Maths & Physics Book Reviews — Freshman Year of College: Autumn and Winter

下一篇：数理教材阅读进度及读后简评（大一春夏）

Next: Maths & Physics Book Reviews (Freshman Year of College: Spring and Summer)

学一门课之前，总是会到处找各种教材的评价，花很多时间试图找到一本别人口中最好的，好像选对了教材就能学懂似的，结果发现找一本相对不错的开始静下心学，同时多参考各种书目才是正道。等学完之后，好不容易有了些许理解，却又懒得再记录下来。于是我打算开始撰写并维护这一系列文章，记录自己学习数理基础课时认真读过以及参考过的教材，既是督促自己温故知新，也是给大家提供一个参考。

Before starting a course, I always go hunting for textbook reviews, spending ages trying to find the book everyone says is best, as though picking the right textbook would somehow make me understand the subject. In the end, it turns out the way to go is to pick a reasonably good one, settle down and actually study, and consult other books along the way. But once I have finally learned something, I am too lazy to write it down. So I decided to start this series and keep it going, recording the textbooks I have read carefully or used as references for my basic maths and physics courses. Partly to make myself revisit what I have learned, and partly to give others something to go on.

本学期主要学了微积分，线代，拓扑，费曼I（力热光）和经典力学，寒假预习了一下量子。

This semester I mainly studied calculus, linear algebra, topology, Feynman I (mechanics, heat, and optics), and classical mechanics. Over the winter break I also did some preparatory reading in quantum mechanics.

大一秋的数学主要学了高等微积分(1)，线(xie)性(xing)代(dan)数(shu)，基础拓扑学和一些散装的几何知识。

My maths courses in the fall semester of my freshman year of college were Advanced Calculus (1), linear algebra (read: black magic), introductory topology, and assorted bits and pieces of geometry.

• 艾颖华 高等微积分讲义

• Ai Yinghua, Lecture Notes on Advanced Calculus

主要用的是艾神的讲义，拓扑学讲义熟读之后对比Zorich会发现是后者的简化精华版，观点很现代，课堂上常常渗透了范畴、拓扑、微分几何等现代数学的思想，且为物理系的需要，简化了很多不必要的证明及定理，强调了许多物理中会用到的对象（ \(\delta\) 函数、Feynman图等），非常好，唯一的缺点是无法开放获取。

We mainly used the legendary Ai's notes. After studying his topology notes closely and comparing them with Zorich, you find that they are a distilled, simplified version of the latter, with a very modern viewpoint. His classes frequently brought in ideas from modern mathematics, including categories, topology, and differential geometry. To suit physics students, he also streamlined many unnecessary proofs and theorems and emphasized objects used in physics, such as the \(\delta\) function and Feynman diagrams. Excellent; the only drawback is that the notes are not openly available.

• B. A. Zorich, 数学分析（第一卷）

• B. A. Zorich, Mathematical Analysis, Volume I

没有仔细读，只是在复习的时候简略通读过。个人认为是一本很适合物理系同学的参考书，前提是略读（跳/挑），不究细节，只求建立直觉上的理解，因为如果精读会消耗大量时间，并且所有我询问的物理系老师都反对精读这本书。书中有很多叙述直接在物理情境中进行，与应用结合紧密，具备绝大多数AYH讲义的优点。习题没看过不做评价，据数学系朋友称有很多诡异物理题。

I did not study this carefully; I only skimmed it from beginning to end while reviewing. I think it makes a very good reference for physics students, provided that you skim selectively, skip around, and aim for intuitive understanding rather than getting caught up in the details: close reading would take a great deal of time. Every physics instructor I asked advised against reading it intensively. Many discussions are set directly in physical contexts, with close ties to applications, and the book shares most of the strengths of AYH's notes. I have not looked at the exercises, so I cannot comment on them, but friends in the maths department tell me that there are plenty of strange physics problems.

