美国大学本科数学专业的必修课及教材（Required courses and materials for undergraduate mathematics in the United States）What are the required courses and teaching materials for undergraduate math majors in the United States? Questioner: 2008-10-18 22:01 _ blue shadow mourning drunk, | reward points: 100 | Views: 2387I'm going to America next year undergraduate mathematics, professional choice, now want to own a preview, hope to understand the required curriculum in the United States about 40 of university mathematics and the use of the teaching materials are (what is the most important about mathematics curriculum) hope that good hearted people tell me, thank you...2008-10-31 19:10 satisfied answer American undergraduate mathematics, Graduate basic curriculum reference bookFirst academic yearGeometry and topology:1, James, R., Munkres, Topology: the new topology of teaching materials for undergraduate senior or graduate freshmen;2, Basic, Topology, by, Armstrong: Undergraduate topology textbooks;3, Kelley, General, Topology: the classic textbook of general topology, but the older point of view;4, Willard, General, Topology: new classical textbook of general topology;5, Glen, Bredon, Topology, and, geometry: Graduate freshmen topology and geometry textbooks;6, Introduction, to, Topological,, Manifolds, by, John, M., Lee: Graduate freshman topology and geometry textbook, is a new book;7, From, calculus, to, cohomology, by, Madsen: good undergraduate algebra topology and differential manifold teaching materials.Algebra：1, Abstract, Algebra, Dummit: the best undergraduate algebra reference books, standard graduate students, first-year algebra textbooks;2, Algebra Lang: standard graduate student, grade one or two algebra teaching material, very difficult, suitable for reference books;3, Algebra, Hungerford: standard graduate freshmen algebra textbooks, suitable for reference books;4, Algebra, M, Artin: standard undergraduate algebra textbooks;5, Advanced, Modern, Algebra, by, Rotman: newer graduatealgebra textbooks, very comprehensive;6, Algebra:a, graduate, course, by, Isaacs: newer graduate algebra textbooks;7, Basic, algebra, Vol, I&II, by, Jacobson: classical algebra comprehensive reference book, suitable for graduate reference.Analysis basis:1, Walter, Rudin, Principles, of, mathematical, analysis: standard reference books for undergraduate mathematical analysis;2, Walter, Rudin, Real, and, complex, analysis: standard graduate freshmen analysis textbooks;3, Lars, V., Ahlfors, Complex, analysis: senior undergraduate and graduate students in the first grade classic analysis of teaching materials;4, Functions, of, One, Complex, Variable, I, J.B.Conway: graduate level single variable complex analysis classic;5, Lang, Complex, analysis: graduate level single variable complex analysis reference book;6, Complex, Analysis, by, Elias, M., Stein: newer graduate level single variable complex analysis textbooks;7, Lang, Real, and, Functional, analysis: graduate levelanalytical reference books;8, Royden, Real, analysis: standard graduate students in the first year of the actual analysis of teaching materials;9, Folland, Real, analysis: standard graduate students in the first year of the actual analysis of teaching materials.Second academic yearAlgebra：1, Commutative, ring, theory, by, H., Matsumura: newer graduate exchange algebra standard textbook;2, Commutative, Algebra, I&II, by, Oscar, Zariski, Pierre, Samuel: classical commutative algebra reference book;3, An, introduction, to, Commutative, Algebra, by, Atiyah: standard introductory textbook on commutative algebra;4, An, introduction, to, homological, algebra, by, Weibel: newer graduate students' two year coherence algebra textbooks;5, A, Course, in, Homological, Algebra, by, P.J.Hilton, U.Stammbach: classical and comprehensive homological algebra reference book;6, Homological, Algebra, by, Cartan: classical homological algebra reference books;7, Methods, of, Homological, Algebra, by, Sergei, I., Gelfand, Yuri, I., Manin: advanced and classical homological algebra reference books;8, Homology, by, Saunders, Mac, Lane: an introduction to the classical homological algebra system;9, Commutative, Algebra, with, a,, view, toward, Algebraic, Geometry, by, Eisenbud: Advanced Algebra geometry, commutative algebra reference book, the latest exchange algebra comprehensive reference.Algebraic topology:1, Algebraic, Topology, A., Hatcher: the latest graduate algebra topology standard textbook;2, Spaniers, "Algebraic, Topology": classical algebraic topology reference book;3, Differential, forms, in, algebraic, topology, by, Raoul, Bott, and, Tu, Loring, W.: Graduate algebra topology standard textbook;4, Massey, A, basic, course, in, Algebraic, topology: classical graduate algebra topology textbooks;5, Fulton, Algebraic, topology:a, first, course: very good algebra algebra reference for freshmen and graduate students in their freshman year;6, Glen, Bredon, Topology, and, geometry: standard graduate algebra topology textbooks, there is a considerable space to talk about smooth manifolds;7, Algebraic, Topology, Homology, and, Homotopy: advanced and classical algebraic topological reference books;8, A, Concise, Course, in,, Algebraic, Topology, by, J.P.May: Graduate algebra topology introductory materials, covering a wide range;9, Elements, of, Homotopy, Theory, by, G.W., Whitehead: advanced and classical algebraic topological reference books.Real analysis and functional analysis:1, Royden, Real, analysis: standard graduate analysis textbooks;2, Walter, Rudin, Real, and, complex, analysis: standard graduate analysis textbooks;3, Halmos, "Measure Theory": Classic graduate analysis of teaching materials, suitable for reference books;4, Walter, Rudin, Functional, analysis: standard graduate functional analysis textbooks;5, Conway, A, course, of, Functional, analysis: standard graduate functional analysis textbooks; 6, Folland, Real,analysis: standard graduate student analysis of teaching materials;7, Functional, Analysis, by, Lax: advanced graduate functional analysis textbooks;8, Functional, Analysis, by, Yoshida: advanced graduate functional analysis reference book;9, Measure, Theory, Donald, L., Cohn: classical measurement theory reference book.Differential topology Li Qun and Lie algebra1, Hirsch, Differential, topology: standard graduate differential topology textbooks, quite difficult;2, Lang, Differential, and, Riemannian, manifolds: graduate reference books of Differential Manifolds, higher difficulty;3, Warner, Foundations, of, Differentiable, manifolds, and, Lie, groups: standard graduate Differential Manifolds teaching materials, there is considerable space about Li Qun;4, Representation, theory:, a, first, course, by, W., Fulton, and, J., Harris: Li Qun and its representation standards;5, Lie, groups, and, algebraic, groups, by, A., L., Onishchik, E., B., Vinberg: Li Qun's reference book;6, Lectures, on, Lie, Groups, W.Y.Hsiang: Li Qun's referencebook;7, Introduction, to, Smooth, Manifolds, by, John, M., Lee: the newer standard textbook on smooth manifolds;8, Lie, Groups, Lie, Algebras, and, Their, Representation, by, V.S., Varadarajan: the most important reference book of Li Qun and Li algebra;9, Humphreys,李代数及其表示理论，介绍SpringerVerlag，gtm9：标准的李代数入门教材。
