Sugaku Long Toreiru "Daigaku He no Sugaku" ni Chosen Kansu Hen (Blue Backs)

[Machine Translation] The appearance and properties of a wide variety of functions are grasped all at once. The "landscape of mathematics" spreads out before your eyes. When you look at the mountains in front of you, you will be struck by their grandeur and abundance of shapes. This is the spectacular mountain of functions we are aiming for in this book. As you head for the summit and read through the dialogues between the teacher and students, you will be able to view the functions of high school mathematics, including quadratic functions, expressions and figures, fractional and irrational functions, exponential and logarithmic functions, and the composite formula for trigonometric functions. Near the summit, the view opens up to reveal a new ridge. Once you have mastered the relationship between functions and coordinates in this book, you will be able to see the next landscape, the world of analysis starting from differential and integral calculus.

多彩な関数の姿と性質を一気にまとめて把握する。目の前に広がる「数学の風景」。連なる山々に目をやると、ひときわ雄大で豊かな形が目に飛び込んできます。それこそが本書で目指す、壮観な関数の山です。頂に向かい、先生と生徒の対話を読み進めると「2次関数」「式と図形」「分数関数・無理関数」「指数関数・対数関数」「三角関数の合成公式」と高校数学の関数を眺望することができます。頂付近ではさらに視界が開け、新たな尾根があらわれます。本書で関数と座標の関係をマスターすれば、次なる風景、微分積分からはじまる解析の世界が見えてきます。