Hint#
If you don't have much time and don't want to read my long story, you can directly read the experience at the end of the article. But if you have plenty of time and are willing to listen to a year and a half long story, then feel free to continue reading~
All the materials mentioned in this article are publicly available on GitHub:
2021, The Ups and Downs of Advanced Mathematics C#
Looking back at the scene when I was studying Advanced Mathematics C last year (or it seems like the year before last), I was quite interested in advanced mathematics at that time (because it was the easiest course for me compared to biology and chemistry). I often read ahead of the teacher's progress with the book at the beginning of the semester, completed assignments in advance, and spent leisure time reading textbooks/helping high school classmates solve problems.
During the midterm exam of Advanced Mathematics C, I thought I could get a perfect score because I happened to see the exam questions in the textbook the night before the exam. However, due to a small detail in the symbol, I ended up with a normal distribution. But at that time, I didn't care about this mistake (almost getting a perfect score was enough for me to show off to many friends, that's what I thought at that time). I started to relax, skip classes, fall behind the teacher's progress, submit assignments just before the deadline, and couldn't even finish reading the textbook...
So, in the background of wasting time on other courses and activities, when facing a difficult final exam, my overall score dropped (81 for the overall score, and around 70 for the final exam score calculated based on the overall score). But unfortunately, this setback didn't make me realize my mistake. During that winter vacation, instead of previewing/reviewing advanced mathematics, I spent my time playing games...
In the second semester of my freshman year, I took Advanced Mathematics C, which covered series. I tried to keep up with the teacher's progress and thought I was doing well until the midterm exam. I got a bloody 52 on the exam, which shattered my confidence. I could only think of one word at that time: "despair."
Fortunately, due to the outbreak of the Beijing epidemic, I was able to pass/fail this course, saving my GPA by luck.
"It's a relief, it's a relief"
2022, Advanced Mathematics B#
Because I planned to pursue a double major in computer science, I had to take Advanced Mathematics B this semester.
Indeed, compared to many students in the class of 2022, my experience in taking Advanced Mathematics C became my significant advantage. I could easily pick up the concepts and knowledge about limits, instead of getting confused with the epsilon-delta language. However, this time, I remembered the lesson from last year and didn't become complacent just because I was ahead of others. Instead, I followed the advice of a computer science friend who took Advanced Mathematics A and actively solved extra practice problems to consolidate my knowledge and improve my problem-solving skills. As a result, I started studying Xie Huimin's Mathematical Analysis reference book. Although my enthusiasm for studying Xie Huimin's book only lasted for about three weeks due to the increased workload of medical courses and my own laziness, I still believe that studying Xie Huimin's book allowed me to completely reconstruct my shaky foundation in advanced mathematics and significantly enhance my skills in series transformations and integration.
Due to schedule conflicts, I didn't have the opportunity to attend regular classes from the beginning of the semester. However, I always attended the problem-solving sessions taught by the teaching assistant xyt on Tuesday nights. It was through xyt's problem-solving sessions and his well-prepared lecture notes that I was able to focus on special problem-solving techniques and key knowledge points while aimlessly studying Xie Huimin's book. As xyt said, "You don't have to study Xie Huimin's book. I've already included everything useful in my lecture notes." xyt is truly a great and interesting teaching assistant. He often tells jokes during the problem-solving sessions, such as "If I hadn't failed to solve the last problem in the CMO back then, I wouldn't be here. - You ask me where I would be, of course, next door" hhh
As the midterm exam approached, I fell into a cycle of "washing clothes in a dark room." It was well-known that the scope of the Advanced Mathematics B exam was extensive, and I was anxious because I never attended classes. I couldn't focus on reading the textbook, and reviewing Xie Huimin's book only made me regret, "Oh, how did I forget how to solve this problem that I saw before!" I solved some past exam questions, and the average score was 60... In this aimless state, I opened the anonymous forum and wanted to see how other students were dealing with this period. Unexpectedly, I found many people asking questions, and I immediately thought that "helping classmates" might be a good choice. That's how I ended up with a bunch of solved problems in post #4255209. To be honest, when I was doing this, I also wondered, "Why should I help my competitors?" But the answer to this question might be what my high school teacher said, "You are not competitors, but classmates who help each other." In the past, our goal with high school classmates was the college entrance examination, and now our goal is to compete for grades in the School of Mathematical Sciences (not competitors, but classmates who help each other).
Perhaps it was because my luck was good the night before, I successfully aced the midterm exam the next day and got a perfect score, which I had never achieved at Peking University before. To say how excited I was at that time, it wasn't that much. After a brief excitement, I felt a sense of relief, "It's a relief, it's a relief. It wasn't in vain that I studied Xie Huimin so much and stayed up late before the exam."
Objectively speaking, this perfect score was largely due to the advantage of the exam paper itself. The 2022 midterm exam was the easiest one in recent years, and I was lucky enough to connect the last question with the integral mentioned by xyt in the problem-solving sessions, . However, what's even more dramatic is that when I showed this exam paper to my roommate, he immediately recognized this question as the final exam question from the Advanced Mathematics C course two years ago (Poisson integral #4257222). But obviously, I didn't solve it when I took Advanced Mathematics C, and I completely forgot about it when I took Advanced Mathematics B (sad...
