preface
This article was originally calculated in the “Data structure and Algorithm Analysis” (3) section of the linear table, originally is to discuss how to learn data structure, but I think the things discussed are general, plus recently also happened to write a miscellaneous sense, simply included in the miscellaneous sense. Why is it mixed feeling? Because it is very unsystematic, there is some feeling of reading some articles, some books and so on, there is also the feeling of looking back on the past and so on, there is also the feeling of some things I have experienced. In fact, sometimes I want to break them up into essays just like Lu Xun, but I think the length is too short. I think this is also a kind of fault. I always want to think that the amount is enough.
Talk about learning
Many times we understand to be not moved some concept or feel something hard to learning, the reason is half and half, half may be really hard to on these concepts, half may be on his way of learning, always take his past may have successful way to learn to learn new concepts, new things, but this to some extent and inertia, After all, this learning method has been successful in the past, and there is no big problem with continuing to use it. However, this cannot be generalized. I think of an idiom that seems to evaluate this learning strategy by sticking to experience and not being flexible.
The world is a heterogeneous place, and when we find ourselves stuck in one place for a long time, or not at all, it may be a sign that our learning strategies may be faulty and that we need to change our learning strategies. We inherited from a conventional learning strategies from the school, more specific by inheritance from high school before that time, the time of learning strategy is to listen, for some of the more important the concept of teacher is often required to recite, usually in order to emphasize the importance of these concepts, high school teacher will only speak a few years ago the concept, and then do the topic.
If you get a good score, you will usually get praise from your teacher or your parents. I think this way of learning for a long time will sometimes form a kind of reflexive learning strategy, that is, when you need to learn again, you will also use this strategy, reciting and doing exercises. But for the most part this doesn’t work in every situation, because not everything you study has a syllabus and an exam syllabus, and the syllabus and the exam syllabus tell you what’s important.
But I think something like an exam outline is necessary, because knowledge is limitless and life is limitless, so even if there is no such thing as an exam outline, we also need to draw an outline or a goal for ourselves. This goal is similar to the end of a run. If the goal is too big, it is subconsciously or practically impossible to achieve, even though our heart is strongly willing to move towards it.
What about after we have the exam syllabus, how do we study? This is the first step. I think of my friend who is a medical student, and WHEN I went to play with her, I saw her textbook, and I vaguely remember it was about human bones, and each bone had a poem, and my friend smiled and said to me, This is more than 300 Tang poems, but just write it down, you know how desperate I was when I took the exam. To some extent recitation is also an obstacle for us to learn some knowledge, but for recitation we still have a way to deal with, if memory is not good, then spend more time, spend a little effort, can always recite down. The difficulty is understanding.
Some concepts, the corresponding knowledge is the answer to the question, we should also pay attention to the thinking behind the problem, not just to look after is only limited to the single problem answer, but in the thought process behind the solve the problem, the former is a hen’s egg, while the latter is a hen, can bring us more eggs.
Euler believed that there was no point in teaching mathematics if students could not be taught the thought process behind mathematical problems. Leibniz also said: In my opinion, nothing is more important than to explore the source of invention. Poincare (known as the last Mathematical generalist) himself has a great interest in Mathematical thinking, and has a great lecture on problem solving called Mathematical Creation, if you are interested.
But what about the math textbooks we grew up with? It’s basically Euclidean: from definitions to theorems to inferences. This also distorts the real process of mathematical discovery, which is largely derived from questions to create corresponding concepts, definitions, and inferences. I think of the university “advanced mathematics” tongji edition, “linear algebra” tongji edition, these two are typical Euclidean teaching materials, simple to raise two sentences, and then began to lay out the definition, concept, theorem. But I don’t want to completely deny Euclid type, theoretical system, which helps to build their own mathematics knowledge structure, but is a bit that I don’t like the reason is that lack the arm little leg theorem is introduced, may be simple to engineering raw material, do not need to feel some fixed in engineering, some certificate is not given, linear algebra, too, Finally, THE quadratic form was introduced. I had no idea what it was. It was like a monster built by many concepts. Some people might say that math itself is abstract, and yes, I agree with that, but math textbooks should not be limited to just putting in theorems that the author knows, maybe giving students a little bit of intuition about math.
Simply I go to direct library to turn over other teaching materials finally, my teacher recommends to see in science big “mathematical analysis”, myself go looking for the linear algebra teaching materials of mathematics department directly again, turned over several, also be to do not have experience. Different authors for the arrangement of the same theorem, have different habits, interpretation in the “linear algebra” tongji version felt anything is not clear, can see clear in other materials, this let me indulge, computer courses are all behind, I study in the senior year began to pop out, of course this is another story.
