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What courses does the mathematics major in colleges and universities include?
Generally, the professional settings of different schools will be slightly different. Let me talk about the courses I have taken ~

A 985 undergraduate mathematics:

Freshman: Analytic Geometry, Mathematical Analysis (3 semesters), Advanced Algebra (2 semesters), Topology;

Sophomore: complex variable function, ordinary differential equation, real variable function, partial differential equation, number theory and algebraic structure, abstract algebra, probability theory, mathematical experiment.

Junior year and senior year: (depending on the direction, the course is slightly different, so you need to choose some courses) Mathematical statistics, functional analysis, differential geometry, number theory foundation, operational research foundation, calculation method, numerical calculation method, automatic control principle, database and data structure, mechanical foundation, applied statistical method, linear system theory, numerical solution of differential equations, harmonic analysis, statistical software, system identification and parameters. Elementary algebraic topology, group representation theory, modular form, meromorphic function theory, complex dynamical system, multiple complex variable function theory, differential geometry, differential dynamical system, optimal control, mathematical content, method and significance, mathematical history, simulation and Monte Carlo method, mathematical culture, mathematical topics, mathematical model, algebraic representation theory.

Attachment: Mathematics majors do not study the book Advanced Mathematics.