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Now you may have the question : What do I need to learn/study ? Which one I have to study first ?

At least in engineering, my recommendation is as follows. I would study those topics in Green circle first and then pick anything on Gray circle depending on which area of engineering you will be working on. According to my experience, those topics on Green circle would apply to whatever area in engineering you will be working on and you may see a little different items on Gray circle depending on the specific area you will be working on.



These are huge topics. Each one of the topics shown above would be with thick text books. So if you just buy only one or two books with these titles, you would have a big pile of textbooks. Do I really have to study every books from cover to cover (from the first page to the last page) ?. I don't think so. To be honest, I don't think it is possible either. I think one of the biggest problem in school curriculum is to trying to achieve what is practically unachievable. They are trying to teach too much in too short time, but in reality almost nothing is learned not even mention to being digested. (In some sense, I think I can understand why school curriculum has become like this. Because there are many students which will be working in very wide spectrum of area which may require different set of mathematical skills, they may try to cover everything in the hope that they would help student with whatever area they will be working. But unfortunately our brain is not designed to absorb/digest such a many things in such a short time.)



What is my suggestion ?


My suggestion is

  • to extract bare minimum topics that is most widely used in each topics to pack into a volumn of one text book
  • to study repeatedly until you understand those topics as you speak in your language (See 'Math is a Language')


Then how do I know which specific topics I have to extract from each thick textbook ?

  • If you are already working in a specific engineering area as a job or as a graduate course, I think you are already in good position to figure out what to study. Just make a list of topics whenever you see the new mathematical topics from journal, paper or industry specification.
  • If you are still in school (undergraduate), I hope this site can be a good tip/guide for you.