I started to read from "3.1 The Ultraviolet Catastrophe" and this sentence
"The number of different wavelengths of electromagnetic radiation, N(λ)dλ, with wavelengths in a small interval between λ and λ + dλ, (dλ means a small interval in wavelength) can be shown to be proportional to 1/λ⁴."
doesn't make sense. It should not talk about a number of wavelengths, but the number of allowed standing-wave modes (number of eigenmodes that a mathematical solution to the electric field in the relevant situation has) in the small wavelength interval.
"The number of different wavelengths of electromagnetic radiation, N(λ)dλ, with wavelengths in a small interval between λ and λ + dλ, (dλ means a small interval in wavelength) can be shown to be proportional to 1/λ⁴."
doesn't make sense. It should not talk about a number of wavelengths, but the number of allowed standing-wave modes (number of eigenmodes that a mathematical solution to the electric field in the relevant situation has) in the small wavelength interval.