表面上是线性代数，由于是数学中心的老师执教（XD！），整个课程变异成了前半学期标准线性代数，后半学期张量+群环域+群表示论，习题质量很高，让人收获很大，花的时间精力也很多。但是很遗憾，讲义目前还比较简略零散，所以在学习的过程中参考了不少书。还记得开课的时候XD邪魅一笑，说：“不知道有没有同学已经学过线性代数的，但我可以保证，我这门课的内容绝对有你没学过的。”

Nominally, this was linear algebra. But with an instructor from the university's mathematics center (XD!), the course mutated into standard linear algebra for the first half of the semester, followed by tensors, groups, rings, fields, and group representation theory in the second half. The problem sets were excellent and taught me a lot, though they also took a great deal of time and effort. Unfortunately, the notes were still rather brief and fragmentary, so I consulted quite a few books. I still remember XD opening the course with a mischievous smile: “I don't know whether any of you have already studied linear algebra, but I can guarantee that this course will contain things you haven't learned.”

• Sheldon Axler, Linear Algebra Done Right

• Sheldon Axler, Linear Algebra Done Right

Done Right是一本声名远扬的书了，我仔细通读了一遍，名副其实，值得精读。全书立足于线性映射叙述所有的线代内容，属于进入抽象层面的第一步，对一开始培养maths maturity很有帮助。对特征空间及Jordan型，复数与奇异值分解等问题的处理令人记忆犹新。美中不足的是内容较少（短小精悍），因此在有一定基础后只能当闲书看了（其实是自己拖太久买了一直晾着）。

Done Right is famous, and I read it carefully from cover to cover. It lives up to the name and is worth a close read. The whole book develops linear algebra through linear maps, a first step into abstraction that really helps build mathematical maturity early on. Its treatment of eigenspaces and Jordan form, complex numbers, and singular value decomposition is still fresh in my mind. The only catch is that there is not that much in it—short but substantial—so once you have some background, it is more of a casual read. (Really, I just put it off for too long after buying it and left it sitting there.)

另外我买了一本英文第三版精装收藏，书里有不少小彩蛋，比如页码 \(22\approx 7\pi\) 等，挺有意思。

I also bought the hardcover third English edition for my collection. There are quite a few little Easter eggs, such as the page number \(22\approx 7\pi\), which are fun.

• @Tautochrone 的线性代数手写笔记

• @Tautochrone, Handwritten Notes on Linear Algebra

写得非常好！我偷偷下载下来合成了一个pdf编上大纲，在复习线代期中的时候完整通读了一遍，平时遇到一些老师以为平凡，而我完全摸不着头脑的地方，常常会翻阅。涉及的Topic较一般线代更广，包括了所有的标准线代内容，同时专门严肃地处理了多重线性代数（张量），证明很详尽，同时也有作者自己的评论和理解，精读略读皆宜。

These are extremely well written! I sneakily downloaded them, combined them into a PDF, and added an outline. I read the whole thing while preparing for the linear algebra midterm, and often returned to it whenever an instructor thought something was trivial while I had no idea what was going on. The topics go beyond a typical linear algebra course: the notes cover all the standard material and give a serious, dedicated treatment of multilinear algebra and tensors. The proofs are detailed, and the author adds personal comments and insights. Good for a close read or a skim.

其余升级内容（简易抽代、群表示和特征标等）因为没时间通读，就只能到处胡乱学，参考过且较有帮助的包括AYH 拓扑学讲义, S. Hassani Mathematical Physics, Harvard Math55a Lecture Notes, 李新征老师的群论及其在凝聚态物理中的应用，N. Jeevanjee An Introduction to Tensors and Group Theory for Physicists.

For the extra material—basic abstract algebra, group representations, characters, and so on—I had no time to read anything systematically, so I pieced things together from wherever I could. Helpful references included AYH's Lecture Notes on Topology, S. Hassani's Mathematical Physics, the Harvard Math 55a lecture notes, Li Xinzheng's Group Theory and Its Applications in Condensed Matter Physics, and N. Jeevanjee's An Introduction to Tensors and Group Theory for Physicists.

2021/6/13补充，群表示论部分可以参考GTM42 Serre Linear Representations of Finite Groups的第一部分，据作者本人说本来就是写给化学家的。

Added June 13, 2021: for group representation theory, the first part of Serre’s Linear Representations of Finite Groups (GTM 42) is a useful reference. According to the author himself, it was originally written for chemists.

主要包括点集拓扑和一点点代数拓扑（基本群、同伦、闭曲面分类、de Rham上同调等）。

This mainly covered point-set topology and a little algebraic topology: the fundamental group, homotopy, classification of closed surfaces, de Rham cohomology, and so on.

