course content
1, the origin and early development of mathematics
The Generation and Form of the Concept of (1) Number
(2) Valley civilization and early mathematics.
2. Ancient Greek Mathematics
(1) demonstrates the origin of mathematics.
② Alexander school
3. The heyday of ancient mathematics in China.
(1) Zhou Pi 'ai and Nine Chapters Arithmetic
(2) Mathematics in Wei, Jin, Southern and Northern Dynasties
(3) Mathematics in Song and Yuan Dynasties
4. Mathematics in India and Arabia
(1) Mathematics in Ancient India
(2) Arab achievements in algebra, trigonometry and geometry.
The emphases and difficulties of this part: Greek mathematics in Athens, the main achievements of Alexandria school, China's nine chapters arithmetic, China's remainder theorem, Indian mathematics and achievements in Arabic algebra, trigonometry and geometry.
(2) Assessment knowledge and requirements
1. Part of the history of elementary mathematics development requires a level of "understanding".
The Generation and Form of the Concept of (1) Number
② Egyptian mathematics and Mesopotamian mathematics.
(3) Late Alexander and the decline of Greek mathematics.
④ Pythagorean school
2. In the history of elementary mathematics development, it is required to reach the level of "understanding and mastering".
(1) Greek Mathematics in Athens
A. Three major geometric problems
B. Early exploration of the concept of infinity
C. Advocating logical deductive structure
(2) The main achievements of Alexander School.
A. The main achievements of Euclid's Elements of Geometry
B. Archimedes' mathematical achievements
C. Apollonius' conic curve theory
(3) The main achievements of China's ancient mathematics.
A. Zhou Kuai Shu Jing and Nine Chapters of Arithmetic
B. The main achievements of Liu Hui and Zu Chongzhi's father and son
C. China's remainder theorem
(4) Indian mathematics and Arabic mathematics.
A. ancient rope sutra
B. the invention of zero number
C. Arab achievements in algebra, trigonometry and geometry.
Title: The second part is the guidance of the important and difficult points in the development history of modern mathematics.
The second part is the history of modern mathematics.
course content
1, the rise of modern mathematics
(1) Transition to Modern Mathematics
A. the emergence of algebra
B. the development of trigonometry
C. From perspective to projective geometry
D. computing technology and the birth of logarithm
(2) The birth of analytic geometry
2. The establishment of calculus
(1) Half a century's brewing
A. the volume of Kepler and the rotator
B. cavalieri irreducibility principle
C. Cartesian circle method
D. Fermat's method of finding the maximum and minimum values
E. Barrow differential triangle
F. arithmetica infinitorum of Wallis
(2) Newton's "flow counting"
A. Preliminary construction of flow counting
B. Development of flow counting
Newton's principle and calculus
(3) Leibniz's calculus
A. Characteristic triangle
B. Establishment of analytical calculus
C. the development of leibniz calculus
3, the era of analysis
Further development of (1) calculus
A. integration technology and elliptic integration
B. the generalization of calculus to multivariate functions
C. infinite series theory
D. Deepening the concept of function
E. An attempt to make calculus strict
(2) The application of calculus and the formation of new branches.
A. Formation of ordinary differential equations
B. Generation of partial differential equations
C. Generation of variational method
(3)/kloc-geometry and algebra in the 8th century
A. the formation of differential geometry
B. Equation theory
C. progress in number theory
4. Algebra freshmen
Solvability of (1) Algebraic Equation and Discovery of Groups
(2) From quaternion to hypercomplex number
(3) The formation of Boolean algebra
(4) The birth of algebraic number theory.
5, the change of geometry
(1) Euclidean geometric parallel postulate
(2) The birth of non-Euclidean geometry
(3) The development and confirmation of non-Euclidean geometry.
(4) the prosperity of projective geometry
(5) the unity of geometry
6. Rigidity of analysis
(1) Cauchy and the Basis of Analysis
(2) Analysis algorithm
A. Achievements of Wilstrass
B. Real number theory
C. the birth of set theory
(3) the expansion of analysis
A. Establish a complex analysis
B. the formation of analytic number theory
C. mathematical physics and differential equations
The emphases and difficulties of this part are: the generation of algebra, the birth of analytic geometry, Kepler and rotator, cavalieri's principle of no division, Descartes' circle method, Fermat's method of finding maximum and minimum, Barrow's differential triangle, arithmetica infinitorum of Wallis, Newton's "flow number technique", Leibniz's calculus, the popularization of calculus to multivariate functions, the theory of infinite series, the deepening of function concept and the formation of ordinary differential equations.
(2) Assessment knowledge and requirements
1. In the history of modern mathematics development, it is required to reach the level of "understanding"
(1) From perspective to projective geometry
(2) Computing technology and the birth of logarithm.
(3) Integral technology and elliptic integral.
(4) deepen the concept of function
(5) The attempt of strict calculus.
(6) Solvability of algebraic equations and discovery of groups
(7) From quaternion to hypercomplex number
(8) Analysis algorithm
2. In the history of modern mathematics development, it is required to reach the level of "understanding and mastering"
The emergence of algebra (1),
(2) The birth of analytic geometry
(3) the establishment of calculus
A. the volume of Kepler and the rotator
B. cavalieri irreducibility principle
C. Cartesian circle method
D. Fermat's method of finding the maximum and minimum values
E. Barrow differential triangle
F. arithmetica infinitorum of Wallis
Newton's "Flow Number" and Leibniz's Calculus
(3) the era of analysis
A. the generalization of calculus to multivariate functions
B. Infinite series theory
C. Deepening the concept of function
D. Formation of ordinary differential equations and partial differential equations
E. the formation of differential geometry
F. Progress in number theory
(4) Freshman algebra
(5) The development and confirmation of non-Euclidean geometry and the unification of geometry.
(6) the rigidity of analysis
A. Cauchy and analytical basis
B. Expansion of analysis (establishment of complex analysis and formation of analytic number theory)
Title: The third part is an overview of the development of modern mathematics.
The third part is an overview of the development of modern mathematics.
1, a part of the history of modern mathematics development, requires a degree of "understanding"
(1) The infiltration of mathematics into other sciences (mathematical physics, biological mathematics, mathematical economics)
(2) Mathematics under the influence of computer (development of computational mathematics, pure mathematics research and mathematics of computer and computer science)
(3) The generalization of Gauss-Bonner formula.
(4) Milnoch ball
(5) Four-color problem
(6) Proof of Fermat's Last Theorem
(7) Mathematics and social progress
2. In the history of modern mathematics development, it is required to reach the level of "understanding and mastering"
(1) prelude to the new century (Hilbert's mathematical problems)
(2) Higher Abstraction (Lebesgue Integral and Real Variable Function Theory, Functional Analysis, Abstract Algebra, Topology, Axiomatic Probability Theory)
(3) In-depth discussion on the basis (paradox of set theory, three schools of thought (logicism, intuitionism and formalism).
(4) The development of mathematical logic (axiomatic set theory, proof theory, model theory, recursion theory).
(5) A new era of applied mathematics
(6) Independent applied disciplines (mathematical statistics, operational research, cybernetics)
(7) Socialization of mathematics (socialization of mathematics education, establishment of specialized mathematics publications, establishment of mathematics societies and mathematics awards).
(8) The development of modern mathematics in China.