Math

Day 1– Math in the school context: mathematical claims, Buchberger's model for mathematical discovery
====Day 2–Math: Conjecture and proof==== ====Day 3–Math: Discovered or invented? Math and reality.==== ====Day 4–The nature of math, math as a creative art==== ====Day 5–More about axioms, math as a human endeavor====
 * most students have been exposd to math for nine to ten yars of mth and therefore now it as an essential to life as we know it
 * however, most students view individual knowledge growth as a function pf personal experiences brought out by a specific curriclum
 * as we go further into our education we are exposed to more methods of justification
 * there are steps to using math: finding the problem, then mathematical problems and equations are turned into theorums, then these theorums are applied to actual mathematical problems
 * The mathematical proof of Elucid: solid as a rock and as aesthetically pleasing as a fine work of art. Or so the majority of mathematicians would claim.
 * mathematical knowledge stems from many different mans and methods
 * "Is math better defined by its method or by its subject matter?"
 * math has been created and developed b mathematicians for centuries, and technicially is not a way of knowledge
 * this provides people a way of saying that math is not actually a way of knowing because it was created by humans
 * however, many matematical sceanarios that were said to have been made up, areactaully present in nature
 * many mathematical sequences occur naturally in nature and in art sucha s the Fibonacci sequence and the golden section
 * Fibonacci is present in the family trees of bees and can also be used to create a nautilus shell
 * and the golden section is the continuos halving of a square to create an infinite spiral
 * mathematics is the language used by nature
 * a system must be workable, ie. consistent
 * another example of this is Euclid's Fifth Postulate that eventually led to the formation of the non-Euclid geometrics of Lobachevsky and Riemann
 * Now a days math is used by society as a way to come to serious and very important conclusions though theroms and tests and laws