Senior students study for one year and learn several things for half a year. In the future, there will be lectures on mathematics courses such as mathematical analysis and probability theory. If it is a regular school, this course is an important basic course, and it will generally be strictly controlled!
If you are not a math major, it is relatively easy for freshmen to learn advanced mathematics. If you are a liberal arts major, you don't have to study math. As for boredom, it depends on whether you study well or not. If you learn well, you are not afraid of anything and are not bored. If you can't learn, then hey, I don't need to say more. The key is to work hard by yourself.
Learning methods of college mathematics
First, the most important thing in college mathematics learning is to cultivate mathematics quality and computing ability.
What is mathematics quality? It is a kind of consciousness to accurately understand profound mathematical concepts, establish mathematical models for practical problems, and accurately find the correct methods to solve problems. This quality needs to be gradually cultivated and honed in the process of learning mathematics.
The final solution of mathematical problems is always inseparable from operation, which is a basic skill. Euler's shortest paper and Gauss's "Regular heptagon can be made with rulers and compasses" are both because they have extraordinary computing ability and can achieve outstanding mathematical achievements in their teens.
Second, pay attention to the characteristics of college mathematics
College mathematics has the following three remarkable characteristics.
1, accuracy. Mathematics has been famous for its preciseness, conciseness and accuracy since its birth. Advanced mathematics embodies this style, and the whole analytical mathematics is based on extremely accurate language. The accuracy of this language can be said to be priceless. It has been implemented for more than one hundred years.
2. Abstraction. Some concepts in advanced mathematics are abstract, such as limit, differentiability and integrability. Imagine if mathematics lost its abstraction and always studied specific problems one by one, would the development of mathematics be as prosperous as it is today? Then our math science becomes a thick solution to the problem. Imagine, can Euler turn the "seven bridges problem" into a "problem" without abstract thinking?
The main manifestations of abstraction are: defining a series of new concepts. Lenin said that "the life of natural science is a concept", which is generally abstracted from practical things, but it contains richer connotations than the original practical problems. It can be said that an important aspect of the success or failure of college mathematics learning is the understanding and mastery of concepts.
To learn abstract concepts, we should grasp the following links.
1, remember one or two examples of introducing concepts to avoid abstract dizziness;
2. Remember one or two counterexamples that are contrary to the concept and deepen the understanding of the concept from many aspects;
3. Understand the relationship between concepts and other existing concepts, avoid dividing many concepts into isolated dogmas, and link the relationships between concepts with examples, theorems and formulas.
3. Rich skills
This ability requires creative work with the mathematical methods we mentioned earlier, and can also be obtained by learning from predecessors and books. However, it must be pointed out that any superb skills are inseparable from the assistance of basic computing skills.
Third, the methods of college mathematics learning
1, how to have a class
There are fewer class hours in university courses, mainly relying on students to study by themselves. Therefore, the content of a class is often quite large, and the pace of lectures is fast. How to effectively master the content of classroom teaching, there are several suggestions for university reference.
(1) "A teacher who can make students understand is not a good teacher", which is the view pursued by American university professors and the characteristic of university classrooms. Because knowledge is decomposed and refined, it will make students' ability to acquire knowledge decline, which is not conducive to the cultivation of students' self-learning ability. Therefore, don't expect to understand everything in class, and don't get stuck somewhere and stop listening.
2. Listening to concepts in class, paying special attention to what the teacher emphasizes, is often prone to mistakes; Listen to the method of theorem proving, don't be too rigid to understand every small step in the process of proving, but understand the main steps and supplement them after class.
(3) It is not easy to pay attention to a class from beginning to end. Therefore, it is suggested that students focus on concept description, theorem proving methods and introduction of error-prone places, and learn to allocate energy and physical strength reasonably.
2, reading a book
(1), I suggest you choose a question guide, problem solving and review materials as your reference book.
2. The characteristics of reading are: more confusion and less gain. I suggest that you grasp several main concepts and theorems in reading and try to deduce other concepts and conclusions from them. This is also the reading method advocated by Mr. Hua. That is: first read the book "thin" and classify the knowledge. When you finish reading a book "thinly", you should try to read the book again "thickly" and add your experience, examples you learned from reference books, new proof methods, etc. To enrich it and make the book really become your own "writing" book. This process of reading "thick" often requires us to guess and explore the author's ideas like detectives and turn over their draft papers. This stage can be said to be the advanced stage of your reading, and it is the main source for you to really learn mathematical methods and master mathematical skills. If you don't go through this stage, you just read the words that can't be concise in the book, and you don't learn the "living thoughts" of mathematics.
Step 3 practice
(1), the practice of conceptual problems should be the most important, I suggest you spend more time.
(2) Practice more basic arithmetic problems, pay attention to accuracy and speed, pay less attention to the reference solution after reading, and rely on the auxiliary hints of the answers, so it is easy to do the arithmetic problems correctly in the exam.
Don't let go of the wrong exercises. Remember, when this question tests you, your mistakes are often designed in advance, so you should be alert.
To sum up, as long as you are careful, master the methods, study hard and learn advanced mathematics well, you will be relaxed and comfortable.