• 艾颖华 拓扑学讲义

• Ai Yinghua, Lecture Notes on Topology

一开始花了几节课介绍了简单的范畴论，接下来全部用这一语言叙述所有内容。为了进入代数拓扑，还补了不少群论的知识，对线代课产生了莫大的帮助，叙述的点集拓扑也加深了对微积分的理解，个人感觉大一学一点简单的拓扑，尤其是熟悉了基本的范畴论语言，对整个大一数学的整体理解有非常大的帮助，对形成maths maturity有很大帮助，是个英明的决定（跟我一起去听课的数学系朋友也有同感），而且在此基础上就可以试图理解拓扑群、李群等搭积木搭出来的概念了。但很可惜的是艾神说因为时间太紧（要去CMO阅卷），以后不会再开这门课了。唯一的缺点依然是无法开放获取……

The course began with a few lectures on elementary category theory, then used that language throughout. To get into algebraic topology, we also covered quite a bit of group theory, which helped enormously with linear algebra. The point-set topology deepened my understanding of calculus too. I personally found that learning a little topology in freshman year of college, especially becoming familiar with basic categorical language, greatly improved my overall understanding of freshman-level college mathematics and helped develop mathematical maturity. An excellent decision, if I do say so myself (my friend from the maths department who went along thought so too). With that foundation, you can start making sense of concepts assembled like building blocks, such as topological groups and Lie groups. Sadly, Ai said that he would not offer the course again because he was too pressed for time—he had to go grade the Chinese Mathematical Olympiad. The only drawback, again, is that the notes are not openly available…

由于艾神讲得太好太细了，所以课外没有花很多时间读书，推荐的参考书有J. R. Munkres Topology, 尤承业 基础拓扑学讲义。艾神同时特别推荐了From Calculus to Cohomology一书。

Ai explained things so well and in such detail that I did not spend much time reading outside class. Recommended references included J. R. Munkres's Topology and You Chengye's Lecture Notes on Introductory Topology. Ai also particularly recommended From Calculus to Cohomology.

• Fredric Schuller, Geometric Anatomy of Theoretical Physics

• Fredric Schuller, Geometric Anatomy of Theoretical Physics

这是一套视频课程，介绍了很多与物理相关的几何知识，目前我只看了一小半，但已经对我理解许多概念有了非常大的帮助，有很多独到的观点，但是量很大，所以非常推荐慢慢看。

This video course introduces a great deal of geometry relevant to physics. I have watched somewhat less than half so far, but it has already helped enormously with many concepts and offers many distinctive insights. There is a lot of material, so I strongly recommend taking it slowly.

由于高中竞赛已经有很好的基础了，所以这学期普物唯一干的一件事就是完整仔细读了一遍Feynman的讲义。

Because preparing for physics Olympiads in high school had already given me a solid foundation, the only thing I did for introductory physics this semester was read Feynman’s lectures carefully from beginning to end.

• R. P. Feynman, Feynman Lectures on Physics Volume I

• R. P. Feynman, The Feynman Lectures on Physics, Volume I

我的评价简单来说就是必读，写得实在是太好了！好到几乎每一章都有让人读得非常激动，忍不住要用荧光笔划下来的论述，隔几章还会有令人想整段划下的叙述。目前我印象比较深刻包括但不限于

My verdict, in a word: essential. It is just so good! Almost every chapter has something that gets me so excited I have to reach for a highlighter, and every few chapters there is a whole passage I want to highlight. Things that have particularly stayed with me include, but are not limited to:

1. 对质量的数学表述的建构过程
2. 对数学与物理之间关系的论述
3. 费马原理与波动光学、路径积分
4. 反射折射的本质
5. 菲涅尔公式的推导
6. 量子与不确定性原理及其哲学含义
7. 熵、混乱程度和时间箭头
8. 涨落与麦克斯韦妖
9. 对称性

1. How the mathematical description of mass is constructed
2. The discussion of the relationship between mathematics and physics
3. Fermat’s principle, wave optics, and path integrals
4. The nature of reflection and refraction
5. The derivation of the Fresnel equations
6. Quantum mechanics, the uncertainty principle, and their philosophical implications
7. Entropy, disorder, and the arrow of time
8. Fluctuations and Maxwell’s demon
9. Symmetry

个人认为恰恰是已经完整学过一遍普物的人最适合看，Feynman的很多思考方式是标准教材里从来没见过的，并且真正能够让你明白到底发生了什么。

I think it is precisely people who have already been through a full introductory physics course who will get the most out of it. Many of Feynman’s ways of thinking are unlike anything I have seen in standard textbooks, and really help you understand what is going on.

