Paradoxes and Infinities
|Sites Offered||BRI, LAN, SCZ|
|Previously Offered||ATN,EST, HKU, SUN|
From the CTY Summer Catalog:
The second sentence is true. The first sentence is false. Are these sentences true or false? How is it that observing an orange pumpkin is seemingly evidence for the claim that all ravens are black? Students in this course explore conundrums like these as they analyze a range of mathematical and philosophical paradoxes.
Students begin by considering Zeno’s paradoxes of space and time, such as The Racecourse in which Achilles continually travels half of the remaining distance and so seemingly can never reach the finish line. To address this class of paradoxes, students are introduced to the concepts of infinite series and limits. Students also explore paradoxes of set theory, self-reference, and truth, such as Russell’s Paradox, which asks who shaves a barber who shaves all and only those who do not shave themselves. Students analyze the Paradox of the Ravens as they study paradoxes of probability and inductive reasoning. Finally, they examine the concept of infinity and its paradoxes and demonstrate that some infinities are bigger than others.
Through their investigations, students acquire skills and concepts that are foundational for higher-level mathematics. Students learn and apply the basics of set theory, logic, and mathematical proof. They leave the course with more nuanced problem-solving skills, an enriched mathematical vocabulary, and an appreciation for and insight into some of the most perplexing questions ever posed.
BRI 16.2: Paradoxes and Infinities B was known for their litness. Everyone was constantly confused and always either playing with a rubrics cube or throwing playing cards at each other. Many of the campers were known for always sleeping during break or class in general. It was also due to this class that the Bleen Team phenomenon occurred. The A team occurred too, originating from PDOX B, consisting of Bonnie Chan, Zyanya Singh, Albert Guo, Elisa "A" Mezhirov, and Abnner Olivares. However, as advised by Abnner, this must be pronounced as ah, since they mustn't be used for copyright. This would be the common thing that Elisa would remember, and always laugh about.
EST 16.1: This class was simply amazing. PDOX at Easton 16.1 was probably the single most functional-dysfunctional class in existence, whether it be because of the wide age range of the people in the class, or the tendency of particular people to regularly check their phones in class, which they were keen to plug in to the wall to charge at the very start of the session. Possibly the most notable events to have occurred in the class were the crucifixion of BEE onto a tree in the green, the uttering of the word 'penetration' during a Foursquare tournament when a mulch chip very aptly so penetrated a ball, the endless printout puzzles we were given to solve, and the frequency with which the class was shown Kurzgesagt and Vsauce videos. Notable members of the class included Theo "Chipmunk" Faugeres, Trrishaant Sarin, Kabir Singh, and Sebastian Reardon. The class unfortunately intersected with a tumultuous period in time, that being the release of Pokémon GO, and the craze seized not only every student within the campus but also some instructors and TAs, among which were those teaching this class. PDOX 16.1. was a great time. It is unfortunate, however, that, after the end of the session, few people in the class kept in touch, and, likely, even fewer still visit the memory of those sunny days in the green or those grey skies seen from Pardee.