Advanced mathematics
linear algebra
function of a complex variable
ordinary differential equation
methods of mathematical physics
probability statistics
In addition, there may be other subjects depending on the major.
What does college mathematics include?
"Mathematics in University" is collectively called "College Mathematics", and the Education Department of the Ministry of Education has a "College Mathematics Curriculum Steering Committee". There are many "sub-ability steering committees" below, and "engineering mathematics curriculum sub-steering Committee" is just one of them.
The Steering Committee of Engineering Mathematics has six courses: advanced mathematics, linear algebra, probability theory and mathematical statistics, complex variable function and integral transformation, mathematical equation and special function and calculation method.
Less economic management, advanced mathematics (economic management is generally called calculus)
The contents of advanced mathematics include: function and limit, differential calculus of univariate function, integral calculus of univariate function, analytic geometry of space, differential calculus of multivariate function, integral calculus of multivariate function (multiple integral and curve and surface integral), series (polynomial series, power series and Fourier series), differential equation and preliminary field theory (gradient, divergence and curl).
(3) What courses should be refined for college mathematics majors?
Professional basic courses:
Analytic geometry
Mathematical analysis one, two, three
Advanced algebra I and II
ordinary differential equation
abstract algebra
Fundamentals of probability theory
function of a complex variable
Modern algebra
Professional core courses:
real variable function
partial differential equation
probability theory
analysis situs
functional analysis
differential geometry
Mathematical equation
Specialized elective courses:
Discrete Mathematics (last semester of sophomore year)
Numerical calculation and experiment (second semester of sophomore year)
Analysis (1)
Algebra (1)
Galois theory
complex analysis
algebraic number theory
Introduction to dynamic systems
Basic number theory
Partial differential equations (continued)
Geographical topology
theoretical mechanics
mathematical modeling
Differential topology
harmonic analysis
Geometric theory of ordinary differential equations
Selected lectures on analytical topics
Combinatorial Mathematics and Graph Theory
Category theory
Compact riemann surface
A Preliminary Study on Riemannian Geometry
Part of modern theory
Commutative algebra
algebraic topology
Homology algebra
Manifolds and geometry
Wavelet and harmonic analysis
Lie group lie algebra
Analysis Ⅱ
Algebra Ⅱ
algebraic k theory
algebraic geometry
Multi-repetition variable basis
Functional analysis (continued)
What are the basic courses for college mathematics majors?
Professional basic courses include mathematical analysis, advanced algebra, analytic geometry, probability theory and mathematical statistics: these three courses are the old three, which will be used in the postgraduate entrance examination; The new three courses of modern mathematics are: topology, real variable function and functional analysis, modern algebra (also called abstract algebra); Other common branches include complex variable function, ordinary differential, operation, optimization and mathematical model.
What are the specialized courses of martial arts mathematics?
Specialized courses in mathematics are:
First, mathematical analysis.
Also called advanced calculus, the oldest and most basic branch of analysis. Generally speaking, it refers to a relatively complete mathematical subject with the general theory of calculus and infinite series as the main content, including their theoretical basis (basic theory of real number, function and limit). It is also a basic course for college mathematics majors.
The branch of analysis in mathematics is a branch of mathematics that specializes in studying real numbers and complex numbers and their functions. Its development began with calculus and extended to the continuity, differentiability and integrability of functions. These characteristics help us to study the material world and discover the laws of nature.
Second, advanced algebra
Elementary algebra starts with the simplest one-dimensional linear equation. On the one hand, elementary algebra further discusses binary and ternary linear equations, on the other hand, it studies equations that are larger than quadratic and can be reduced to quadratic. Along these two directions, algebra discusses the linear equations with any number of unknowns, also known as linear equations, and also studies the univariate equations with higher degrees.
This stage is called advanced algebra. Advanced algebra is a general term for the development of algebra to an advanced stage, including many branches. Higher algebra offered by universities now generally includes two parts: linear algebra and polynomial algebra.
Third, the theory of complex variable function
Complex variable function theory is a basic branch of mathematics, and its research object is complex variable function. The theory of complex variable function has a long history, rich content and perfect theory. It is widely used in many branches of mathematics, mechanics and engineering science. Complex numbers originate from finding the roots of algebraic equations.
The concept of complex number originated from finding the roots of equations. When finding the roots of quadratic and cubic algebraic equations, the square root of negative numbers appeared. For a long time, people couldn't understand this figure. However, with the development of mathematics, the importance of such numbers is increasingly apparent. The general form of a complex number is: a+bi, where I is an imaginary unit.
Fourth, abstract algebra.
Abstract algebra, also called modern algebra, came into being in19th century. Galois [181-1832] used the concept of "group" in1832, which completely solved the possibility of solving rooted algebraic equations.
He was the first mathematician who put forward the concept of "group" and is generally called the founder of modern algebra. He changed algebra from the science of solving equations to the science of studying algebraic operation structure, that is, he pushed algebra from elementary algebra to abstract algebra.
Verb (abbreviation for verb) modern algebra
Modern algebra is abstract algebra. Algebra is a branch of mathematics, which can be roughly divided into elementary algebra and abstract algebra. Elementary algebra refers to the theory of algebraic equations developed before the first half of19th century. This paper mainly studies whether an algebraic equation (group) is solvable, how to find all the roots (including approximate roots) of the algebraic equation, and what properties the roots of the algebraic equation have.
1832, French mathematician galois used the idea of "group" to completely solve the possibility of solving rooted polynomial equations. He was the first mathematician who put forward the concept of "group" and is generally called the founder of modern algebra. He changed algebra from the science of solving algebraic equations to the science of studying algebraic operation structure, that is, he pushed algebra from elementary algebra to abstract algebra, that is, modern algebra.