Hello 
I think it depends. For example, I wasn't the brightest guy when it came to algorithms and functions, but now they're routine. If you're willing to learn, it's not that difficult. To design, you need to understand what you are working on, and what do you want the output to be, how to make it reach and attract the user, give reasons to choose you over a competitor, the coloring and the graphics must match your main target group's interest... Much thought goes into design, but I think it's something you don't taught to you, but rather learn it on your own as you experiment. Take examples from sites you're using and think about them.
Then you have the back-end, what the developer sees and where they act. This has to be flawless, code-wise, otherwise your whole dynamic page might have huge unwanted bugs or problems. You also need to think what can be implemented when designing, while having the languages you'll use in mind. You need to know what each language is for and what it does, its pros and cons, and so on.
To sum up, if you are willing to learn, you only need a basic grasp of mathematical theories in order to understand basic web design/develop elements. Other than that, it depends on how much you are willing to learn. I've poured hundreds of hours looking at new codes, languages, scripts, techniques, outside of my course's subjects, because I wanted to improve and be more flexible. I'd advise you do the same! Also, good books will help, but do your research on the book's quality first. Long winded post, but I wanted to be informative
I think it depends. For example, I wasn't the brightest guy when it came to algorithms and functions, but now they're routine. If you're willing to learn, it's not that difficult. To design, you need to understand what you are working on, and what do you want the output to be, how to make it reach and attract the user, give reasons to choose you over a competitor, the coloring and the graphics must match your main target group's interest... Much thought goes into design, but I think it's something you don't taught to you, but rather learn it on your own as you experiment. Take examples from sites you're using and think about them.
Then you have the back-end, what the developer sees and where they act. This has to be flawless, code-wise, otherwise your whole dynamic page might have huge unwanted bugs or problems. You also need to think what can be implemented when designing, while having the languages you'll use in mind. You need to know what each language is for and what it does, its pros and cons, and so on.
To sum up, if you are willing to learn, you only need a basic grasp of mathematical theories in order to understand basic web design/develop elements. Other than that, it depends on how much you are willing to learn. I've poured hundreds of hours looking at new codes, languages, scripts, techniques, outside of my course's subjects, because I wanted to improve and be more flexible. I'd advise you do the same! Also, good books will help, but do your research on the book's quality first. Long winded post, but I wanted to be informative