最简单的例子是反射折射的本质：高中就教我们反射和折射，有费马原理、惠更斯原理，看起来好像很有道理，其实根本没道理，凭啥光在介质里速度变慢了？没有这个，你这些原理根本用不了。你说介质一大坨好像阻挡了光？其实毫无道理，因为原子和原子之间间距大了去了，阻挡啥？后来解麦克斯韦方程组的边界条件，一通算发现算出了折射定律，用介电常数解释光速的变化，看起来很有道理，其实只是数学，根本没有理解。

The simplest example is what reflection and refraction actually are. We learn about them in high school: Fermat's principle, Huygens' principle. It all sounds so reasonable, except it explains nothing. Why on earth does light slow down in a medium? Without knowing that, you cannot even use these principles. You say this big lump of material gets in the way of the light? That makes no sense. There is loads of space between the atoms—what exactly is getting in the way? Later, you solve Maxwell's equations with boundary conditions, grind through the calculations, and out comes the law of refraction. You explain the change in light speed with permittivity. It all looks reasonable, but it is just maths. You still have not understood what is happening.

而Feynman的方法是从光是电荷振动产生的电磁辐射出发，发现电磁辐射里振动的电场会驱动介质里的电子，电子受迫振动，于是自己也辐射电磁波，和原来的电磁波一干涉，就导致了各种效应，比如不透明的东西本质上就是两个波在透射方向上相互抵消了。就用这一套模型就足以完整推出菲涅尔公式。

Feynman instead starts from light as electromagnetic radiation produced by oscillating charges. The oscillating electric field drives the electrons in the medium into forced oscillation, so they radiate electromagnetic waves of their own. Their waves interfere with the original wave, producing the various effects. For instance, opacity is essentially the cancellation of the two waves in the transmission direction. This model alone is enough to derive the Fresnel equations in full.

总之是强烈推荐，认真精读！唯一的缺点是如果只看它会缺乏习题等基本功的训练。

I strongly recommend it: read it closely and carefully! The only drawback is that reading it alone leaves you short of practice in exercises and other basic skills.

作为四大力学里最基本的一个，我这学期花了很大力气参考了很多书试图学好它。经典力学主要可以分成理论和应用两部分。理论其实并不复杂，主要就是Lagrange和Hamilton两套体系，再高级一点可以用微分几何的语言叙述。应用部分比较复杂，主要是有心力与散射、小振动、刚体、摄动法等，给理论提供了充足的例子。

As this is the most fundamental of the four core theoretical physics subjects, I put a great deal of effort into learning it this semester and consulted many books. Classical mechanics can roughly be divided into theory and applications. The theory is not very complicated: mainly the Lagrangian and Hamiltonian frameworks, with differential geometry providing a more advanced language. The applications are more involved: central forces and scattering, small oscillations, rigid bodies, perturbation methods, and so on. They supply ample examples for the theory.

• 李岩松 分析力学讲义

• Li Yansong, Lecture Notes on Analytical Mechanics

这是我们课堂用的讲义，完整仔细推过，容量极大，十分深入，一般经典力学不讲的摄动法、连续系统和混沌都各有专门一章处理，但是要压缩在3学分的课一学期上完，实在是强人所难，只能飙车。内容和难度大致相当于MIT Classical Mechanics I & II & III的总和（我为啥会知道呢，因为有一次讲义实在看不懂，结果没想到在MIT 8.09 Classical Mechanics III的讲义里翻到了相似度极高的片段）。推导有些关键步骤会省略，然后上课的时候一语点醒，但你要是已经跟不上了就会直接错过......缺点还是无法开放获取，但据说和Goldstein几 乎 差 不 多。

These were our course notes, and I worked carefully through all the derivations. They cover a huge amount of material, in considerable depth. Perturbation methods, continuous systems, and chaos—topics often omitted from classical mechanics courses—each get a chapter. But squeezing all this into a one-semester, three-credit course is asking too much; you just have to floor it. The scope and difficulty roughly match MIT Classical Mechanics I, II, and III put together. (How do I know? Once I was completely lost in our notes, only to turn up an uncannily similar passage in the MIT 8.09 Classical Mechanics III notes.) Some key steps are omitted from the written derivations and clarified with a remark in class, but if you are already lost, you miss them altogether… The drawback is, again, that the notes are not openly available, though I have heard that they are pretty. much. the. same. as Goldstein.

