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Pascal's triangle, Golden Ratio, Measuring pi
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ECS-235A, Lecture 16, October 26, 2022
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Please watch this recording to learn more about writing Paper Part I
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Lecture 2022-03-03. Examples of probability calculations interspersed with foundations. Definition of a probability space. Sum rule, product rule, inclusion/exclusion. Random variables and…
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Lecture 2022-03-01. Review of counting principles. Then, another day of examples, these leading to probability calculations.
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Lecture 2022-02-24. Principles of counting: sum rule, product rule, inclusion/exclusion. Exponentiation, factorial, permutations, and combinations. Lots of examples.
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Lecture 2022-02-22. Three statements of the pigeonhole principle (PHP) and quite a few examples of its use. Reviewing some number theory. The Division Theorem. Euclid's algorithm. Finding…
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Lecture 2022-02-17. Using the Fundamental Theorem of Arithmetic to answer questions like how many divisors a number has. Karatsuba multiplication. Writing and solving recurrence relations. Binary…
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Lecture 2022-02-10. The language of number theory, and the Peano axioms for it. The last axiom: the principle of mathematical induction. Different forms of it. Using induction for establishing…
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Lecture 2022-02-08. Equinumerous sets. Another proof that the rationals are countable. Uncountability of the set of all languages over {0,1}. When do things become impractical? Concrete dividing…
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Injective, surjective, and bijective functions. Examples. Two methods to shuffle cards. Countably infinite sets.
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ECS-020 Lecture 2022-02-01. Reviewing definitions. Equivalence relations and the idea that they induce partitions. Three ways of conceptualizing integers mod n. Functions. Computing functions that…
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