Analog design generally requires more analytical mathematics such as calculus including Laplace transforms and Fourier analysis, but a good knowledge of Algebra and complex numbers can get you a long way. Laplace transforms are used to calculate the response of circuits with reactive impedances. Fourier Transforms are used to determine the frequency components and circuit response to complex signals such as pulses and square-waves. For analog circuit design, it helps to have a certain "intuitive" understanding of circuits to determine what circuits are needed to do a particular analog processing task. To develop that requires some experience with circuit design. A Spice analog simulator can help in experimenting with and understanding various circuit designs, but is not a substitute for building a circuit.
Digital design generally requires less analytical math other than Boolean algebra. You do need to develop a good understanding of what all the various gates, flip-flops, drivers, and registers do and which ones are best used to perform a specific digital function.