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Colorful one-to-one (1-1) mappings. When you twist any plane figure, every point in the new distorted image can be traced back to the original figure. College textbooks that include topics in function theory are sparingly illustrated. Readers need better graphics in order to visualize the abstract concepts of modern mathematics. With adequate pictures, images, virtually any text can become instantly interesting. Adding colors to any graphic or diagram will quickly attract the attention of the reader.
There's no reason to hold that modern topics should be necessarily abstract. Geometry is essentially a visual science, so why not other matters like set theory, or functions theory.
One-to-one mappings is one of those subject that is better understood with the help of some infographic like this one.
For the PDF version of this infographic follow this link.
The Golden EBook of Graphs of Mathematical Functions.
Maybe Descartes never imagined how far was going to evolve his system and how much beauty is in his coordinate system. What if we add coloring to the math plots? What if we add real-life picture transformations to the mathematical equations? What are one-to-one (1-1) transformations? How can a 2-dimensional figure be transformed into a 3-dimensional surface? This book has some elementary answers to those profound questions.
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