After the midterm exam, I faced a busy schedule with medical courses and mathematics courses. The time I spent studying Xie Huimin's book decreased even further. In November, due to the outbreak of the epidemic, I went home directly, and my laziness grew, making me even more inclined to procrastinate. I couldn't even manage to listen to xyt's problem-solving sessions in their entirety (although the fifth chapter on curved surfaces was a bit too easy). The planned review schedule was not executed on time. Fortunately, the only fortunate thing in all the unfortunate events was that I developed a high fever of 39.7°C the day before the exam and was able to apply for a deferred exam.
I probably tested negative for the virus two days after the exam, but looking at the remaining days of 2022, the idea of escaping came to my mind again. "Let's start reviewing in 2023. After all, there is still plenty of time, and the content is not that much." As it turned out, this was just a way to shift the pressure. From the beginning of 2023 until the exam, there were 13 days. I had to review linear algebra as well as advanced mathematics. Although I applied for a pass/fail for linear algebra, the limited time for review obviously increased the risk of failing. So, starting from the beginning of 2023, I almost studied mathematics every day. I spent about three days studying chapters seven and eight of Xie Huimin's book (integral mean value theorem and applications of differential calculus), and then I had to turn around and study linear algebra until the linear algebra exam on the 8th.
After the linear algebra exam on the 8th, I fell back into my old habit of slacking off and not studying. I spent a day in a daze before waking up and realizing that I only had three days left before the advanced mathematics exam!!!
So, for the next three days, I almost lived a life of "solve problems after waking up, solve problems until falling asleep." My daily routine was completely reversed to match the time zone of UTC+8. "Deadlines are the top priority." In these three days, I not only carefully reviewed the remaining content in the textbook but also solved four sets of past exams: the 2020 final exam, the 2021 final exam, the 2022A exam, and the mock exam prepared by xyt.
After solving these problems, just like before the midterm exam, I shared all of them on the anonymous forum (#4612715). But after completing these, I returned to the state of "washing clothes in a dark room" before the exam. I didn't want to read the textbook or review Xie Huimin's book. However, unlike before the midterm exam, there were fewer deferred exams this time, and I couldn't pass the time by helping others solve problems...
So, in the last four hours before the exam, I wasted my time chatting with classmates and mindlessly searching for "advanced mathematics" on the anonymous forum (.
Finally, at 15:00, the exam ended.
Thanks to the teachers in the School of Mathematical Sciences, the exam paper for Advanced Mathematics B was well-balanced, without biased or tricky questions, and had some repeated questions. It was a moderately difficult exam.
With that, my journey in Advanced Mathematics B came to a temporary end.
My winter vacation finally began.
But I didn't feel as excited as I had imagined, nor did I yawn continuously after staying up for 18 hours.
I had nothing to do.
So, I decided to write something, hoping to help my classmates and future students.
And that's how this article came to be.
Words of Wisdom#
As someone who has gone through a year of Advanced Mathematics C and just finished taking Advanced Mathematics B, I have gained a lot of insights and experiences.
This semester, because I was in the School of Medicine, I didn't attend a single class from the beginning to the end. I should really thank the pass/fail and deferred exam policies brought about by the COVID-19 pandemic for allowing me to survive this intense semester of medical and mathematics courses.
For most people, Advanced Mathematics is the first course they take in college, and it is characterized by "many credits, extensive content, and separation of teaching and assessment." Each of these keywords is intimidating, but honestly, I think Advanced Mathematics is the course that is closest to my high school learning experience. As long as you read the textbook carefully and do the exercises, repeating this cycle, you don't have to worry about your performance in regular assessments (as long as you submit assignments on time, you will get full marks). There is no need to go through the agony of writing research papers - you either know how to solve the problems or you don't, just like in high school math.
Here are my sincere suggestions:
- The knowledge taught in class is always the most important. Reading the textbook carefully once has a higher priority than any other review method. Only by reading and understanding the textbook can you truly grasp the knowledge taught in class and have a solid foundation to tackle difficult problems.
- If possible, find a study partner. You can exchange past exam questions and share your notes, which can be very helpful. Of course, if you are willing, you can add me as a study partner (I really welcome everyone, even if you have social anxiety!).
- Remember, you are at Peking University. You can't achieve top rankings just by doing a little bit of work like in high school. Advanced Mathematics B is worth investing more time in because it carries 5 credits. As a reference, my computer science classmates (Advanced Mathematics A, 95+) spent more than 30 hours of their free time each week, and I myself (Advanced Mathematics B) spent more than 20 hours of my free time each week, reaching more than 9 hours per day before the exam.
- The priority of review materials (personal opinion, for reference only): textbook > xyt's lecture notes > past exam questions ≈ your own notes > xyt's mock exams > extra practice problems like Xie Huimin's book.
- As a supplement to the previous point, about 60% of my problem-solving skills came from xyt's lecture notes, and 40% came from Xie Huimin's book.
- If you are a humanities student and don't have great confidence in your abilities, don't skip classes.
- If you want to score above 90, extra practice problems are necessary. Exposing yourself to some out-of-syllabus techniques is very beneficial for deepening your understanding of the course material and preparing for the exam.
- As a supplement to the previous point, xyt's exact words were "The marginal benefit of doing Xie Huimin's book is actually quite low."
- You can help classmates solve problems before the exam. This not only helps them but also helps yourself. Don't have the mindset of "If I help them, they will surpass me." Just treat it as a random test to assess your own abilities.
- If your winter vacation allows, it might be a good idea to preview the knowledge for the next semester.