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 (seems like it was already two years ago), 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 at the beginning of the semester, completed assignments in advance, and spent my free time reading textbooks and helping my high school classmates with problem-solving.
During the midterm exam for Advanced Mathematics C, I thought I would 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 instead of a perfect score. But at that time, I didn't really care about this mistake (almost getting a perfect score was already enough for me to show off to many friends, that's what I thought at that time). I slowly started to relax, skip classes, fall behind the teacher's progress, and couldn't even finish reading the textbook...
So, in the background of me slacking off and other courses taking up my time, when faced with a final exam paper that was not easy, my overall grade plummeted (81 for the overall grade, around 70 for the final exam grade). Unfortunately, this setback didn't make me realize my mistake. During that winter vacation, I still didn't do any preview/review of advanced mathematics, but instead spent my days indulging in games...
In the second semester of my freshman year, I took Advanced Mathematics C again, and this time it was about series. I tried to keep up with the teacher's progress and thought I was doing well, until the midterm exam when I got a brutal score of 52. My confidence was shattered, and I could only think of one word at that time: "despair".
But fortunately, due to the outbreak of the pandemic in Beijing, I was able to pass/fail this course, saving my GPA by luck.
"Well, that's good."
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 of taking Advanced Mathematics C became my significant advantage. I could easily pick up the concepts and knowledge about limits, instead of being confused by the epsilon-delta language. But 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 friend majoring in computer science 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 increasing 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 of advanced mathematics and significantly improve 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 some special problem-solving techniques and key points mentioned by xyt. As xyt said, "You don't have to study Xie Huimin's book, I have already included the useful parts in my lecture notes." xyt was truly a great and interesting teaching assistant. He often told jokes during the problem-solving sessions, like "If I hadn't failed to solve the last question of 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 vicious cycle of "washing clothes in the darkroom". The scope of the Advanced Mathematics B exam was well-known for being challenging, and I was anxious because I hadn't been attending classes and couldn't focus on studying. I couldn't concentrate on reading the textbook, and reviewing Xie Huimin's book only made me frustrated, thinking, "How come I understood this problem when I first saw it, but now I can't solve it?" I solved some past exam papers, but my average score was only 60... Lost and aimless, I opened an anonymous forum to see how other students were dealing with this period of time, but unexpectedly, I found many people asking questions. I suddenly thought that "helping classmates" might be a good choice, so I posted a bunch of solutions to the problems in post #4255209. To be honest, when I was doing this, I also wondered why I should 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 was the college entrance examination, but now our goal is to get good grades in the School of Mathematical Sciences (not competing with 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 of 100, which I had never achieved at Peking University before. To say how excited I was at that time, it wasn't really that exciting. After a brief moment of excitement, I mostly felt relieved, thinking, "Well, that's good. 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 actually due to a significant advantage in the exam paper - the midterm exam in 2022 was the easiest one in recent years, and I was lucky enough to connect the last question in the exam with the integral mentioned by xyt in the problem-solving sessions, . But what's even more dramatic is that when I showed this exam paper to my roommate, he immediately recognized that this question was the final exam question from the second semester of Advanced Mathematics C two years ago (Poisson integral #4257222). However, 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 entered a period of time with doubled workload in medical courses and mathematics courses. The time I spent studying Xie Huimin's book further decreased, and in November, due to the outbreak of the pandemic, I went home directly, and my own inertia grew stronger. I became more and more lazy and even found it difficult to finish listening to xyt's problem-solving sessions (although it was also because the fifth chapter on curved surfaces was a bit too easy). The planned review schedule was not followed, but luckily, the day before the exam, I had a high fever of 39.7°C 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 thought of escaping came to my mind again. "Let's start reviewing in 2023, there's still plenty of time, and not much content." It turned out that this was just a way of shifting the pressure - from the first day of 2023 to the exam, there were 13 days, and 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 start studying 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 - started slacking off and not studying. I spent a day in a daze before realizing that there were only three days left until the advanced mathematics exam!!!
So, for the last three days, I almost lived a life of "solve problems when awake, sleep when tired". My daily routine was completely reversed to the Eastern Time Zone, and "deadline is the first productivity" became my motto. In these three days, I not only carefully read the remaining content in the textbook but also solved four sets of past exam papers: the 2020 final exam, the 2021 final exam, the 2022A paper, and xyt's mock exam paper, all in one day before the exam (strictly speaking, until 6 am today)...
After solving these problems, I still shared them on an anonymous forum like I did before the midterm exam (#4612715). But after solving these problems, I returned to the state of "washing clothes in the darkroom" before the exam. I didn't want to read the textbook or review Xie Huimin's book. However, unlike the midterm exam, because there were fewer people eligible for deferred exams, I couldn't pass the time by helping others with problem-solving...
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, the exam ended at 15:00.
Thanks to the teachers in the School of Mathematical Sciences, the exam paper for Advanced Mathematics B was a set of questions without bias or tricky questions, with some important questions and a moderate level of difficulty.
Thus, 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 repeatedly because I had stayed up for 18 hours straight.
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 experienced a year of Advanced Mathematics C and just finished taking Advanced Mathematics B, I have gained many insights that I would like to share.
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 that has "many credits, a lot of content, and separate teaching and testing". 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), and you won't have the same anxiety as when writing an essay - you either know how to solve the problem or you don't, just like in high school math problems.
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 papers and share your notes, which can be very helpful. Of course, if you're willing, you can add me as a study partner (I really welcome everyone, even if you're socially anxious!)
- Remember, you are at Peking University. You can't achieve top grades just by doing a little bit of work like in high school. Advanced Mathematics B is worth spending more time on because it carries 5 credits. As a reference, my computer science classmates (Advanced Mathematics A, 95+) spend more than 30 hours of their free time each week, and I myself (Advanced Mathematics B) spend more than 20 hours of my free time each week, and it can reach 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 papers ≈ your own notes > xyt's mock exam papers > extra practice problems like Xie Huimin's book.
- As a supplement to the previous point, I feel that 60% of my problem-solving skills come from xyt's lecture notes, and 40% come 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 get a 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 knowledge taught in class and preparing for the exam.
- As a supplement to the previous point, xyt once said, "The marginal benefit of solving Xie Huimin's book is actually quite low."
- You can help classmates answer questions 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 see how well you can perform.
- If your winter vacation allows, you might as well preview the knowledge for the next semester.