Try to think about the subject. A walk (for instance) can assist the heart to deliver in blood for the brain. 4.) Remembering the chapter or section. It also helps to allow you to relax your mind. Whatever people may say that memorization is essential in math. How do I study mathematics? However, one can also be knowledgeable about it.1
This can be very difficult and typically takes a lot of time to figure out your own method. It’s for instance, it’s crucial to be aware of (most all of) the evidence. I generally do a study of a chapter or section by dividing it into several parts. If you can only recall the essential steps, you’ll be able to easily recreate the evidence.1 I discovered that although it made my studying time a little slower, it also improved my comprehension dramatically. You could also keep a few images, visuals or even examples in your head to help you remember the ideas.
The methods I use: At the end of the day, the subject matter should become automatic. 1.) Go through the chapter or section.1 Don’t spend time trying to push all of your thoughts into your brain instead, try to be an integral part of the chapters. Review the definitions as well as theorem assertions. 5.) Making the problem. Don’t look up the proofs.
Try to solve all of the exercises in the book even if they’re repeated.1 Take a look at the exercises and try to solve the problems. Repeating the exercises helps you remember the subject more effectively. Don’t spend too much time working on them, but try to determine the difficulties when solving these problems. Don’t skip the more difficult questions. You might be missing the pertinent definitions or formulas or it’s just taking some time.1 Don’t be afraid to seek help if you are unable to find the answer, but give it an honest shot prior to soliciting assistance.
2.) Study the entire chapter or section meticulously. 6.) Notes. Make sure to comprehend every word and every step of the process. Note down the most important sections of the chapter at the amount of detail you want.1 Find the gaps. Include helpful mindmaps and illustrations. Try to figure out the exercises from the textbook.
Keep an inventory of the most important instances and counterexamples. It’s recommended to attempt to prove theorems before reading the proof. Try every new definition or theorem on the examples/counterexamples on that list.1
Don’t spend too much your time on this, however, do take a moment to think about the issue. It may seem to be an overwhelming task however, it’s certainly the most effective way to master math. 3.) Explore the subject by asking yourself these questions If you are given a definition, 1.) Offer an illustration of something that fits the definition. 2.) Give an example of what is satisfying the definition.) Offer a counterexample of anything that is not in line with the definition d) Explore the connections with different definitions.1
It is important to remember that learning mathematics will take a significant amount of time. Consider, for instance: is every bounded function a continuous function? Are all continuous functions bounded? (e) Explore what we value in the definition. f) Draw an image. Doing things too quickly is not a good idea.1 In a theorem, a) Offer an illustration of an event which meets the conditions of the theorem.
It’s better to spend two pages in a day that you truly understand and can remember, rather than taking one day to read twenty pages you don’t remember in the next week. Then try to prove the result for the theorem that you have chosen for that instance.1 What do you think of videos for lectures?
B) Offer an illustration of something that fulfills all of the conditions except one, and in which you find that your theorem isn’t work.) Do the opposite of the theorem apply? D) Do we have a way to enhance the result? e) Look into exactly what is happening in particular cases, the extreme, or the limiting instances f) Is this theorem connected to an earlier one?1 It is it a opposite of a previous theorem? It is it a specific situation, perhaps more general in nature than a prior theorem? G) Draw a drawing h) Create a mindmap describing previous theorems and their interrelation. They can be extremely useful however, I’m a little hesitant toward these devices.1
In a proof, a) Find the key actions b) What strategies within the evidence have you seen previously? Do you have techniques you can employ in the future? c) Try writing all the evidence in a single sentence, and focusing on the essential step(s). The reason for this is that people depend too heavily on them.1 D) Reconstruct the proof by making use of the most important steps.
3.) Try to reconstruct the evidence again and time until you truly comprehend it. This is a problem since lecture videos create an illusion of understanding, instead of real understanding. It’s fine if not able answer any of these questions.1 There are times that people go through videos and think they know the subject well. What is important is that you thought about it carefully.
Unfortunately, this isn’t the situation. Try to think about the topic. This is why it’s crucial to be aware that videos aren’t an alternative to books . 4.) The section or chapter you are studying should be memorized.1 Therefore, you must always use the book as your first-line resource. It doesn’t matter what anyone says it is crucial to remember in math. Reading the book and (very crucial!) the issues it presents is crucial.
But , it is possible to be smart about it. Videos can be useful as supplementary material.1 For instance, it’s essential to understand (most in) the facts. For instance, you could take a look at a video prior to go through the chapter of the book, or even after. However, if you are able to remember the most important steps, you’ll be able to quickly reconstruct the evidence. Always complement the video with a book.1 Also, it is possible to keep a visualisation, images or examples in your brain to help you retain the principles.
Additionally, there is an art of understanding math. The final goal is that the concepts should be an automatic process. It is not for everyone to be able to do it. Therefore, don’t try to force the material into your mind Instead, you should try to become as one.1 This is why it’s important to be taught. 5.) Answering the questions. If you only watch videos, you will not attain the level of mathematical proficiency which is required.
Try to complete all the questions in the book even if they’re repeated. However, it is a great addition to your study! Repeating them helps you learn the concepts more effectively.1 Similar observations apply to online courses like Coursera. Be sure to not skip tougher issues.
What books and subjects should I read about? These are the subjects I will cover in the coming posts. Don’t be afraid get help if can’t locate it, but make sure you give the problem an opportunity to try before seeking assistance.1
6.) Take notes. The Complete Guide on Self Study Mathematics. Write down the key parts of the chapter at the level of detail that you would like.