My experience here is not to be bound by the past learning method. If the current learning method does not work well, maybe changing or introducing an auxiliary learning method is also a good learning strategy. Just like mathematics, we need not only Euclidean, but also from the way of thinking and solving problems to introduce definitions, theorems, inferences.
We say regular learning some extent there is a cognitive process of the concept of, but people can’t understand what he had not experienced, our understanding and the past is already the relevant information will be more easy to accept things, the brain will be more easy to establish a new link between knowledge and knowledge, with the help of past experience to understand something new.
Therefore, when we learn a new concept, we can push it out by introducing problems. In order to solve some problems, the concept is pushed out. Also consider focusing on the thinking behind the problem solving, which is often more important than learning new concepts, since different concepts may derive from the same thinking. It is also important to understand the whole of a problem, not just the parts, as Poincare notes in Mathematical Creation: Once you have a general idea of the general process of solving a problem, even if a local detail is lacking, it can be deduced (filled in) under the guidance of that general view.
Here is a related thought psychology experiment: it is known that a good go player can remember a very complex end game, while a novice can hardly remember half of it. The reason is that a go expert has domain knowledge: knowledge of all kinds of go moves, knowledge of all kinds of situations. With that knowledge, you just have to remember the general picture of the situation, and you can deduce the details. In fact, when experts were asked to remember a randomly placed chess game, they did no better than laymen.
Perception of time
I feel time is flowing at an accelerating speed. I see my college classmate getting married and my high school classmate having a second child. But sometimes, I feel time passes slowly, such as from Monday to Friday. At that time, I just graduated from university and had some ideas about the future. After all, I just got out of school and could not have any ideas about the future. However, my thoughts at that time were always affected by the reality, and some plans were postponed until this year. When you have some sort of expectation and imagination of life, the but again feel not achieve them tomorrow, and three months can achieve a year probably still not achieve them, and may not have to think about three years later can do it, you’d think three years is very long, can give the expectation and imagination to three years in the future.
However, if you just give your expectation and imagination to the future without putting it into action, then when you arrive at the future, the future may also be your expectation and imagination. You can not blame this period of time. Time is omnipotent, but time is not omnipotent, if you do not have a little understanding of it. We have many metaphors for time. I sometimes think that the reason why we use metaphors for things is that we feel that others cannot directly perceive things when they read the words representing them, so we use metaphors. Just like braised pork in brown sauce, I don’t have to use metaphor, I believe you can also imagine the appearance of braised pork in brown sauce.
Some people will feel that the journey from 30 to 40 has gone half way, and suddenly have a feeling that the decade seems to have gone too fast. How come the half way has passed? And 20 to 30 feels like a long time. Thirty years on, and seven years on, I can look back and imagine nothing exciting. The reason may be:
Common memories tend to stick together, and iconic memories tend to stand out. Psychologists believe that our perception of time is related to our experiences. If an event is “exciting” to us, the memory stays in our minds longer.
It’s true that every major life event we experience from the age of 20 to 30 is exciting and unique to us. Naturally, it stands out in our memories, such as the wedding of a best friend, attending a best friend’s wedding, or the death of a loved one. Maybe you still have her in your mind when you were a child. But what you don’t realize is that he is getting older. After 30, there seems to be a lack of those big things.
But we often say waste time, why waste time? The reason may be that we don’t feel like we’re doing anything meaningful during this time. If we measure time, maybe waste time will be a little less, after all, after work, belong to their own personal time is becoming less and less, so we have to use good time, so how to measure time? By measuring time, I mean the amount of time you spend tracking meaningful events during the week, or keeping track of your own time on the weekend. What did you do on the weekend? I’m going to give you too detailed a time measurement strategy, and if it’s too specific, it’s not universal, so I think I’ll just give you the idea of keeping a record of what you did during that time, which will give you a sense of time, and your perception of time will become more and more accurate.
What do we find beautiful?
This week I saw such news: xiao Ran, a 33-year-old hangzhou woman network celebrity, died of liposuction infection. This makes me think again about what beauty we regard as, we often say tang Dynasty takes fat as beauty, but the subtext is the fatter the more beautiful? I don’t think necessarily so, obesity is associated with complications, but these complications lead to fat person is very painful, I don’t think beauty should be in pain will cost, I think we should be in health, for beauty, for the beauty of women supplement on the new connotation, not only in body, not too fat, don’t be too thin, should be multiple, should not be limited in the outside, We also need to add more content to the beauty of women.
Write in the last
These miscellaneous feelings are for some affairs of feeling and hair, behind may also send some miscellaneous feelings, not limited to the scope of the computer, will be a bit more. The part about learning is mainly inspired by liu Weipeng’s “Learning to Know why (Taking Algorithm as an example)”, and the perception of time is inspired by the passage of time and “The Heart method of Programmer’s Advancement”.