• Landau 力学

• Landau, Mechanics

写的非常好，强烈推荐，认真精读。书本身短小精悍，所以阅读起来压力不大，我随着课时完整精读了一遍。有很多独到的评论和叙述，而且Landau的习题都是有详细解答的，非常好。另外有一个常见的误解，觉得Landau会跳步，容易看不懂，其实Landau经常会先抛出结论，然后在紧接着的下一段阐述或者证明它，个人觉得步骤其实挺详尽的，只是有的时候你先看到他抛出的结论，被吓到了，没看后面的证明，就以为很难懂。这跟排版也有一定的关系，我发现读的时候一定要注意什么时候换了一段，段首缩进了，说明后面讲的和前面的已经换了一个主题了，不注意的话就容易云里雾里的。

Really well written. Highly recommended—read it properly, and read it closely. The book is concise, so it is not too intimidating, and I read it closely alongside the course. It has many distinctive comments and explanations, and Landau's exercises come with detailed solutions, which is excellent. There is also a common misconception that Landau skips steps and is hard to follow. In fact, he often states a conclusion first, then explains or proves it in the very next paragraph. I think the steps are quite detailed; sometimes you are simply frightened by the initial conclusion and assume it is difficult before reading the proof that follows. The layout has something to do with it too: pay attention to paragraph breaks and indentation, which signal that the subject has shifted. If you miss those transitions, it is easy to lose the thread.

• 刘川 理论力学

• Liu Chuan, Theoretical Mechanics

这本书我是从图书馆借的，当时想的是多参考几本，而这本是互联网上名声最大的一本，最后在复习的时候完整地略读过一遍。个人认为很有Landau的风格（有不少地方很 相 似），所以读过Landau之后就会觉得比较无聊（可能是读过Landau之后必然的结果......）。和主流教材的区别在于一上来是从狭义相对论构建Lagrangian的，并且在有心力部分严肃地处理了Lagrange点等受限三体问题，以及有一个简（wu）易（yong）的群论介绍，其他的都差不多。但个人感觉并没有很大的意义，所以读过Landau的就不推荐再读了，而且书中有不少跳步的地方，如果去翻以简洁著称的Landau，会发现一模一样的地方Landau反而有推导。个人认为可能是讲义在汇编成书时有不少课堂内容没有编入，因此广泛的好评其实是针对刘川老师的课堂再配上讲义的，没有了课就大打折扣。

I borrowed this from the library because I wanted a few more references, and it was the one with the biggest reputation online. I ended up skimming the whole thing while reviewing the material. To me it feels very Landau-like (some parts are very, very similar), so after Landau it seems a little dull (perhaps an inevitable side effect of having read Landau…). What sets it apart from standard textbooks is that it starts by constructing the Lagrangian from special relativity, gives restricted three-body problems such as Lagrange points a serious treatment in the central-force section, and includes a simple (read: useless) introduction to group theory. Otherwise, much the same. Personally, I did not find these differences all that meaningful, so if you have read Landau, I would not recommend reading this as well. There are quite a few skipped steps, too: look up the exact same place in Landau, supposedly the master of brevity, and he actually gives the derivation. My guess is that quite a bit of classroom material never made it into the book when the lecture notes were compiled. So perhaps all that praise is really for Liu Chuan's classes together with the notes; take away the classes, and you lose a lot.

• I. W. Stewart, Advanced Classical Mechanics (MIT 8.09 & 8.309 Classical Mechanics III Lecture Notes)

• I. W. Stewart, Advanced Classical Mechanics (MIT 8.09 & 8.309 Classical Mechanics III Lecture Notes)

这个Lecture Notes是我在看LYS讲义的摄动法部分云里雾里的时候参考的，因为是III的内容，所以主要讲的是Hamilton力学，加上摄动法、流体、混沌和非线性的部分。个人认为讲的是很清楚的，推导也比较详尽，可以用作高级Topic的参考材料。对应的I和II的Notes我没看过，不过估计也不错。

I consulted these notes when I was lost in the perturbation-methods section of LYS's notes. As the third course in the sequence, they mainly cover Hamiltonian mechanics, together with perturbation methods, fluids, chaos, and nonlinear topics. I found the explanations clear and the derivations fairly detailed. They are useful references for advanced topics. I have not read the corresponding notes for I and II, but I imagine they are good too.

