Description
Book Synopsisthirdly, as a kind of postscript to elementary analysis-as in a senior undergraduate course designed to reinforce students' understanding of elementary analysis and of elementary mathematics by considering the mathematical and historical connections between them.
Table of ContentsI From Calculus to Analysis.- I.1 What’s Wrong with the Calculus?.- I.2 Growth and Change in Mathematics.- II Number.- II.1 Mathematics: Rational or Irrational?.- II.2 Constructive and Non-constructive Methods in Mathematics.- II.3 Common Measures, Highest Common Factors and the Game of Euclid.- II.4 Sides and Diagonals of Regular Polygons.- II.5 Numbers and Arithmetic—A Quick Review.- II.6 Infinite Decimals (Part 1).- II.7 Infinite Decimals (Part 2).- II.8 Recurring Nines.- II.9 Fractions and Recurring Decimals.- II.10 The Fundamental Property of Real Numbers.- II.11 The Arithmetic of Infinite Decimals.- II.12 Reflections on Recurring Themes.- II.13 Continued Fractions.- III Geometry.- III.1 Numbers and Geometry.- III.2 The Role of Geometrical Intuition.- III.3 Comparing Areas.- III.4 Comparing Volumes.- III.5 Curves and Surfaces.- IV Functions.- IV.1 What Is a Number?.- IV.2 What Is a Function?.- IV.3 What Is an Exponential Function?.
