Is it necessary to study mathematical analysis and advanced algebra to study theoretical physics?

Of course it is necessary, especially for mathematical analysis.

Not a general necessity, but a very, very necessary! You have to know that put calculus.

Pull it out of higher physics, that's incredible! As for advanced algebra, I personally think that although it is not as important as mathematical analysis in physics, it is also very necessary to learn it well, because there are many formulas in mathematical analysis that are expressed with the help of the conclusions of advanced algebra. For example, in physics, it is often necessary to solve many differential equations, and many mathematical analyses and conclusions of advanced algebra must be used in the middle of the period.

As for the teaching materials, it will vary from person to person. However, I personally think that the current domestic textbooks are all similar. There are also many sets of textbooks from higher education presses. Like Peking University, Tsinghua University, Tongji, Fudan.

The textbooks of the Department of Mathematics of Zhejiang University are very good, but they may be a little difficult.

There is no need! I'm a math major. Do you know the difference between mathematical analysis and advanced mathematics? It is enough to study advanced mathematics in engineering; As for theoretical physics, although it is also a science subject, I still don't think it's necessary to study mathematical analysis.

Mathematical analysis is rigorous, and propositions that appear to be true must be proved. Physics is about using mathematics as a tool, not as an object of study, so it is enough to study advanced mathematics. Mathematical analysis emphasizes analysis, and there are more proof questions; Advanced mathematics focuses on application and has many calculation problems.

The most commonly used mathematical tools in college physics are integrals, derivatives, and series, and they are all computational in nature. Of course, it's good to learn mathematical analysis, but I'm just saying that it's not necessary to study mathematical analysis, it's enough to study advanced mathematics.

As for advanced algebra, I personally think it's not necessary, it's enough to learn linear algebra. In the same way, there are more advanced algebra theories, and linear algebra emphasizes computation.

I think it's just as hard. Because analysis and algebra can be graded from low to high, more and more abstract, and the point of view is getting higher and higher.

Mathematical Analysis: Mainly includes calculus and series theory. Calculus is the foundation of advanced mathematics and has a wide range of applications, basically all fields involving functions require knowledge of calculus.

In series, Fourier series and Fourier transform are mainly used in the field of signal analysis, including filtering, data compression, power system monitoring, etc., and the manufacture of electronic products is inseparable from it.

Real Variable Function (Real Analysis): One of the enhanced versions of mathematical analysis. It is mainly used in fields such as economics that focus on data analysis.

Complex Variable Functions (Complex Analysis): Mathematical Analysis Enhanced Edition II. A widely used discipline has a wide range of applications in aeronautical mechanics, fluid mechanics, solid mechanics, information engineering, electrical engineering and other fields, so engineering students should learn this course.

Advanced algebra, which mainly includes linear algebra and polynomial theory. Linear algebra can be said to be a widely used branch of mathematics at present, data structure, program algorithms, mechanical design, electronic circuits, electronic signals, automatic control, economic analysis, management science, medicine, accounting, etc. all need to use the knowledge of linear algebra, is a compulsory course for students majoring in economics and management, science and engineering, and computer science.

Advanced geometry: including spatial analytic geometry, projective geometry, spherical geometry, etc., mainly used in architectural design and engineering drawing.

Analytics, advanced algebra, and advanced geometry are the three pillars of modern mathematics.

Differential equations: including ordinary differential equations and partial differential equations, one of the important tools. It is needed in fluid mechanics, superconducting technology, quantum mechanics, stability analysis in mathematical finance, materials science, pattern recognition, signal (image) processing, industrial control, power transmission and distribution, remote sensing measurement and control, infectious disease analysis, weather forecasting and other fields.

Functional analysis: Mainly studies functions on infinite dimensional spaces. Because it is relatively abstract, it is not directly applied in technology, and is generally applied to theories such as continuum mechanics, quantum physics, computational mathematics, infinite-dimensional commodity space, cybernetics, and optimization theory.

No, you don't. The major of physics cultivates high-level professionals who master the basic theories and methods of physics, have a good mathematical foundation and experimental skills, and can engage in scientific research, teaching, technology and related management in physics or related scientific and technological fields.

The main courses include mathematics, mechanics, thermal, optics, electromagnetism, atomic physics, mathematical physical methods, theoretical mechanics, thermodynamics and statistical physics, electrodynamics, quantum mechanics, solid state physics, structure and physical properties, and introduction to computational physics.

No, you don't. bai

The Physics DDU major cultivates high-level professionals who master the basic theories and methods of physics, have good mathematical foundation and experimental skills, and can engage in scientific research, teaching, technology and related management in the field of physics or related science and technology.

The main courses are Advanced Mathematics, Mechanics, Thermal, Optics, Electromagnetism, Atomic Physics, Methods of Mathematical Physics, Theoretical Mechanics, Thermodynamics and Statistical Physics, Electrodynamics, Quantum Mechanics, Solid State Physics, Structure and Physical Properties, Introduction to Computational Physics, etc.

Mathematics and physics both belong to the science subject, and both need to have the ability to think, draw inferences, and numbers.

Good things to learn.

If you want to learn mathematics and physics well, you must first understand the formulas and theorems in the textbook clearly, if you don't understand clearly, you won't be able to think about it, the knowledge of science is to draw inferences from one another, you can't memorize it, only if you really understand, you can, and it is easy to solve similar problems. Come on!

There are many calculus that need to be applied to mathematical analysis in physics, but most of them only need to be calculated, with the conclusions of mathematical analysis.

It seems that the process of pushing the right is not used much. Physics should be calculus, mathematical analysis is a basic course in mathematics majors, and some majors take two years to study this course. If you're interested in mathematical analysis, you can learn it, but it's boring.

