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🤔 Why?

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Curriculum Level

• Why is the symbol for momentum $p$?
• Why is the sample variance divided by $(n-1)$?
• Why is factorial 0 defined as $0! = 1$?

First-Year Topics

• Notation and naming of hyperbolic functions $\sinh$ and $\cosh$
• Why is the limit of a sequence redefined in university mathematics?
• Why is sequence convergence defined more rigorously in university mathematics?
• Why should you be cautious when using recursive functions?
• Why do we study Taylor series (power series)?

Second-Year Topics

• Why is the del operator $\nabla$ not a vector?
  • Why is the gradient $\nabla f$ not a product of $\nabla$ and $f$?
  • Why is the divergence $\nabla \cdot \mathbf{F}$ not the dot product of $\nabla$ and $\mathbf{F}$?
  • Why is the curl $\nabla \times \mathbf{F}$ not the cross product of $\nabla$ and $\mathbf{F}$?
• Why is the symbol for the magnetic field $\mathbf{B}$? (+ Which one represents the magnetic field: $\mathbf{B}$ or $\mathbf{H}$?)

Third-Year Topics

• Why shouldn’t we use $r, \theta$ as variables in cylindrical coordinates?
• Why is the inner product of functions defined as a definite integral?
• Why is the notation for partial derivatives different ($d \to \partial$)?
• Knuth’s up-arrow notation: Why is exponentiation represented by ^ in programming?

Fourth-Year Topics

• Why is a functional called a functional?
• Why are there multiple definitions of the Fourier transform?
• The history of the delta function and why Dirac used it

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