Number theory: mainly analytic number theory, direct function is complex, you know. Then analytic number theory is the application of fractions in number theory, starting with Euler. In addition, vinogradov, a mathematician of the Soviet Union, creatively put forward the "triangle sum method", which plays an important role in solving some difficult problems in number theory. Geometric number theory is very helpful to spatial research. I'm not sure about that. All I know is that space needs to be used. If you are pure physics, study better.
Functionality: very important. Reference books recommend Qian Weichang's variational method and finite element method. You only need to read the first chapter (the fastest falling body). You must like functional and study it deeply. It started with Newton, but it was Bernoulli who gave him a question and promoted the development of his variational method. Deng Ge once again foresaw the future, and functional dominated many physical developments in the 20th century.
Operation: I personally think that theoretical physics can be drilled without depth. If it is applied physics, it will be used more. Simply put, this is the graph theory and queuing theory that are often seen in mathematical modeling. It is up to you.
Fractal: theoretical physics must be learned, and Brownian motion is used for the first time. In addition, give another example. In 1970s, the French mathematician Mandelbrot explored how long the British coastline was in his works. This problem depends on the scale used in the measurement. If kilometers are the unit of measurement, then some twists and turns from a few meters to dozens of meters will be ignored; In meters, the measured total length will increase, but things below centimeter level cannot be reflected. Due to high tide and low tide, the land-water boundary of coastline is irregular in various degrees. There are natural restrictions on the coastline in both directions. Take several protruding points on the outer edge of the British island and connect them with straight lines to get a lower bound of coastline length. There is no point in using a longer scale than this. Fractal also requires high computer skills.
Fuzzy mathematics: a course of theoretical physics. It started with set theory, Cantor, those things. The significance of set theory can be seen from one side, which extends the abstract ability of mathematics to the depths of human cognition. A set of objects determines a set of attributes. People can explain the concept (connotation) by explaining the attribute, and can also explain it by specifying the object. The sum of the objects that conform to the concept is called the extension of the concept, and the extension is actually a set. Study the application of fuzzy mathematics. Fuzzy mathematics takes uncertain things as the research object. The appearance of fuzzy sets is the need for mathematics to adapt to the description of complex things. Chad's merit lies in the use of fuzzy set theory to find and solve fuzzy objects and make them accurate, so that the mathematics of deterministic objects can communicate with the mathematics of uncertain objects, making up for the shortcomings of accurate mathematics and random mathematics description in the past.
In addition, you can also look at catastrophe mathematics and computer simulation.
Hands! Decline Baidu Encyclopedia! !