• Arnold, 经典力学的数学方法

• Arnold, Mathematical Methods of Classical Mechanics

这本书高中就买了（好高骛远的名词党石锤辣），一直没敢读，主要是风评说它超难。这个寒假学完经典力学之后开始读，发现也就这样，把正文部分完整略读了一遍。因此学完经典力学之后，如果对抽象数学有一定兴趣的，推荐一定要读一下，写得很好。但只需要略读，追求建立直觉上的理解即可，不必深究细节和证明。

I bought this back in high school (proof that I was already chasing fancy terminology way over my head), but never dared open it because everyone said it was ridiculously hard. This winter, after finishing classical mechanics, I started reading and thought: oh, is that all? I skimmed the entire main text. So once you have learned classical mechanics, if you have any interest in abstract maths, do read this. It is very good. But a skim is enough: aim for an intuitive understanding, without getting stuck on the details and proofs.

关于先修要求，其实前言里说得听明白的，只要求有微积分、线代和ODE的基础，不需要微分几何的基础。事实上也的确如此，并且我作为没学过ODE的，发现只要把书中所有出现的“李雅普诺夫稳定性”都只从直觉上理解就行了。当然我在读这本书之前已经接触了不少拓扑和微分几何（那套视频）的知识，所以有一定maths maturity是比较重要的，因为只有这样才能看出很多定义为何自然，为何只能这样定义，很多定理为什么直觉上就应该是对的。

As for prerequisites, the preface is quite clear: only calculus, linear algebra, and ordinary differential equations are required, not differential geometry. That really is the case. Even though I had not studied ODEs, I found that I could get by with an intuitive understanding whenever “Lyapunov stability” appeared. Of course, I had already encountered quite a bit of topology and differential geometry through the video course mentioned above. Having some mathematical maturity does matter: it helps you see why definitions are natural, why they have to take that form, and why many theorems should intuitively be true.

数学上，这本书本身也是给物理系同学极好的微分形式和几何的教材，我是在这本书上搞明白变分法不是随便乱 \(\delta\) 的，明白Legendre变换，微分形式，Stokes定理的内涵（边界算子 \(\partial\) 是外微分算子 \(\text{d}\) 的伴随），de Rham上同调的含义（与Poincare引理和洞的关系）以及一点点辛几何等等。

Mathematically, the book is itself an excellent introduction to differential forms and geometry for physics students. It taught me that variational calculus is not just about tossing \(\delta\)'s around. It clarified Legendre transforms, differential forms, the meaning of Stokes' theorem (the boundary operator \(\partial\) is the adjoint of the exterior derivative \(\text{d}\)), the meaning of de Rham cohomology and its connection to the Poincaré lemma and holes, and a little symplectic geometry, among other things.

而在物理上，这本书通过高观点的几何工具带来了非常独到的物理理解。印象深刻的包括诺特定理的叙述和证明（非常优雅，而课上是暴算作用量的变化），Liouville相体积不变定理的N种证明（最优雅的版本就是保辛结构），各种最小作用量原理的区别和联系（相空间在不同子空间上的投影），用辛变换谱的特性分析参数共振，以及可积系统的Arnold-Liouville定理与作用-角变量的内涵（同胚于n维环面 \(T^n=\{(\varphi_1,\cdots,\varphi_n)\ \text{mod}\ 2\pi\}\) ）等等。

Physically, its geometric tools provide unusually insightful perspectives. Memorable examples include the statement and proof of Noether's theorem—very elegant, whereas in class we brute-forced the variation of the action; the many proofs of Liouville's phase-volume theorem, the most elegant being preservation of the symplectic structure; the differences and connections among the various least-action principles, understood as projections of phase space onto different subspaces; the use of spectral properties of symplectic transformations to study parametric resonance; and the Arnold–Liouville theorem for integrable systems and the meaning of action-angle variables, involving a space homeomorphic to the n-torus \(T^n=\{(\varphi_1,\cdots,\varphi_n)\ \text{mod}\ 2\pi\}\).