Mathematical analysis is not concerned with calculations, but with the derivation of theorems, that is, the proof of theorems.

If students who study physics have mathematical analysis as the foundation, mathematical analysis focuses on analysis, and if they can cultivate this kind of analytical thinking, it will be very beneficial to the future learning and reasoning of physical appearance. However, mathematical analysis is a relatively complete and relatively large system, and students who study physics can focus more on the learning of univariate calculus and multivariable calculus, while like real number theory, some knowledge of number theory does not need to spend too much effort, because these contents themselves are complex and obscure, and they are not widely used in physics.

No, I majored in physics and advanced mathematics. Physics is still more applied, and those proofs are of little significance.

Of course you need to. Physics, Chemistry, Mathematics. The three doors are not separated.

In mathematics, you should need to understand a little, and it is easy to understand it with mathematical proofs.

Not mathematical analysis, but higher mathematics.

Or algebraic geometry is more difficult.

Algebraic geometry is a branch of mathematics that combines abstract algebra, especially commutative algebra, with geometry. It can be thought of as the study of the set of solutions of a system of algebraic equations. Algebraic geometry takes algebraic clusters as the object of study.

An algebraic cluster is a trajectory of a point determined by one or more algebraic equations for spatial coordinates. For example, an algebraic cluster in 3D space is an algebraic curve and an algebraic surface. Algebraic geometry is the study of the geometric properties of algebraic curves and algebraic surfaces in general.

Algebraic geometry has extensive connections with many sub-disciplines of mathematics, such as complex analysis, number theory, analytic geometry, differential geometry, commutative algebra, algebraic groups, topology, etc. The development of algebraic geometry and the development of these disciplines play a mutually reinforcing role.

Mathematical analysis is comparatively more difficult.

I'm just learning it, and I feel that analysis is more difficult.

The high generation ratio analysis is abstract, and the difficulty is about the same.

I am a mathematics major, and mathematical analysis is the basic subject of our mathematics major, which of course also includes advanced algebra; And like other disciplines, physics, etc., it may be more difficult to learn such a too professional book, so it is to learn advanced mathematics and linear algebra, and you are right to say that it is a simplified version, it is indeed much simpler.

Mathematical analysis and advanced algebra are both examples of advanced mathematics. Mathematics studied at university is subject to the category of advanced mathematics, with the exception of elementary mathematics (algebra and geometry).

Advanced mathematics contains a wider range of content, but the knowledge points are superficial, and mathematical analysis has a detailed ** for each knowledge point.

Usually mathematical analysis and linear algebra are courses for mathematics majors, while advanced mathematics and advanced algebra are common textbooks for other majors.

Mathematical analysis is more rigorous than calculus.

College Mathematics includes: Analytics.

Algebra, geometry, randomness, and a combination of these basic sciences. For Analytics, the course weights include: Mathematical Analysis (the most basic), Complex Variable Functions, Real Variable Functions, Functional Analysis, etc. As you said, Advanced Mathematics is a simplified version of mathematical analysis.

For algebra, courses include: advanced algebra (the most basic), modern algebra (also called abstract algebra), etc. Higher algebra includes linear algebra and polynomial algebra. Linear algebra (like f(x)=ax+b is called linear because it is a straight line) studies straight lines.

Polynomials (which contain not only primary, quadratic, but also higher-order functions) are used to replace a very complex function with satisfactory results.

For geometry, it is mainly analytical.

Stochastic, including: probability theory, mathematical statistics, stochastic processes and other comprehensive disciplines: ordinary differential equations, partial differential equations, etc.

Try to learn the basic knowledge as well as possible. The following foundations are mainly required:

1. Derivatives and functions, complex functions.

with points. 2. Derivatives and functions should be learned well, and this part will be further studied in college, and the study of calculus in college is most closely related to the derivative of functions in high school.

and the limit part, which should be learned well, and some space geometry is also used.

3. The study of complex functions and integrals has a little relationship with the complex numbers in high school, the basic definition and part of the application in high school are the basic definitions and applications, and the calculus will be linked together in college for in-depth study, so learning the complex part well will help you better in the future.

Further Mathematics. Compared with elementary mathematics, the objects and methods of mathematics are more complicated.

Broadly speaking, mathematics other than elementary mathematics is advanced mathematics, and there are also more advanced mathematics, such as algebra, geometry, and simple set theory.

If it is preliminary, logically preliminarily called secondary mathematics, it is regarded as a transition between elementary mathematics at the primary and secondary school level and advanced mathematics at the university level.

It is generally believed that higher mathematics is made up of calculus.

A basic discipline formed by the in-depth algebra, geometry, and the intersection between them. Topics include: limits, calculus, spatial analytic geometry, and linear algebra.

Series, ordinary differential equations.

Derivatives and functions should be learned well, this part will be further studied in college, the study of calculus in college, and the most closely related to high school is the derivative and limit part of the function, which should be learned well, and space geometry is also used.

Compared with elementary mathematics, the objects and methods of mathematics are more complicated. Broadly speaking, mathematics other than elementary mathematics is advanced mathematics, and there are also algebra that will be more advanced in middle school.

Geometry, as well as simple set theory and logic, are called intermediate mathematics, and they will be used as a transition between elementary mathematics at the primary and secondary school levels and advanced mathematics at the university level.

It is generally believed that advanced mathematics is a fundamental discipline formed by calculus, more advanced algebra, geometry, and the intersection between them.

Topics include: limits, calculus, analytic geometry and linear algebra, series, and ordinary differential equations. Basic subjects for engineering and science graduate examinations.