Books

一些教科书的短评，基本都是上课配套的所以评价基本都是和课程绑定的

很多只是偶尔借鉴一下的没评价

Math

Proofs: A Long-Form Mathematics Textbook - Jay Cummings

The first proof-related textbook I have read. The remarks are so detailed, and the additional topics are so interesting. I learned so much from this book, it prepared me fully for mat157 and other proof courses. It is also worth go over again because of the interesting topics after each chapter.

Real Analysis: A Long-Form Mathematics Textbook - Jay Cummings

Very traditional US style first real analysis course textbook. I really like how cheap this book is. Content wise this book is very beginner friendly, but often too over-complicated and over-explaining to me… This book is definitely helpful for reference, when having some trouble understanding the materials in, for example, Spivak.

Calculus in One Dimension I & II - Tyler Holden

I feel like Tyler over-complicated some of the proofs throughout the book, his rigorous style is probably not beginner-friendly. But the practice questions are nice, and is very aligning with standard 137/9, 157/9, so is probably a good reference book for these courses.

An Excursion Through Elementary Mathematics - Antonio Caminha Muniz Neto

First Volume

Don’t trust the word “elementary” too much… The first volume literally covered most of my mat157/159 topics, even further for some topics. Most of the questions are from competitions and hints / solutions are provided for all questions which is so amazing… I enjoyed exploring the Putnam / IMO questions.

Linear Algebra (4th Edition) - Stephen H. Friedberg

This book is very similar to JT’s mat240 textbook probably except the beginning part (and the mat247 part). I really feel this book should be read after finishing the books like Gilbert Strang’s Introduction to Linear Algebra or 3blue1brown’s youtube videos. The order of the contents are kinda unintuitive without any prior linear algebra knowledge.

Topology (Second Edition) - James R. Munkres

I only finished the general topology section, and it is truly amazing (the algebraic topology section looks amazing too based on the foreshadows in the general topology section such as quotient topology). There are many definitions within the general topology section, however Munkres connected them through intuitive explanations and a very smooth order. My prof dcw also introduced CCC, filters and ultrafilters especially for Tychonoff’s theorem, because how general topology (point set topology) is very related to set theory, I can see why my prof brings this idea to the course, and it seems pretty useful as well for many ideas. In general, Munkres (2000) Topology with Solutions | dbFin helped me speed run the textbook questions, combining with the fact that Munkres is such a great book, I neither struggled too much nor spent too many time on Topology. Nevertheless, the availability of the solutions on dbFin and math stack exchange and the greatness of the book both make this the best book for introduction to topology.

Linear Algebra Done Right (3rd Edition) - Sheldon Axler

There are so many different ways to introduce the basic of linear algebra, it feels weird for me to learn in this way after reading Friedberg, and Strang’s MIT lectures, but definitely a great book emphasizing on functor, inner product, linear functional, and extending to complex F.

A Walk Through Combinatorics, An introduction to Enumeration, Graph Theory, and Selected Other Topics (Fifth Edition) - Miklos Bona

The provided solutions are awesome for study. The book is a relatively easy book to follow (same as Intro to Combinatorics), nothing too outstanding, quite standard.

数理逻辑十二讲 - 宋方敏 吴骏

第一本不是翻译英语的中文数学书，很多地方反而因为用词有点不明白。很喜欢中间关于ZFC的说明和后面model language与first order logic的关联，但总的来说还是一本全是定义没有直觉(intuition)的讲义，内容还是很有意思的，虽然很多时候过于枯燥或者平凡了。

A Brief History of Mathematics - Karl Fink

First, before reading the book, the reader needs to have a decent background of every elementary mathematics topics, including Calculus, solving equations, some complex analysis, conic, etc. Second, the reader should also has a decent knowledge of the outstanding mathematicians (their era, their areas of interest, …), including Newton, Gauss, Leibniz, Euler, Euclid, Pythagorean, Abel, Pascal, Lagrange, Cauchy, Weierstrass, Bernuollis, etc. Otherwise, the massive number of names presented in the book, especially since it is separated based on area, is very confusion to match the eras. Hence, I can’t view this book as a introductory book to people who do not know much mathematicians, more like a wordy journey full of random mathematicians’ names, that give a brief order of how the elementary mathematicians was evolved, for people who at least know the major topics of undergrad mathematics. Therefore, for both content wise, and pre-requisite wise, this book isn’t quite good…

Computer Science

Introduction to Algorithms - C.L.R.S.

I really like the coloring of the fourth edition. The book covers most of the topics taught in undergrad theoretical CS courses, without some variation, including data structure, algorithm design, computational complexity, etc. Even though the selected topics are not as detailed as books specified for the topics, the introductions are still amazing, and the concepts are well explained. The most amazing part of this book is that Github / Web has all of the solutions to the problems, for all editions.

Grokking Algorithms: An illustrated guide for programmers and other curious people - Aditya Y. Bhargava

The book is very beginner friendly, the topics are very intuitive and brief, following a logical order. The book is very short, so worth reading during 108 & 148 I guess.

Programming Pearls & More Programming Pearls: Confessions of a Coder - Jon Bentley

The ideas through the book are so fundamental, essential, and applied. We might not learn something very advanced or very fancy, but after understanding the book, at least when dealing with some problems, we know how to step back and think critically how to resolve the problems (from a broad perspective at least). But yeah, the 2 books are quite small so they don’t cover everything we need, but the essential ones. Worth reading for people with decent programming experiences, and probably for people who wanna learn how to create efficient algorithms (e.g. for competitive programming).

Clean Architecture - Robert Martin

This is the book my professor uses for csc207, to me it still seems like such complete architecture is way more complicated than needed for up to middle side project, the idea of separating different components, responsibilities, functions is awesome, but it’s just so boring and slow to construct such architecture especially as an undergrad student which his project worth almost nothing… But knowing these kinds of architectures are definitely super helpful for the professional industrial programmers. I actually find the SOLID principles, and the design patterns to be more useful and applicable as they really overlap with the clean architecture OOP’s 3 main concepts are also so related to them. The entire 300 pages book took me less than one day to read, the concepts are actually very light, the order is awesome, but this book still needs to be familiar with many professional vocabularies at the start, I had to google many words throughout the day.

Statistics

Others

Your Memory: How It Works and How to Improve It - Kenneth L. Higbee

Very nice book. I don’t know why I already know all the techniques provided throughout the book, but this book formalizes the informal methods I use to more formal and recognizable ways. I think the crucial part of this book, which is building an imaginary memory system in mind, requires a lot of practice, but beside this, the other parts help so much for daily memorization, such as PIN memorization, phone number / ID memorization, etc. The main disadvantage of these techniques is that for content involving logic, using weird tricks isn’t a good way, instead we should try first understand line by line what the words are stating, then with a more general image in mind, we can then derive the details.

A Brief History of Time - Stephen Hawking

Amazing book summarizing all the current physics topics. It’s a lot easier to read if the reader has some background of the terminologies / ideas, e.g. manifold, and the idea of dimension, etc. I have so many insights, questions, and ideas while reading this book, as the book mentioned, many of the modern theories are not fully proven. My insights might work better as well, but it’s very hard to convince everyone else, to collaborate with all other theories, and to be proven.