# semester review (2024 Fall)

大二上

[TOC]

## Analysis (Honor Program) (I)

分析一

:::info
* number : MATH5232
* course type : elective / honor course
(cover the compulsory course "Introduction to Analysis (I)")
* lecturer : 沈俊嚴
* textbook : Pugh. Real Mathematical Analysis
* range : chapter 2 ~ section 6.6
* supplement : Banach space
* credits : 5 (4 main classes + 1 TA class)
:::

The lecturer approached the course with meticulous preparation. Remarkably, he never referred to his notes during lectures until week 14, maintaining a smooth and well-paced delivery of the content throughout the semester. Instances of blanking out were rare.

The course began with basic topology, which served as the primary focus before the midterm. Afterward, the syllabus shifted to Riemann integration and function spaces. Subsequently, the lecturer provided a brief recap of multivariable calculus and introduced the concept of Banach spaces, including integration on it and the inverse function theorem. The course concluded with measure theory, covering topics such as measurability, Lebesgue integration, and the slice theorem. The course *Analysis (II)* will continue from this topic.

Homework was entirely sourced from the textbook, consisting of five problems per week, except for the start of the semester and the week preceding exams. Some problems were marked with a “\*” each week, while we encountered one marked with “\*\*”. Overall, the exercises were manageable once the core concepts were understood.

(...)

The midterm and final exams consisted of six and seven problems, lasting 2.5 and 3 hours, respectively. Approximately 60 points of each exam were derived from or directly from homework problems. Some of these questions were lengthy, with the final exam requiring around 1.5 hours to complete the homework-based section alone. Most students, myself included, found the midterm easier than the final exam.

:::warning

grade : A+

:::spoiler grading

* homework (40%) : 49.6/50 (10 best out of 11)
* midterm exam (25%) : 94
* final exam (35%) : 76

theoretical score : 89.76

A+ rate: 32.14%

:::

## Algebra (Honor Program) (I)

代數一

:::info
* number : MATH7006
* course type : elective / honor course
(cover the compulsory course "Introduction to Algebra (I)")
* lecturer : 林惠雯
* textbook : No textbook
* ingredients : topics related to groups including classical group theory, representation of finite groups and homological algebra
* credits : 5 (4 main classes + 1 TA class)
:::

This Algebra honors program was intense, covering numerous topics related to group theory. The lessons were delivered at a dense pace throughout the semester, and no classes were canceled even for events like the typhoon, sports day, or NTU’s anniversary. (On the typhoon day off, we were assigned to study the lecturer’s notes independently.)

Before the midterm, we focused on the foundational language and methods of group theory, applying them to classify finite groups. Afterward, we learned how to compute the character table of finite groups and explored the underlying theory. The course then transitioned to studying extension problems through homological algebra. With a deeper understanding of modules, we revisited group representation and delve into induced representations.

:::spoiler syllabus :
such an intense semester
:::

After each class, we were assigned a homework set consisting of 3 or 4 problems (so 6~8 per week), which typically took the entire weekend to complete.
The homework often included problems which became are easier to solve after learning the materials in the following week, compelling us to rely on more elementary methods, though sometimes these approach felf nearly impossible. Finishing the homework is time-comsuming; I frequently sought help from classmates, achieving an acceptable completion rate.

I'd say I've learned a lot throughout the semester but struggled to fully digest the materials at times, given the rapid pace of new concepts introduced in the following class, especially after midterm. Often, I felt like understood the proofs on a surface level, without grasping the overarching structure at first. However, when I reviewed the course content before the final exam, I gradually developed a comprehensive understanding of the ingredients provided in the lessons. Unfortunately, I lacked the time thoroughly memorize them, which made me recall them during the final exam extremely challenging. Given the limited time and having other finals to prepare at once, I had decided to merely focus on getting familiar with the properties and revisit the homework.

Looking ahead to Algebra II, I plan to delve more into lecture content before tackling homework. I aim to better memorize and internalize the core ideas in the proofs and avoid becoming overly fixated with completing homework from the start. I reckon this arrangement more effective for studying, considering how absurdly limited the final weeks are for exam preparation.

