This article written by paper writing help from Bidforwriting.com describes effective strategies for learning higher mathematics concepts that will be useful to those who are learning mathematics on their own.
We all wish we were better at math. Many of the tips below will be helpful to those learning math and beyond.
1. Mathematics is not a chore, but a mind game
Mathematics is not only not so much a subject in higher education as a powerful language for presenting abstract ideas. With strict, consistent sets of rules, mathematics can help you concretize any concept.
These rules should be treated with respect, for they have been developed over a long period of time by the best minds. Your mind must be open to it: blind memorization will not work. Memorization of mathematical facts by those who learn mathematics usually occurs naturally in the course of repeated use of the basics previously learned.
2. Be confident in yourself
Although many people have a fear of mathematics, research shows that a student’s perception of his or her own intelligence as an object to be developed leads to a good dynamic of learning. That is, you must first believe in your own abilities. Mathematics is accessible to everyone. You can learn anything if you have the right motivation.
Don’t worry if you don’t understand a math concept right off the bat. It has been proven that the brain develops even when you make mistakes. Don’t worry if someone has an easier time solving a problem. More often than not, it’s just a matter of experience and mental discipline. Our selection of books and courses can help you get a head start in mathematics.
3. Study what you’re interested in first.
If you’re studying math on your own, start with areas that interest you personally. Don’t waste time on topics that you find boring (but seemingly necessary).
Many of those who have studied or are still studying mathematics have encountered a similar situation. What at a particular moment is not interesting in the current stage of learning becomes understandable and even fascinating later on after you have gone through the topics that are now curious. Interest can develop out of a need for a certain type of knowledge. If you are interested in artificial intelligence, you immediately understand where linear algebra, probability theory, etc. will come in handy.
Try to focus on only one topic within the allotted time frame. It is better to switch between global areas rather than related mathematical concepts.
4. Don’t try to memorize anything on purpose
It is the material that you constantly use that is fixed in your memory. It is worth remembering once again that learning is not one of those things that are done at once by a single effort of will. If you study at least a little bit each day, your brain perceives what you are learning not as a random event, but as necessary material to make life easier. This leads to more successful absorption of the material than deliberate memorization.
If you need reference material, such as a collection of formulas, use thematic reference books. Including brief ones – the same cheat sheets that are easy to find by searching for “[topic of study] cheat sheets.
5. Solve problems all the time
To learn math you need to solve problems. And, of course, it is better if they are problems that are not boring to solve. At brilliant.org, we’ve done a tremendous job of gathering material from different areas of mathematics in a variety of writing styles.
If the task takes a long time to solve, leave it, and start again later. Come back to it until you’ve solved it, but don’t spend too much time on it at once. At some point, your brain will learn enough from other tasks to solve the more difficult one.
If you feel like you’re stumped, don’t hesitate to ask for help, including online – from those who are still learning math or are already experts. Seeing the situation with different eyes, you will discover previously unknown sources of approaches to the solution.
6. Take breaks, rest, and eat right
Exercise daily, but not too long in a row, and take breaks. Maintain a balance of thought work and rest. Do not neglect breaks and switches of thoughts to other things. In such moments, imperceptibly for you, the brain continues to process and assimilate information.
It is extremely important to do a warm-up. Blood carries nutrition to your brain tissues, and if blood flow is difficult, it’s harder to learn. Make it a rule to warm up every 45-50 minutes: walk around the room, squat, and do exercises. For the blood to be oxygenated, exercise in a well-ventilated room.
A change of scenery is also important. After studying for half a day, go for a walk or do sports, and do your homework. After a week of study, go on a vacation to the countryside. A change of scenery gives a feeling of freshness and gives a new perspective on the tasks at hand.
Do not neglect nutrition. It should be balanced. Thinking processes belong to the group of the most energy-consuming tasks that the human body solves. You can “motivate” your brain with small snacks after solving a predetermined number of tasks, dividing your meals evenly depending on the number and difficulty of tasks. Consume more omega-3 polyunsaturated fatty acids – they directly affect the concentration of thought and brain activity. Drink enough water.
Avoid stress. One common type of stress on the body is lack of sleep. Sleep deprivation catastrophically reduces mental performance. It’s not just nighttime sleep that helps you recover, but a short nap during the daytime as well.
For those learning math, there are many tools to gamify the process. Among the best known are the video games Variant: Limits and True: learn(), in which learning takes place through solving puzzles.
If you wonder how math is used in the development of popular games, read our article.
8. Watch the video
When learning math, it’s important to be in a continuous stream of thought. You can learn new visual abstractions and solutions by watching videos on various math topics. To that end, we’ve prepared a selection of 7 useful Youtube feeds.
9. Make an Adjustable Curriculum
What gets measured gets improved. Make a syllabus with milestones. Such a framework increases concentration. It’s like you become your own supervisor, issuing instructions. At the same time, you are both the one teaching math and the one teaching math.
Examples of such plans: a long-term plan for learning Computer Science or a more specialized one for Deep Learning and Neural Networks.
10. Study together and teach others
Many scholarly studies have proven that teaching and studying together can help you learn better. In order to get a message across to someone else, you not only have to read it, but you also have to understand it. This provides additional motivation as it puts a commitment on your shoulders. By working in conjunction with a buddy or a student, it becomes easier for both of you to motivate yourself to study periodically.
In a pinch, you can be the listener yourself. Explain the topic from beginning to end to an imaginary student. You will see that from this angle you were able to realize it more deeply. This approach obliges you to understand all the obscure areas.