CS 55 at Pomona College is an introduction to discrete mathematics: the study of logic, set theory, inductive structures, the natural numbers and integers, counting, probability, and graph theory. We could have called the course “how to think like a computer scientist”.

From the course catalog:

Introduction to the study of finite mathematical structures and the ways to build them, count them and analyze them. Topics and examples chosen to relate to concepts of interest in the design and analysis of computer algorithms, including permutations and combinations, graphs and trees and codes. Emphasis on creative problem solving and learning to read and write proofs.

Or, from Bertrand Russell, as discrete a mathematician as you might find:

The eternal world is trivial, and … mathematics is only the art of saying the same thing in different words.

Prerequisites: CS 51 or equivalent (AP CS, CS 5 at Mudd, or significant programming experience).

# Office hours and mentor sessions

The entries here are ordered by increasing closeness to assignment due dates (Wednesdays in class).

Day | Time | Location | |
---|---|---|---|

Sonia Grunwald | Saturday | 2–4pm | Edmunds 2nd floor |

Mark Hallman | Sunday | 3–5pm | Edmunds 2nd floor |

Emily Chen | Sunday | 7–9pm | Edmunds 2nd floor |

Mary Jac Heuman | Monday | 3–5pm | Edmunds 2nd floor |

Alex Hof | Monday | 7–9pm | Edmunds 2nd floor |

Prof. Michael Greenberg | Tuesday | 1–3pm | Edmunds 225 |

I’m available at other times by appointment—send me an email.

# Meetings

Please note that the chapter numbers for readings are for Rosen’s 7th Edition.

Date | Topic | Reading | ||
---|---|---|---|---|

1 | 01-18 | Logic (Prof. Bruce’s slides) | 1.1, 1.2, 1.3 | |

2 | 01-23 | Quantifiers | 1.4, 1.5, 1.7 | |

3 | 01-25 | Naïve set theory | 2.1, 2.2 | HW01 due |

4 | 01-30 | Relations | 9.1, 9.2 | |

5 | 02-01 | Functions | 2.3 | HW02 due |

6 | 02-06 | More functions | 2.4, 2.5 | |

7 | 02-08 | Sequences, summations, and countability | 3.2 | |

8 | 02-13 | Asymptotics | 5.1, 5.2 | HW03 due |

9 | 02-15 | Induction | 5.3, 5.4 | |

10 | 02-20 | Recursive definitions | 4.1 | HW04 due |

11 | 02-22 | Countability review; strong induction | 4.1 | |

12 | 02-27 | Induction review | 4.3, 4.4 | HW05 due |

13 | 03-01 | Sample midterm | 4.5, 4.6 | |

14 | 03-06 | Review | HW06 due | |

15 | 03-08 | Midterm in class |
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03-13 | Spring break |
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03-15 | Spring break |
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03-20 | No class |
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16 | 03-22 | Permutations | 6.1, 6.3, 6.5 | |

17 | 03-27 | The Pigeonhole Principle; The Binomial Theorem | 6.2, 6.4 | |

18 | 03-29 | Discrete probability | 7.1 | HW07 due |

19 | 04-03 | Probability theory | 7.2 | |

20 | 04-05 | Bayes’s Theorem | 7.3, 7.4 | HW08 due |

21 | 04-10 | Equivalence relations | 9.5 | |

22 | 04-12 | Working with relations | 9.3, 9.4, 10.1 | HW09 due |

23 | 04-17 | Lattices and order | 9.6 | |

24 | 04-19 | Graphs | 10.1 | HW10 due |

25 | 04-24 | Graph representations | 10.2, 10.3 | |

26 | 04-26 | Paths and circuits | 10.4, 10.5 | HW11 due |

27 | 05-01 | Trees | 11.1, 11.5 | |

28 | 05-03 | Flex day/review | HW12 due | |

05-08 | Final exam at 9am in Seaver Commons 103 |