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Recommended study materials for Fudan University’s advanced algebra course

This textbook has been awarded the title of national planning textbook for general higher education during the “Tenth Five-Year Plan”, “Eleventh Five-Year Plan” and “Twelfth Five-Year Plan”. Universities currently using this textbook include: School of Mathematical Sciences of Fudan University, Department of Mathematical Sciences of Tsinghua University, "Qiushi Mathematics Class" of Zhejiang University's Top Talent Program, Financial Mathematics Experimental Class of Shanghai University of Finance and Economics, Mathematics Experimental Class of Hangzhou Normal University, School of Mathematics and Computer Science of Gannan Normal University, etc.

01 · How to study advanced algebra courses

02 · Textbook "Advanced Algebra (Third Edition)"

This textbook has been awarded the title of national planning textbook for general higher education during the “Tenth Five-Year Plan”, “Eleventh Five-Year Plan” and “Twelfth Five-Year Plan”. Universities currently using this textbook include: School of Mathematical Sciences of Fudan University, Department of Mathematical Sciences of Tsinghua University, "Qiushi Mathematics Class" of Zhejiang University's Top Talent Program, Financial Mathematics Experimental Class of Shanghai University of Finance and Economics, Mathematics Experimental Class of Hangzhou Normal University, School of Mathematics and Computer Science of Gannan Normal University, etc.

03 · Learning method guide "Advanced Algebra (Third Edition)"

This book is a study method guide accompanying Fudan's advanced algebra textbook. Because of its white cover, it has been called the "Advanced Algebra White Paper" by previous students.

04 · Advanced Algebra Weekly Questions

05 · Advanced Algebra Online Course (Station B)

06 · Advanced Algebra Exercise Course Teaching Video (Station B)

07 · WeChat public account--Xie Qihong Advanced Algebra

08 · Teaching paper (formally published)

  1. A brief discussion on some techniques in advanced algebraic propositions, College Mathematics, 2013, 29(3), 127–130.

  2. Application of rank in matrix similarity, Advanced Mathematics Research, 2012, 15(1), 30–32.

  3. A look at some techniques in advanced algebra from an elementary problem, Advanced Mathematics Research, 2013, 16(4), 53–55.

  4. Two techniques in evaluating literal determinants, College Mathematics, 2013, 29(4), 94–98.

  5. Determining whether a matrix can be diagonalized from two exercises, Advanced Mathematics Research, 2014, 17(4), 82–85.

  6. Characteristic polynomial-induced direct sum decomposition of linear transformations, Advanced Mathematics Research, 2015, 18(1), 40–43.

  7. Looking at the standard form theory of matrices from the generalization of an exercise, Advanced Mathematics Research, 2016, 19(2), 1–3.

  8. Using polynomial techniques to replace the perturbation method, College Mathematics, 2014, 30(6), 52–55.

  9. Talking about the teaching connection of advanced algebra from AB and BA, Advanced Mathematics Research, 2015, 18(6), 29–32.

  10. Propositional ideas and analysis of an advanced algebra test question, College Mathematics, 2015, 31(1), 70–74.

  11. Several applications of cyclic subspaces, University Mathematics, 2016, 32(1), 1–6.

  12. Invariance of several concepts in advanced algebra under base domain expansion, College Mathematics, 2015, 31(6), 50–55.

  13. Several applications of Galois theory in advanced algebra, College Mathematics, 2016, 32(6), 8–12.

  14. Further applications of cyclic subspaces, University Mathematics, 2017, 33(1), 17–25.

  15. A natural extension of a common exercise in advanced algebra, College Mathematics, 2019, 35(6), 96–99.

09 · Teaching blog post (not yet officially published)

  1. Some experiences on Fudan University’s advanced algebra exam questions

  2. Combinatorial definition of determinant and its application--Pfaffian of antisymmetric matrix

  3. Properties of circulant matrices and their applications

  4. Several proofs and generalizations that real symmetric matrices can be diagonalized

  5. Summary of relevant properties of antisymmetric arrays

  6. Other diagonalizable criteria and their applications

  7. Direct proof of matrix similarity in standard form

  8. Geometry of the Jordan Block

  9. Look at the application of determinant calculation in quadratic form simplification from three exercises

  10. Seven solutions to question 9 of Level 16 Advanced Generation II

  11. Multiple proofs for question 10 of Level 16 Advanced Generation II

  12. Three proof methods for the fifth major question in the 18th-level Senior II midterm exam and their promotion

  13. Three proof methods and their promotion for the seventh major question of the 18-level senior II mid-term exam

  14. Three proof methods and their extensions for the sixth major question of the 19th grade senior I mid-term exam

  15. Three proof methods for the seventh major question of the 19th grade senior I mid-term exam and their promotion

  16. Two proof methods and their promotion for the seventh major question of the 19th-level Senior II mid-term exam

10 · Answers to the final questions of previous advanced algebra final exams

This collection collects and compiles detailed analyzes and solutions to the final exam questions in advanced algebra from the 2013 undergraduate level to the 2019 level at Fudan University of Mathematics. Most of the questions provide several solutions or proofs.

11 · Selection of major questions from previous advanced algebra midterm exams

We have collected and sorted out selected questions from the Advanced Algebra mid-term exams of Fudan University of Mathematics from undergraduate level 2008 to 2019, and provided answer tips. Among them, the more difficult test questions in the past two years have been provided with detailed answers.

12 · Other information

National college student mathematics competition advanced algebra tutoring course materials, analysis of previous advanced algebra final exams, academic year records of advanced algebra online courses, and related blog posts, etc.

Machine-translated from the Chinese original 复旦大学高等代数课程学习资料推荐 (published 2020-11-16). WeChat original ↗