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Advanced High-School MathematicsDavid B. SurowskiShanghai American SchoolSingapore American SchoolJanuary 29, 2011iPreface/AcknowledgmentThe present expanded set of notes initially grew out of an attempt toflesh out the International Baccalaureate (IB) mathematics FurtherMathematics curriculum, all in preparation for my teaching this during during the AY 20072008 school year. Such a course is offered onlyunder special circumstances and is typically reserved for those rare students who have finished their second year of IB mathematics HL intheir junior year and need a capstone mathematics course in theirsenior year. During the above school year I had two such IB mathematics students. However, feeling that a few more students wouldmake for a more robust learning environment, I recruited several of my20062007 AP Calculus (BC) students to partake of this rare offeringresulting. The result was one of the most singular experiences Ive hadin my nearly 40-year teaching career: the brain power represented inthis class of 11 blue-chip students surely rivaled that of any assemblageof high-school students anywhere and at any time!After having already finished the first draft of these notes I becameaware that there was already a book in print which gave adequatecoverage of the IB syllabus, namely the Haese and Harris text1 whichcovered the four IB Mathematics HL option topics, together with achapter on the retired option topic on Eucli

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