总而言之，对于爱好抽象数学的物理系朋友们，这本书是非常值得推荐的，这种风格的仅此一家。美中不足的地方在于书中的习题几乎都没有答案，所以适合跳跳跳地略读，以及部分翻译有点奇怪（比如推论会翻译成“系”，正则会翻译成“典则”），同时有几处小Typo，不过无伤大雅。

For physics students who enjoy abstract mathematics, I highly recommend this book. Its style is one of a kind. The drawbacks are that almost none of the exercises have answers, so skim it—skip, skip, skip, and some choices in the Chinese translation are odd—for example, “corollary” is rendered as 系 and “canonical” as 典则. There are also a few minor typos, but nothing serious.

由于下学期选了量子力学，又是一门极其重要的课，想尽量好好学明白，于是寒假先看了一些书预习一下。

I had signed up for quantum mechanics the following semester. It is such an important course that I wanted to understand it as well as I could, so I spent part of winter break reading ahead.

• Leonard Susskind, Quantum Mechanics: The Theoretical Minimum

• Leonard Susskind, Quantum Mechanics: The Theoretical Minimum

这本书也是短小精悍，推导简单，很适合当入门闲书读，但是观点很有意思，有很多独到的见解，因此非常推荐，我完整地读过一遍。这本书的特点主要有两个，其一是完全立足于自旋这个二能级系统，将量子力学的原理和逻辑讲得非常透彻，让量子力学与经典直觉的尖锐矛盾从一开始就突出出来，只有在最后几章才回到一般的一维系统，最后以谐振子的代数解法告终；其二是花了大量篇幅讨论纠缠，将“对整体系统完全了解，不能得到对子系统的完全了解”这一反直觉事实描述得很透彻，同时借助与仪器的纠缠对测量问题做了一定阐述，但点到为止，没有给读者强加某一诠释，个人觉得处理得很好。美中不足的是全书的层级很初等，内容较少，只适合入门。

This is another short but substantial book, with simple derivations. A great casual read to get started with, but with interesting ideas and plenty of insights of its own. I really recommend it. I read it all. It has two main features. First, it builds almost entirely on spin as a two-level system, explaining the principles and logic of quantum mechanics thoroughly and exposing the sharp conflict with classical intuition from the very beginning. It only returns to general one-dimensional systems in the final chapters, ending with the algebraic solution of the harmonic oscillator. Second, it devotes a great deal of space to entanglement, making the counterintuitive fact that complete knowledge of a whole system does not imply complete knowledge of its subsystems very clear. It also discusses the measurement problem through entanglement with an apparatus, but stops short of imposing a particular interpretation on the reader. I think this is handled very well. Its drawback is that the level is elementary and the scope limited: it is only an introduction.

• Allan Adams, MIT 8.04 Quantum Physics I, 2013 Spring

• Allan Adams, MIT 8.04 Quantum Physics I, Spring 2013

这门课b站上也有搬运的，但是需要注意p19p20有部分音画不同步，可以去原网站上看。

The lectures have also been reposted on Bilibili, but parts 19 and 20 have some audio/video synchronization problems. You can watch those on the original site.

这门课我完整地看了一遍，并且把Problem Set（有答案）全做了一遍，个人感觉很好，非常推荐，一方面是因为他的资料很完备（有视频、各种演示用的Mathematica文档、含解答的习题、考试等），另一方面是教学和习题质量很高。尤其是前几集用虚构的Hardness和Color的概念将量子力学的矛盾阐释得很清楚又很有趣，让人看了就想跟下去。课程的内容大致相当于Griffiths理论部分的内容，同时加了一点能带理论和量子计算的简介，依然是比较初等的。

I watched the entire course and did every problem set, all of which have solutions. I thought it was excellent and highly recommend it. One reason is the sheer range of materials available: videos, Mathematica files for demonstrations, exercises with solutions, exams, and so on. Another is the high quality of both the teaching and the problems. In particular, the first few lectures use fictional properties called Hardness and Color to explain the contradictions of quantum mechanics clearly and entertainingly, making you want to keep watching. The content roughly matches the theoretical part of Griffiths, with a little band theory and an introduction to quantum computing added. It is still fairly elementary.

