1. AOK

2. D6 Journal (5 th entry) TWE can imagination be objective if it is derived in the mind? If it is always subjective can it lead to knowledge?

3. Knowledge Framework Effective way to examine the AOKs Scope, motivation, & applications Specific terminology and concepts Methods used to produce knowledge Key historical developments Interaction with personal knowledge

4. Scope & Applications What is the AOK about? What practical problems can be solved through applying this knowledge? What makes his area of knowledge important? What are the current open questions in this area- important questions that are currently unanswered? Are there ethical considerations that limit the scope of inquiry? If so, what are they?

5. Concepts/Language How is language used in the production of the knowledge in that AOK? What are the roles of the key concepts and key terms that provide the building blocks for knowledge in this area? What metaphors are appropriate to this AOK? What is the role of convention in this area? Key to analysis of shared knowledge in the area

6. Methodology What are the methods or procedures used in this area and what is it about these methods that generates that knowledge? What are the assumptions underlying these methods? What counts as a fact in this AOK? What role doe models play in this AOK? What ethical thinking constrains the methods used to gain knowledge?

7. Historical Development What is the significance of the key points in the historical development of this AOK? How has the history of this area led to its current form?

8. Links Why is this area significant to the individual? What is the nature of the contribution of individuals to this area? What responsibilities rest upon the individual knower by virtue of his or her knowledge in this area? What are the implications of this area of knowledge for one’s own individual perspective? What assumptions underlie the individual’s own approach to this knowledge?

9. Math What do you remember? Math proofs/axioms – Euclid Proof v Conjecture - Goldbach’s Conjecture Beauty and math – Fractals (Mandelbrot) Math in nature/ Is it discovered or created? What are numbers?

10. Math: Scope/App Concerned with quantity, shape, space, & change Used to create models in natural and human sciences Community assumes that the more or better you are at math the more intelligent Possess qualities such as beauty and elegance – art form Broadly universal and not confined by culture Math truths seem to be certain & timeless

11. Math: Language Defined set of symbols standing for abstract things like sets, relations, numbers Axiom: foundational assumptions in math; must be consistent, fruitful, simple, independent Deduction Rule : 2 premises and 1 conclusion Theorem: arrived at by applying deductive reasoning to axioms Proof: shows a theorem to follow logically from the relevant axioms Conjecture: a hypothesis that seems to work, but has not been shown to be necessarily true (can’t test all possibilities)

12. Math: Methodology Applies reason to axioms to produce theorems Truth is “achieved” if the statements is “proved” Math doesn’t seem to rely on sense perception of the world Math could be considered a language or part of a language Mathematicians need intuition & imagination in order to prove theorems Faith is employed in the identification of axioms

13. Math: History Euclid V Riemann Introduction of negative and imaginary numbers Introduction of calculus Importance of geometry in paintings, architecture, and music

14. Math: KI Why is there sometimes n uneasy fit between math descriptions and the world? Is math invented or discovered? Why should elegance or beauty be relevant to mathematical value?

15. Math: Links to Personal K. Math’s ability to be taken as a proxy for intelligence and therefore self-esteem Mathematical genius cannot always be explained – the insights are often ascribed to intuition, imagination, or emotion Can be more than one method to solve a problem