LPS 105a/205a, PHIL 105a/205a, LSCI 145a
Tuesday/Thursday, 11-12:20, SSL 145
Office hours: by appointment, in SST 759 or online
Over the course of the term we will work through my class notes (which are in the process of being written and edited). I'll continually post updated versions here as I update them. It will be helpful to read through the notes in advance of the week that we go over them - especially for the week of your in-class presentation.
Submit weekly written assignments  on Gradescope.
There are two main goals for this class:
Develop some skills of mathematical proof (both written and verbal)
Learn some basic set theory (both informal and formal)
You will learn both of these things by doing them.
Every week, you will write up the proof of one result we have gone over in class, and turn in the written version on Gradescope. I will give many choices each week of which result to write up - I encourage you to choose one that will provide an appropriate challenge for you, whether that's getting precise on concisely writing up a simple proof, or managing the organization of a more complex proof.
Roughly half of the class time on every day after the first will consist of student presentations of mathematical results. Everyone should sign up to do one of these presentations in Part I and one of these presentations in Part II. I'll be happy to meet with you in the days leading up to your presentations to ensure that you've figured out how your result works, and give some feedback on effectively presenting it.
Your final grade will primarily be based on completing all of these written and in-class proofs, with only slight modifications for quality.
Part I: Informal set theory
Week 0 (9/25): Sets as meanings of words
Week 1 (9/30, 10/2): Sets and numbers
Presenters:
Week 2 (10/7, 10/9): Well-orderings, countable vs uncountable infinities
Presenters:
Week 3 (10/14, 10/16): Many countable infinities
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Week 4 (10/21, 10/23): The real numbers, and the power set of the natural numbers
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Week 5 (10/28, 10/30): The Axiom of Choice, the paradoxes
Presenters:
Part II: Formal axiomatic set theory
Week 6 (11/4, 11/6): The formal language, and the "small" axioms
Presenters:
Week 7 (11/11, 11/13): Power set, separation, and replacement
Presenters:
Week 8 (11/18, 11/20): Binary relations, well-orderings, and the axiom of infinity
Presenters:
Week 9 (11/25, Thanksgiving): Formalized ordinals, and the well-ordering principle
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Week 10 (12/2, 12/4): The Continuum Hypothesis and further topics
Presenters: