Understanding Mathematics

This book is written for the New Senior Secondary Math Curriculum in Hong Kong. Its aim is to provide an alternative approach to learning mathematics, an approach more vigorous than that provided by most standard textbooks in Hong Kong. In this book, besides examples, which are similar to those found in standard textbooks, there are many definitions and theorems etc. Examples tell us how to do. To know what we are doing, we need definitions etc. To understand why we can use a certain method, we need theorems etc. Although, the concept of sets is not included in the math curriculum, it is used implicitly in the concept of domains (of functions) and that of events (in the topic of probability). For this reason, a brief introduction to set languange is given in the first part of Chapter 1.

  • Compulsory Part    (chapters that have been revised are replaced by newer versions)
  • S4 Chapter 1 Sets and Number Systems    (Ver 2010.6.16)
  • S4 Chapter 2 Linear Equations and Straight Lines    (Ver 2010.5.28)
  • S4 Chapter 3 Quadratic Equations    (Ver 2010.5.28)
  • S4 Chapter 4 Complex Numbers    (Ver 2010.5.28)
  • S4 Chapter 5 Functions and Graphs    (Ver 2010.2.19)
  • S4 Chapter 6 Quadratic Functions    (Ver 2010.6.1)
  • S4 Chapter 7 Polynomial Functions    (Ver 2010.7.8)
  • math_chap1--chap7.pdf (2050 KB)
    math.zip (6091 KB, contains the source tex files, style files and eps files for figures; to use the source files, unzip the files and open the file S4.tex and run latex twice)
    nb.zip (1878 KB, contains mathematica notebook files for producing eps files used in different chapters)

  • Module 2
  • Comments and suggestions are welcome. Please send email to math@schung.info