Beyond Infinity, Summer 2020

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Room:
Time: Sunday 1:15PM - 2:45PM
Grades: 9-12
Prerequisites:
Material fee: $0.00

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Description: Join this course if you want to dive into the deep end of mathematical logic. We will discuss how to build numbers as sets, and then use this to systematically build up different kinds of infinite numbers - some of them larger, possibly much larger, than others. We will also find some logical concepts and proof techniques that are rarely (if ever) found in arithmetic, algebra, or even many other areas of math and science, yet are natural in their own way; such concepts include consistency and independence, and famous results such as Gödel's Incompleteness Theorems and Cohen Forcing. Prerequisites: students should be comfortable with logical notation (including symbols for logical and, logical or, and implication); students should also have experience working with axioms, and understand the distinction between axioms and theorems. On the first day of class, we will define "partially ordered set" and "well-ordered set," you can look these up in advance if you want.

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Homeworks

These homeworks are copyrighted material, posted here for use by SchoolNova students and parents. Everyone else is welcome to print a copy of these materials for their personal use; any redistribution or commercial use is prohibited

• Assigned on 06/28: Beyond Infinity 1: Posets  |  
  Welcome to class! Here is the first problem sheet!
  
• Assigned on 07/5: Beyond Infinity 2: Functions, Isomorphism, Well-Ordered Sets, Axioms  |  Beyond Infinity 2: Homework  |  
  
• Assigned on 07/12: Beyond Infinity 3: Ordinals & Axiom of Choice  |  Beyond Infinity 3: Homework  |  
  
• Assigned on 07/19: BI 4: Ordinals And Cardinals  |  Homework: Ordinals And Cardinals  |  
  
• Assigned on 07/26: Beyond Infinity 5: Large Numbers & Big Theorems  |  Beyond Infinity 5: Homework  |  
  
• Assigned on 08/2: Beyond Infinity 6: Models, Forcing, Beyond ZFC  |