:::warning

grade : B+

:::spoiler grading

* homework : 91 (14 homework)
* midterm exam : 62
* final exam : 48

* A club rate : 15/29
(mine: 18/29)

:::

## Introduction to Ordinary Differential Equations

常微分方程導論

:::info
* number : MATH2217
* course type : compulsory
* lecturer : 陳逸昆
* textbook : Boyce, DiPrima, Meade. Elementary Differential Equations and Boundary Value Problems.
* range : (Twelfth Edition) chapter 1 ~ 5 + section 7.1 ~ 7.6
* credits : 4 (including 2 TA classes in every other week)
:::

This course primarily covers elementary methods for solving first-order and second-order linear differential equations, as well as the basics of power series solutions and the Laplace transform. The lectures progress at a slow pace and lack the smooth structure typical of courses designed for math majors. The lecturer closely follows the textbook, including its examples, which makes it relatively easy to study the material independently without attending class. As a result, attendance rates were consistently below 30%, based on my observation.

However, the ease of self-study does not translate to the quizzes or the final exam. The first two quizzes had minimal alignment with the course content, which suggested poor communication between the professor and the TAs. Additionally, the final exam weighs an overwhelming 60% of the overall grade, yet no clear guidance was provided on how to prepare for it.

The textbook omits several proofs related to the existence and uniqueness of solutions for differential equations. Since the lectures follow the textbook closely, the course assessments focus heavily on calculations, particularly solving differential equations. This approach makes the course feel atypical for a math major. (The lecturer has even remarked that he believes the calculus course in the Department of Mathematics is not "normal.")

In the final exam, the distribution of marks was as follows:

- 60% on first-order linear equations (Chapter 1 : 20% / Chapter 2 : 40%)
- 15% on Euler equations (chapter 5 content)
- 30% on Laplace transforms. (chapter 7 content)

I don't recommend this course to students from other departments who are looking for a more cohesive experience with courses specifically designed for math majors.

:::spoiler complaints

:::

:::warning

grade : B+

:::spoiler grading

* presentation (5%) : done (present 1 problem)
* quiz (35%) : 87 (4 best out of 6)
* final exam (60%) : 63 (the average is around 50)

theoretical score : 73.3

average of final grades (after adjustment): 60.58 :question::question::question:

* A club rate : 13/70
(mine: 21/70)
* Pass rate : 52/70

:::

## Principle of Microeconomics (with Recitation)

個體經濟學原理與實習

:::info
* number : ECON2010-01
* course type : elective (elective-compulsory for math major)
* lecturer : 林明仁
* textbook : Acemoglu, Laibson, List. Ecomomics. (Third Edition)
* range : part 1 ~ 3 : chapter 1, 2, 4, 5, 6, 9, 12, 13, 14
* credits : 4 (3 main classes + online TA classes)
:::

Among the four elective-compulsory courses offered, I chose principle of economics to take. (The other three options are general physics, chemistry, and biology.) This course is mandatory for department of economics, international businesses, accounting, etc.

It closely aligns with my ideal course designed for undergrads in term of its difficulty and its teaching style. The workload isn't overwhelming, and the syllabus is easy to follow. The lecturer usually uses practical, approachable examples to explain, making easy to remember. But compared to compulsory courses for math major, this pace is noticeable slower.

The primary lectures are held on Fridays, while the TA sessions are scheduled for Mondays and Wednesdays at noon. The format might vary depending on TAs each year. This year, TAs filmed some videos reviewing the content taught in class.

All the homework and exam problems are created and organized by TAs, who were clearly diligent in their efforts. For this reason, It's possible to perform well simply by watching their videos and practicing the materials, without attending the lectures.

Since I didn't have much time to study in-depth, I merely focused on reviewing the homework before the exams. While I managed to finish the exam just in time (3hrs), I didn't double-check my answers, which costs me several points due to calculation errors.

:::warning

grade : A

:::spoiler grading

* homework (30%) : 30/30 (6 homework(5%) + 1 bonus(+2%))
* midterm exam (30%) : 71 (the average is around 60)
* final exam (40%) : 80.5 (the average is around 70)

theoretical score : 83.5

A+ rate : 12.26%
A & A+ rate : 31.03%

:::

## French (II)(1)

法文二上

:::info
* number : FL3011-02
* course type : elective
* lecturer : 林湘漪 (Louisa)
* textbook : Amical 2
* range : lesson 1 ~ 12
* credits : 3 (4 classes)
:::

This French course progressed at a relatively slow pace, with limited supplementary materials and opportunities for peer interaction in class. However, it was still possible to learn valuable content during the course, particularly with the help of the French TA. The TA, who is from France, speaks English fluently without a noticeable French accent, making it even easier to communicate.

