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文件名称：Advanced High-School Mathematics
文件大小：3.14MB
文件格式：PDF
更新时间：2020-05-15 09:28:28
Mathematics
The basic layout of my notes originally was constrained to the ve
option themes of IB: geometry, discrete mathematics, abstract algebra,
series and ordinary dierential equations, and inferential statistics.
However, I have since added a short chapter on inequalities and constrained
extrema as they amplify and extend themes typically visited
in a standard course in Algebra II. As for the IB option themes, my
organization diers substantially from that of the HH text. Theirs is
one in which the chapters are independent of each other, having very
little articulation among the chapters. This makes their text especially
suitable for the teaching of any given option topic within the context
of IB mathematics HL. Mine, on the other hand, tries to bring out
the strong interdependencies among the chapters. For example, the
HH text places the chapter on abstract algebra (Sets, Relations, and
Groups) before discrete mathematics (Number Theory and Graph Theory),
whereas I feel that the correct sequence is the other way around.
Much of the motivation for abstract algebra can be found in a variety
of topics from both number theory and graph theory. As a result, the
reader will nd that my Abstract Algebra chapter draws heavily from
both of these topics for important examples and motivation.