# History

The following calendar will be populated with links to worksheets, videos, activities and daily posts, so you can catch up on anything you’ve missed and revisit important material.

• Wednesday, August 26th:
• What we did in class: We began discussing sets.  We covered the definition of set, element, equality, cardinality and subsets, as well as some standard sets of numbers and the empty set.  We did lots of examples.
• In-class notes
• Friday, August 28th:
• Monday, August 31st:
• What we did in class:  We shared active reading strategies, we talked about what is a proof, and then we considered the sandbox problem.  As a group we decided on the answer, and then we broke into groups to try to write up proofs.
• After-class daily post link:  Due Wed Sept 2
• Wednesday, September 2nd:
• What we did in class:  We discussed some first examples of proofs based on the sandbox problem (pdf notes).  Then we introduced two types of set-builder notation (link to notes).
• After class daily post link: Due Friday Sept 4
• Wednesday, September 9th:
• What we did in class:  We finished up with some lecture about set builder notation in the contexts of the real line (interval notation), the Cartesian plane (where you draw graphs for example), and the universe of subsets of some set.  Then we began discussing a proof of the fact that if n is odd, then n^2 is odd.  We only got as far as deciding on our definitions.  Here are class notes.
• After class daily post link:  Due Fri Sept 11
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• Friday, September 11th:
• What we did in class:  We finished up about the n^2 odd proof.  Then we introduced and discussed Cartesian products.  Here are notes.
• After class daily post link:  Due Mon Sept 14th
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• Monday, September 14th:
• What we did in class:  We continued Cartesian products, talking about the Multiplication Principle, and we also discussed Power Sets and proved a formula for the cardinality of a Power Set.  Here are notes.
• After class daily post link:  Due Wed Sept 16
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• Wednesday, September 16th:
• What we did today:  We discussed more examples of proofs.  Here are notes.
• After class daily post link:  Due Fri Sept 18
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• Friday, September 18th:
• Monday, September 21st:
• What we did in class today:  We took up some set builder notation, and then did counting (multiplication principle) based on the first worksheet on counting.  Here are notes.
• After class daily post link:  Due Wed Sept 23
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• Wednesday Septmber 23rd:
• What we did in class today:  More on counting: addition principle, overcounting, binomial coefficient, binomial theorem.  Here are notes.
• After class daily post link:  Due Fri Sept 25
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• Friday, September 25th:
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• Monday, September 28th:
• What we did in class today:  More on inclusion-exclusion (a proof) and then an introduction to graphs.  Here are notes.
• After class daily post link:  Due Wed Sept 30
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• Wednesday, September 30th:
• What we did in class today:  We did more examples of how graphs show up in mathematics and then we introduced Boolean algebra.  Here are notes.
• After class daily post link:  Due Fri Oct 2
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• Friday, October 2nd:
• Monday, October 5th:
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• Wednesday, October 7th:
• What we did in class today:  We discussed “if and only if” as a boolean operation.
• We covered Boolean algebra identities, and talked about the contrapositive and contradiction as proof methods.  Here are notes.
• After class daily post link:  Due Fri Oct 9
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• Friday, October 9th:
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• Monday October 12th:
• What we did in class today.  We worked through examples of negation, and quantifiers.  We talked about the idea of an example and a counterexample.  Then for the last ten minutes we did a worksheet on quantifiers, example and counterexample.
• Negation worksheet.
• Quantifiers Negation worksheet
• After class daily post link:  Due Wed Oct 14
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• Wednesday, October 14th:
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• Friday, October 16th:
• Monday, October 19th:
• Wednesday, October 21st:
• What we did in class today:  We took up solutions for some of the badges.  We continued talked about existential proofs.  Here are notes.
• After-class daily post link:  Due Fri Oct 23
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• Friday, October 23rd:
• What we did in class today:  We considered the definitions of convergence and continuity, and we used them to prove something converges and something is continuous (we didn’t quite finish the latter).  Here are notes.
• After-class daily post link:  Due Mon Oct 26
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• Monday, October 26th:
• What we did in class today:  We took up the proof that f(x)=x^2 is continuous at 0, and then we introduced functions, injectivity, surjectivity and bijectivity.  Here are notes.
• After-class daily post link:  Due Wed Oct 28
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• Wednesday, October 28th:
• Friday, October 30th:
• What we did in class today:  We explored injectivity, surjectivity and bijectivity, and then introduced composition of functions.  The lectures were inspired by the worksheets listed above (Oct 28).  Here are notes.
• After-class daily post link:  Due Mon Nov 2
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• Monday, November 2nd:
• What we did in class today:  Composition, inverses.  We began the proof that a function is bijective if and only if it is invertible.  Here are notes.
• After-class daily post link:  Due Wed Nov 4
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• Wednesday, November 4th:
• What we did in class today:  We finished the proof from last class, and then talked about cardinalities of sets.  Here are notes.
• After-class daily post link:  Due Fri Nov 6
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• Friday, November 6th:
• What we did in class today:  Cardinalities — examples of showing things are countable or not.  Here are notes.
• After-class daily post link:  Due Mon Nov 9
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• Monday, November 9th:
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• Wednesday, November 11th:
• Friday, November 13th:
• What we did in class today:  Equivalence relations, equivalence classes, and partitions.  Here are notes.
• After-class daily post link:  Due Mon Nov 16
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• Monday, November 16th:
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• Wednesday, November 18th:
• Friday, November 20th:
• What we did in class today.  We finished up pigeonhole problems, and then I did a bit of office hour on badges questions.
• After-class daily post link:  Due Mon Nov 23
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• Monday, November 23rd:
• What we did in class today:  Graph Theory!  We introduced topics like path, walk, cycle, tree, connected, complete, adjacent, degree.  Here are notes.
• After-class daily post link:  Due Wed Nov 25
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• Wednesday, November 25th:
• What we did in class today: Introduction to induction using a theorem on trees. Here are notes.
• After-class daily post link:  Due Mon Nov 30