Ib Further Mathematics Option Topic Discrete Math Pdf

IB Mathematics (Further Mathematics) Page

This course is nominally offered to those students having entered the IB Mathematics (HL) sequence earlier than their cohort group, leaving them with the need for "further studies" after writing the externally-moderated papers (1,2,3) at the conclusion of the second year of Higher-Level mathematics. For the 2007–2008 academic year there are two such students. Coincidentally, during the 2006–2007 school year I had a number of high-ability juniors who finished a year of AP Calculus (BC) and were looking for a capstone mathematics experience for their senior year here at Shanghai American School. Less than a moment's thought was required to be convinced that admitting them into this IB course would be in everyone's best interest, as with approximately 10 students enrolled, our numbers will be ideal for a quality experience for all.

The curriculum is an amalgamation of the five option topics available to students in the IB Mathematics HL stream:

Advanced Euclidean Geometry
Discrete Mathematics
Abstract Algebra and Group Theory
Series and Differential Equations
Inferential Statistics

The above topics so gathered together form a harmonious misture of the three pillars of mathematics: algebra, geometry, and analysis. I applaud the various IB curriculum committees for both the topical selections as well as the detailed syllabi within each topic.

Unfortunately, there appears to be no single text which presents the above topics to high-school level students with any degree of cohesion. As a result, I took it upon myself to write a set of notes dedicated to just this purpose. The extent to which it accomplishes the above objective remains to be seen.

In very general terms, syllabus of the course will follow the five topics listed above. In turn these five topics correspond exactly to the five chapters in the above set of notes. Here are a few more details:

General Information
Text	Advanced High-School Mathematics
Sequence
Topic	Timeline/Comments
Euclidean Geometry	4–5 weeks + inclass and takehome tests
Discrete Mathematics	Elementary Number Theory: 4 weeks + in-class and takehome tests
	Elementary Graph Theory: 4 weeks: in-class and takehome tests
Abstract Algebra	Set Theory: 2–3 weeks + in-class and takehome tests
	Group Theory: 3–4 weeks + in-class and takehome tests
Series and ODE	Series: 4 weeks + in-class and takehome tests
	Differential Equations: 2–3 weeks + in-class and takehome tests
Inferential Statistics	Overview of discrete and continuous random variables; simulations: 3–4 weeks + in-class and takehome tests
	Confidence intervals and hypothesis testing: 3–4 weeks + in-class and takehome tests