Advanced Algebra Exercise Set 2023 Edition
From the beginning of 2014 to the present, the editor has carried out a weekly question activity for advanced algebra at the School of Mathematical Sciences of Fudan University every semester. As the name suggests, this activity is to publish a very difficult advanced algebra question every teaching week for students who have room for learning to think and answer. It aims to stimulate students' learning motivation and innovation potential through modes such as "solving difficult problems" and "multiple solutions to one question".
The weekly activity of advanced algebra has been practiced in 10 grades from Grade 13 to Grade 22 of Fudan School of Mathematics. For 10 years, editors have always published next week's thinking questions on weekends. The focus of the questions is usually closely related to next week's lecture content, allowing students to preview and think with questions. The weekly questions from grades 13 to 16 of Fudan School of Mathematics are released simultaneously through the Advanced Algebra blog and WeChat group, and students submit paper solutions; the weekly questions from grades 17 to 22 are released simultaneously through the Advanced Algebra blog, WeChat group, and online class group, and students submit picture solutions in the online class group. Over the past 10 years, editors have been carefully correcting students' answers and providing them with timely feedback and suggestions. Practice has proven that the weekly advanced algebra question activity not only enhances communication and interaction between teachers and students, but also achieves good teaching results.
Since the editor returned to Fudan School of Mathematics in early 2009 to teach, he has been engaged in teaching advanced algebra courses and actively promoted the teaching reform and practice of advanced algebra courses. Exam questions are an important part of teaching work, and the editor has also made preliminary explorations in this aspect. In a sense, the weekly questions in Advanced Algebra provide a good opportunity for full practice for the reform and innovation of test propositions. As one of the cornerstones of modern mathematics, advanced algebra (linear algebra), whether it is classroom teaching or exercises and examination questions, can be taught and propositioned from a higher perspective from various branches of modern mathematics. Therefore, in the process of compiling weekly questions, the editor pays special attention to the guidance of scientific research, strives to closely integrate advanced algebra with subsequent professional courses, and strives to showcase the unique ideas, methods and techniques of algebra.
The editor has now compiled the weekly questions of Advanced Algebra (282 questions), the final questions of Fudan's Advanced Algebra final exam (46 questions) and the selected questions of the midterm exam (116 questions) into the "Fudan University Advanced Algebra Exercise Question Collection". About 40% of the questions are compiled or adapted by the editor, and the remaining 60% are selected from the Advanced Algebra exercises or postgraduate entrance examination questions of various brother universities. To facilitate readers' learning and reference, this exercise set also provides solutions or tips for all questions. The editor will update the exercise set in the second half of each year, adding the latest weekly questions for advanced algebra, final exam questions and midterm exam selected questions, and plans to publish this new set of advanced algebra exercises around 2030.
Fudan University’s advanced algebra course was recognized as one of the first batch of national first-class undergraduate courses in 2020. As an important part of the construction of first-class courses, the preparation of this exercise set has received strong support from the School of Mathematical Sciences of Fudan University. I would like to express my heartfelt thanks! Due to the limited editor's level, errors are inevitable. Readers and experts in the field are kindly requested to provide valuable criticism and suggestions.
Machine-translated from the Chinese original 复旦大学高等代数习题集2023版 (published 2023-09-22). WeChat original ↗