Formalism eliminates falsehood; it does not lead to the truth.
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Lists should be numbered from zero.
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Tell the truth, not formal statements. Formal definitions are important, but they are not the essence of mathematics. What the notion really means is much more important than how it appears.
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Motivation is important. One should know why that particular structure is studied before they actually studies them. For example, the idea of symmetry should come before the concept of groups.
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Avoid preliminaries. Better, transform preliminaries into motivating applications. At times, preliminaries can be embedded into the text, e.g., Homological Algebra can (and should) be taught along with Topological Homology Theory. Sometimes, the “preliminary” can be developed together with the main topic, as is the case with ODE and Newtonian Mechanics, Differential Geometry and Hamiltonian Mechanics, Riemannian Geometry and the Theory of General Relativity, Linear Algebra and Quantum Mechanics, etc.