tailieunhanh - ADVANCED HIGH-SCHOOL MATHEMATICS

In Chapter ?? we considered the ways in which one could form new statements from given statements. Now we shall consider an analogous procedure, the formation of new sets from given sets. We shall assume that each of the sets that we use in the combination is a subset of some universal set, and we shall also want the newly formed set to be a subset of the same universal set. As usual, we can specify a newly formed set either by a description or by a listing. | Advanced High-School Mathematics David B. Surowski Shanghai American School Singapore American School January 29 2011 i Preface Acknowledgment The present expanded set of notes initially grew out of an attempt to flesh out the International Baccalaureate IB mathematics Further Mathematics curriculum all in preparation for my teaching this during during the AY 2007-2008 school year. Such a course is offered only under special circumstances and is typically reserved for those rare students who have finished their second year of IB mathematics HL in their junior year and need a capstone mathematics course in their senior year. During the above school year I had two such IB mathematics students. However feeling that a few more students would make for a more robust learning environment I recruited several of my 2006-2007 AP Calculus BC students to partake of this rare offering resulting. The result was one of the most singular experiences I ve had in my nearly 40-year teaching career the brain power represented in this class of 11 blue-chip students surely rivaled that of any assemblage of high-school students anywhere and at any time After having already finished the first draft of these notes I became aware that there was already a book in print which gave adequate coverage of the IB syllabus namely the Haese and Harris text1 which covered the four IB Mathematics HL option topics together with a chapter on the retired option topic on Euclidean geometry. This is a very worthy text and had I initially known of its existence I probably wouldn t have undertaken the writing of the present notes. However as time passed and I became more aware of the many differences between mine and the HH text s views on high-school mathematics I decided that there might be some value in trying to codify my own personal experiences into an advanced mathematics textbook accessible by and interesting to a relatively advanced high-school student without being constrained by the idiosyncracies