Day 10, Mat385

Last time

Next time

Announcements
- No office hour today after class (my granddaughter from Las Vegas is in town, and I am racing home to be with her!:)
- You'll have a quiz over proofs at the end of the hour. We'll be doing a few proofs along the way today.
- 'There is no standard': investigation finds AI algorithms objectify women's bodies: Guardian exclusive: AI tools rate photos of women as more sexually suggestive than those of men, especially if nipples, pregnant bellies or exercise is involved
  Why do these systems seem so biased?
  Modern AI is built using machine learning, a set of algorithms that allow computers to learn from data. When developers use machine learning, they don't write explicit rules telling computers how to perform a task. Instead, they provide computers with training data. People are hired to label images so that computers can analyze their scores and find whatever pattern helps it replicate human decisions.
- Disinformation Researchers Raise Alarms About A.I. Chatbots: Researchers used ChatGPT to produce clean, convincing text that repeated conspiracy theories and misleading narratives.
  "This tool is going to be the most powerful tool for spreading misinformation that has ever been on the internet," said Gordon Crovitz, a co-chief executive of NewsGuard, a company that tracks online misinformation and conducted the experiment last month. "Crafting a new false narrative can now be done at dramatic scale, and much more frequently -- it's like having A.I. agents contributing to disinformation."
  Check Point Research, a group providing cyber threat intelligence, found that cybercriminals were already experimenting with using ChatGPT to create malware. While hacking typically requires a high level of programming knowledge, ChatGPT was giving novice programmers a leg up, said Mark Ostrowski, the head of engineering for Check Point.
Last time:
- We finished off Induction.
- Questions on induction? Two types (or principles).... but they're equivalent.
- Let's start with one more proof: that the first principle of mathematical induction implies well-ordering (by contradiction).
Today: We'll pick up on recursion again: Section 3.1 (Recursive Definitions), while working on highlight worksheet 3.1

Links:

Pascal's triangle

Cayley's 1879 Note on the Four Color Problem:

On the Colouring of Maps
Author(s): Professor Cayley
Source: Proceedings of the Royal Geographical Society and Monthly Record of
Geography, New Monthly Series, Vol. 1, No. 4 (Apr., 1879), pp. 259-261

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