I.The Basic Information of the Course(Time New Rome, 12 points, bold font)
Course Number:202012420035
The EnglishName of theCourse：Homological Algebras
The ChineseName of theCourse：同调代数
In-classHours andAllocationTotal class hours:32, classroom teaching: 32 classhours,
Credit(s):2
Semester:2
AppliedDiscipline(Professional Degree Category)：Master/Doctor in Pure Mathematics
CourseObjectOriented：Academic Master/Doctor
EvaluationMode:Sample:, Process Evaluation.
TeachingMethod:Seminar-style Teaching
CourseOpening Department:
Science andEngineeringDiscipline,
II.Prerequisite Course( Time New Rome 12 points bold font)
Abstract algebras, commutative algebras
III.The Objectives and Requirements of the Course(Time New Rome 12 points, total words: about 200 words)
The course is a basic course for graduate students for Master/Doctor degree in Pure mathematics, especially for Algebras and Representationtheory. The aim of the course is to help students to grasp the basic ideas, theories and methods in Homological algebras and have the ability to apply the knowledge of Homological algebras to solve problems in mathematics.
Homological algebras relates algebra and Topology. We hope student to enlarge their mathematical sight by taking the course. By learning this course, the students should reach the following basic requirements: get familiar with the basic terminologies,concepts, ideals in the Homological Algebras understood the current developments in Algebraic Geometry.
IV. The Content of the Course(Time New Rome, 12 points, bold font, 1000-2000 words)
Description:Other course should reflect the content and cases of “Courses for Ideological and Political education”, besides the Course for Ideological and Political Education.
Sample as follows:
Chapter 1 Introduction to themodules over a ring (6classhours)
1.1Modules and homorphisms
1.2 Injective/Projective Modules
1.3 Invers/direct limit systems
Chapter 2Category theory（8classhours）
2.1Definitions of Categories /natural transformations
2.2 Functors: pull back and push out, Ext( , ) and Tor ( .)
Chapter3 Spectral sequences（8classhours）
3.1 Double complex and spectral sequences
3.2 Convergences and limits
Chapter4 Derived categories
3.1 Derived functors and Derived categories
3.2 Triangle categories and t-structures
Political education：
1,Professor Chen,Zhijie at East China Normal University. Professor Chengreatlycontributedto the Algebraic Geometry, specially in the classification of algebraic surfaces.
Professor Chen also wrote text books for students in mathematics. His lecture note “Linear algebra and geometry” is very popular among undergraduate students. He is the author of “basic algebra” (in Chinese) the references list. His book“Introduction to Latex”promote the use ofTex in Chinese mathematician. Those works made a great contribution to Chinese mathematical education. We should learn his Patriotism and dedication.
2, Jean Lerray, was a France mathematician. He invented the method of spectral sequences in calculating the cohomology in a Word WarIIprison. We should follow his love for science and his country.
V. Reference Books, Reference Literatures, and Reference Materials
A. Text Books, Monographs and References
1. G.E. Bredon Sheaf theory, GTM170世界图书出版社，1999.
2.陈志杰.代数基础.华东师范大学出版社，2001.
3. A. Grothendieck Local Cohomology. Lecture Notes in Math. No. 41.New York: Springer-Verlag, 1967.
4. P. HiltonandU. Stammbach. A Course in Homological Algebra (GTM4). Springer, New York.2004
5. R. Loday Cyclic Homology. Berlin, Heidelberg, New York: Springer-Verlag, 1999
6. J.-L. Osofsky, Homological Dimensions of Modules. CBMS Regional Conf.Ser. Math. 12. Providence, R.I.: AMS, 1973.
7. J. Rotman An Introduction to Homological Algebra. New York: AcademicPress, 1979
8. R.Swan Algebraic K-Theory. Lecture Notes in Math. No. 76. New York: Springer-Verlag, 1968.
9，佟文廷同调代数引论，高等教育出版社 1990
10. C.Weibel An Introduction to Homological Algebra Cambrige Study in Advanced Mathematicas 38
B. Learning Resources (Time New Rome 12 points)
1. http://www.……
2. ftp://ftp.……
3.The name of the platform and website for online course learning
......
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Leader in charge of teaching at the College (Signature)：
Date：
中文
