Mathematical Analysis
The required foundational mathematics courses for freshmen and sophomores include: Mathematical Analysis I to Mathematical Analysis III, Advanced Algebra (Volumes 1 & 2), Analytic Geometry, Abstract Algebra, University Physics, etc.
Scientific and Engineering Computing is not a Computer Science major. It can be understood as computational mathematics, which uses modern mathematical theories and methods to solve various engineering problems. It is a very application-oriented major.
Graduates of this major have a wide range of employment opportunities, including aerospace, radio, remote sensing, architectural design, defense industry, chemical metallurgy, mechanical manufacturing... they can work in any industry as long as it is related to engineering.
Mathematics Department students who leave campus or the front lines of academia often find it a little more difficult to find jobs.
But does it matter?
Is studying math merely about finding a good job, buying a house, a car, and getting married after graduation?
"Of course not." The professor of mathematical analysis said firmly from the podium. His hair was not thick, and the crisscrossing wrinkles on his forehead highlighted his intelligence.
"I don't care which major you are in the School of Mathematics, you must remember this: mathematics is not a tool for making a living, but a great art." Professor Lu was teaching the Mathematical Analysis course, was lecturing on Mathematical Analysis I, a light-colored textbook produced by the School of the Big Mathematics Department.
Most of the mathematical analysis textbooks commonly used in other universities in China are two types with blue covers: the Mathematical Analysis textbooks published by Fudan University (Volumes 1 & 2) and the Mathematical Analysis textbooks published by East China Normal University (Volumes 1 & 2). Both of these textbooks for Mathematical Analysis have blue covers.
The mathematical analysis textbooks published by Yenching University and Shuimu University are different from those published by Yenching University. Yenching University's light-cover version of the mathematical analysis textbook is a set of three volumes: Mathematical Analysis I, Mathematical Analysis II, and Mathematical Analysis III. Tsinghua University's yellow-cover version of the mathematical analysis textbook is also a set of three volumes.
It's considered low- Advanced Mathematics for the Mathematics Department majors not to study advanced calculus; mathematical analysis is one of the more challenging courses for the Mathematics Department majors when they first start out.
"Mathematical Analysis, can anyone tell me the purpose of setting up this course?" Professor Lu glanced around the audience, not giving the students a chance to answer, and answered himself in a very fast-paced manner, "To deeply understand the ultimate meaning of mathematics, the simplest and most effective way is... to do a few problems first."
"Here we go again! Doing homework right after the start of the semester!" The students in the audience were on the verge of tears.
The professors in the mathematics department all have the same style: professors of Advanced Algebra, Analytic Geometry, and mathematical analysis. Their lesson plans will invariably contain the same sentence. "You're all math students, come on, do a few problems first."
That's how mathematics works; you have to do problems during the foundational stage to deepen your understanding of mathematical theories.
What exactly is the purpose of the course "Mathematical Analysis"?
In fact, mathematical analysis is advanced calculus. It mainly consists of calculus and the general theory of Infinite Series, and includes their theoretical foundations to form a relatively complete mathematical discipline.
Mathematics is about understanding and calculation, and mathematical analysis involves a lot of calculation. If a professor only talks about theory, it's just empty talk. So Professor Lu has his students do problems, using problems as a starting point to introduce theory.
For a given problem, a student writes down their solution or specific steps, and then the teacher and students discuss together, identifying the highlights, the weaknesses, and how to improve. In this teaching segment, the professor and students fully interact and explore in depth, rather than the professor simply lecturing and imparting knowledge. This is Professor Lu's teaching philosophy.
"I already explained Mathematical Analysis I to you in the last class, so I believe you have a general understanding of this course," Professor Lu said matter-of-factly.
"Understood, understood." A few students in the classroom nodded, including Shen Qi, Zhou Yu'an, Cai Qing, Luo Ji, and Ou Ye.
Shen Qi, Zhou Yu'an, Cai Qing, and Luo Ji are four students from the Mathematics Department. They live in the same dormitory and participated in the Yenching University Golden Autumn Camp together last year.
Ou Ye is also a product of Yenching University's Golden Autumn Camp; she's a master at calculations.
Numerical calculation is part of mathematical computation, and Ou Ye didn't sit idle this summer either. From her fragmented descriptions, Shen Qi learned that Ou Ye had strengthened her mathematical calculation abilities during the summer vacation. Ou Ye had probably taken the advice of Sun Erxiong and Shen Qi, and she was going further and further down the path of becoming Calculation Ji.
Shen Qi's four roommates and Ou Ye said they already had a general understanding of Mathematical Analysis I and could try a few problems to practice.
A round-faced male student from the Department of Scientific and Engineering Computing looked worried. "Professor Lu, last time you spent one class period covering the entire textbook 'Mathematical Analysis I'. Today is your second class, and you're just giving us problems to solve? How are we supposed to do that?"
Professor Lu was displeased. "I haven't even given you a question, and you're already backing down and showing fear. How can you learn math well with this attitude?"
At this point, Shen Qi spoke up, "Professor Lu, let's set some questions. Mathematics requires solving problems and discussing them to create a chemical reaction, allowing sparks of thought to collide and shine."
"Look, this is the awareness of Olympic Math champion!" Professor Lu said to Shen Qi with great admiration, "Heroes admire heroes."
"You bastard!" All the students in the Department of Science and Engineering Computing cursed inwardly, except for one person who coldly laughed and remained silent.
Just a few days after military training, Professor Lu finished teaching Mathematical Analysis I in one class, followed by a three-day break between the first and second classes.
A complete book on Mathematical Analysis I, even if read word for word, would take several class periods. How did Professor Lu manage to teach the entire book in one class period?
"You can read the book about limits of sequences yourselves; it's too simple."
"The Leibniz formula for the derivative is key, and I'd like to elaborate a bit more on it."
"The Taylor series with various remainders is the most important part, and I'll spend two more minutes explaining it here."
That's how Professor Lu did it; he finished teaching Mathematical Analysis I, which should have taken a whole semester, in one class.
Professor Lu may have his own teaching plan and follow-up plans, but some students cannot accept the current teaching pace.
Normal people cannot keep up with this pace of teaching, but there are always some abnormal people.
Yenching University certainly has geniuses and King of Show Offs, but not everyone is a genius or King of Show Offs.
Of course, there are also ordinary students. Often, some of them hide by Weiming Lake and secretly cry, feeling that their lousy level is far inferior to those geniuses and King of Show Offs in the class. They are so angry that they cry.
Shen Qi, the class monitor from the Mathematics Department, looked relaxed and eager to solve the problem, while a small-eyed boy from the Science and Engineering Computing Department kept sneering; he stood out from the rest of the department.
Professor Lu wrote a problem on the blackboard:
"Calculate I = ∫∫-ydzdx + (z+1)dxdy, where S is the outer side of the portion of the cylindrical surface x^2 + y^2 = 4 intercepted by the planes x + z = 2 and z = 0."
After presenting the questions, Professor Lu said, "Don't rush, everyone gets a turn. The first question on the blackboard will be solved by a representative from the Mathematics Department, who will then explain their thought process, perspectives, and insights. The second question will be solved by the Department of Scientific and Engineering Computing. Please be prepared."