预习量子力学的过程中同时还参考了但没读完的书包括：Landau 量子力学（前4章），Feynman&Hibbs 量子力学与路径积分（前两章）。还有一些以后继续学的时候打算读（但最后可能读不了多少）的材料包括：Dirac The Principles of Quantum Mechanics, Shankar Principles of Quantum Mechanics, A. Peres Quantum Theory: Concepts and Methods, Sakurai Modern Quantum Mechanics, @陈童老师的量子力学新讲, W. H. Zurek Decoherence, Einselection, and the Quantum Origins of the Classical, 吴飚老师的Everett’s Theory of the Universal Wave Function 等等。

Other books I consulted while preparing, but did not finish, were Landau's Quantum Mechanics (the first four chapters) and Feynman and Hibbs's Quantum Mechanics and Path Integrals (the first two). Materials I plan to read as I continue—though I may not get through much of them—include Dirac's The Principles of Quantum Mechanics, Shankar's Principles of Quantum Mechanics, A. Peres's Quantum Theory: Concepts and Methods, Sakurai's Modern Quantum Mechanics, Chen Tong's New Lectures on Quantum Mechanics, W. H. Zurek's Decoherence, Einselection, and the Quantum Origins of the Classical, and Wu Biao's Everett’s Theory of the Universal Wave Function.

最后附上个人读过的普物标准教材里比较推荐的。

Finally, here are some standard introductory physics textbooks that I particularly recommend among those I have read.

力学

Mechanics

不评论，我只读过舒幼生老师的力学，但据说题目对一般大学生太难了？

No verdict here: I have only read Shu Yousheng’s Mechanics, and apparently its problems are too difficult for the average undergraduate?

电磁学

Electromagnetism

梁灿彬老师的电磁学及拓展篇。前者很标准，我也没读过别的，不评价；拓展篇是对一些专题问题的讨论，用对话体写成，很体现梁老的可爱直率，我记得里面还批评了很多教材“扭扭捏捏”讲不清楚，可爱。总之写的是真的好，有很多独到的见解，强烈推荐。

Liang Canbin's Electromagnetism and its supplementary volume. The first is very standard, and I have not read the alternatives, so no comment. The supplement discusses particular topics in dialogue form, and Liang's lovable bluntness really comes through. I remember him taking a swipe at textbooks that “beat around the bush” instead of explaining things properly. So endearing. Anyway, it really is well written, with lots of insights of its own. Highly recommended.

更进一步的是Griffiths的电动力学导论，也写得很清楚，适合普物层面的提高（我倒是不打算再用它学电动了，毕竟刷过一遍了，目前打算用Landau场论学电动）。

A step further is Griffiths's Introduction to Electrodynamics, also very clearly written and a good next step beyond introductory physics. I do not plan to use it again for electrodynamics, though, since I have already worked through it once; at present I plan to use Landau's The Classical Theory of Fields.

热学

Thermal Physics

Blundell（一家）写的热物理概念，这本书真的是深入浅出，起点很低，从概率论入手，终点很高，一直讲到统计物理，而且还有大量对专题的严肃讨论（激波、涨落耗散、非平衡、星体、大气），很有意思。

Concepts in Thermal Physics by the Blundells really makes deep ideas accessible. It starts gently with probability and goes all the way to statistical physics, with many substantial discussions of special topics: shock waves, fluctuation-dissipation, nonequilibrium phenomena, stars, and the atmosphere. Very interesting.

光学

Optics

Ajoy的光学，同样也是深入浅出，推导和阐述非常详尽，简直是傻瓜式了，怕你不会波动，专门给你写了5章从简谐振动开始，一直到Fourier分析。同时还对一些有意思的方法单开专题讲，如矩阵几何光学、全息术、Jones矩阵、光的粒子性、激光和光纤等等。个人觉得比什么现光基不知道高到哪里去了，当然还有另一本著名的教材，Hecht的，我没看过就不评价了。

Ajoy's Optics also makes deep ideas accessible. The derivations and explanations are so detailed that it is practically foolproof. Worried that you might not know about waves? Here, have five whole chapters, from simple harmonic motion all the way to Fourier analysis. It also gives separate treatments of interesting methods and topics: matrix geometrical optics, holography, Jones matrices, the particle nature of light, lasers, optical fibers, and so on. Personally, I think it is leagues above that Fundamentals of Modern Optics textbook. There is also Hecht's famous book, of course, but I have not read it, so no comment.

大一秋冬就到此为止，过几天就要返校了，希望春季学期能好好学习。

That is it for the fall and winter of my freshman year of college. I will be heading back to campus in a few days; hopefully I can get some proper studying done in the spring.