal set theory approach and an intuitive approach. We condired the product and sum rules, the pigeonhole principle, and combinatorics.
Lecture Notes
Further Reading
- Handwritten Notes from class on 3/05: Set theory PDF document
- Handwritten Notes from class on 3/07: Counting PDF document
- Handwritten Notes from class on 3/10: Counting (2) PDF document
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