At the end of each lesson, we hand in a _journal de bord_ (diary) consisting of at least three sentences. These were corrected by the French TA. While correctness did not count towards the overall grade, consistent attendance guaranteed full marks for this component.

The written exams were straightforward to prepare for, as the questions primarily came from the _cahier_ (exercise book) and materials provided on NTU Cool. Listening exercises and verb conjugation were emphasized in each exam. The averages were consistently around 88, 89.

The oral exam focused on pronunciation rather than content. The lecturer graded generously. Prior to the exam, we prepared transcripts that the TA reviewed and corrected, which made the process easier.

BTW, I discovered that ChatGPT is also quite effective for practicing and learning French.
:laughing:

:::warning

grade : A+

:::spoiler grading

* exercises (12%) : 11.5 (livre + cahier)
* journal de bord (9%) : done (=diary)
* test (12%) : 83 (5 best out of 6 online quizzes, each takes 15 minutes)
* écrit 1 (15%) : 91 (=midterm 1)
* écrit 2 (15%) : 91 (=midterm 2)
* écrit 3 (15%) : 96.5 (=final exam)
* jeu de rôle 1 (5%) : 20/20 (midterm 1 oral)
* exposé (9%) : 19.5/20 (midterm 2 oral)
* jeu de rôle 2 (5%) : 19/20 (final oral)

theoretical score : 93.25

A+ rate : 70.83%

:::

## Beginning Handball

手球初級

:::info
* number : PE2050A5
* course type : PE / common compulsory course
* lecturer : 許君恆
* credits : 1 (2 classes)
:::

Each lesson began with warm-up activities, typically involving passing balls in pairs. The lecturer would then teach one or two techniques, followed by practice sessions. During the second hour, we participated in two short handball contests (each lasting 8 minutes) between groups. Overall, the course was not very demanding, but being an outdoor course, it could be physically exhausting in the summer heat. Occasionally, lessons were either moved indoors or canceled due to rain.

Participation in at least two contests between different handball classes was mandatory, with each contest lasting 30 minutes and held at noon between weeks 11 and 15. My contests were scheduled during the first week of this period. ~~Un~~fortunately, we didn’t win any matches and were eliminated in the first round.

The final exam took place in weeks 14 and 15, consisting of three testing items: throwing for distance (擲遠), shooting (射門), and changing direction (閃切). For the throwing test, the requirements were slightly relaxed for females. The other two items primarily assessed movements and footwork. Overall, the final exam was straightforward and manageable.

:::warning

grade : A+

:::spoiler grading

* attending course (45%) : 45/45
* attending competition (25%) : 25/25
* final exam (30%) : 21/30
* bonus : 2 (I have no idea where it comes from)

theoretical score : 93

A+ rate : 70%

:::

## general info


total credits: 22
GPA: 3.84

## general feedback

* I initially hesitated about taking French II, but since I hadn’t yet used my exploration credits, I decided to enroll. The course ended up requiring a much lighter workload and creating less pressure than any of my other courses (except handball), while also boosting my GPA.
* Taking several dense, heavy courses in one semester wasn’t an ideal arrangement.
* Next semester, I’ll be taking a course with Professor Das for the first time. I’m hopeful it will mark a great restart.
* My ideal is to attend all classes and fully focus on the lessons without needing to juggle other homework on easier lessons. However, that goal seems unattainable this semester.

# Brief plan for the winter vacation

I plan to join the following seminars:
- Algebraic Graph Theory
- We've started this since last summer vacation, and we're about to move on to the chapter 9
- reference: https://link.springer.com/book/10.1007/978-1-4613-0163-9
- Paper seminar on entropy methods and polynomial methods
- I choose the "joint problems" to present
- reference:
- https://www.cambridge.org/core/books/polynomial-methods-and-incidence-theory/268C4E4946619A0301E9DC3736DDBA7F
- and some other recent papers
- Using Borsuk-Ulam theorem in Combinatorics
- I choose chapter 3 to present
- reference: https://link.springer.com/book/10.1007/978-3-540-76649-0