Here are some great books which are meant to be read (and have not been mentioned elsewhere in this thread, i.e. Axler and Pugh). Algebra: Chapter 0 by Paolo Aluffi Measurement by Paul Lockhart The Nature of Computation by Moore & Mertens Ideals, Varieties, and Algorithms by Cox, Little, & O'Shea
…real loss", but this only says something about the particular textbook and not the subject itself. I assure you, the actual loss, whether you realize it or not, will be very real. Books like Aluffi's Algebra: Chaper 0 have a very good reason behind them. Category Theory is the chapter zero of the modern understanding of mathematics (and not only).
I'd add to this list Algebra, Chapter 0 by Aluffi. It's very clearly-written, even for a total beginner like me, but not dumbed down at all, and has a boatload of exercises which IMO is very helpful for learning the material. While…
…category theory. But the entire presentation is very elegant. Thinking of Aluffi Chapter 0 where he uses universal property extensively to simplify a lot of proofs. My personal favorite presentation of Algebra, but everyone has an opinion here.
A lot of recommendations depend on what you're trying to learn. But I've enjoyed the following texts to a larger extent than others: - Algebra: Chapter 0 (Aluffi) - Real Mathematical Analysis (Pugh) - Mathematics and its History (Stillwell) - An Introduction to Manifolds (Tu) - Gauge Fields, Knots and Gravity (Baez) - A First Look at Rigorous…
这里推荐几本真正值得去读的好书（而且本帖其他地方还没提到过，比如没提 Axler 和 Pugh）。Paolo Aluffi 的《代数：第0章》；Paul Lockhart 的《度量》；Moore 和 Mertens 的《计算的本质》；Cox、Little 和 O'Shea 的《理想、簇与算法》
Here are some great books which are meant to be read (and have not been mentioned elsewhere in this thread, i.e. Axler and Pugh). Algebra: Chapter 0 by Paolo Aluffi Measurement by Paul Lockhart The Nature of Computation by Moore & Mertens Ideals, Varieties, and Algorithms by Cox, Little, & O'Shea
给找书单的人推荐一下，我个人觉得 Aluffi 的《代数：第0章》（Algebra: Chapter 0）非常棒。网上能找到。
For those looking for book recommendations, I personally found Aluffi's "Algebra: Chapter 0" quite wonderful. It's available online.
……真正的损失”，但这只能说明那本特定教材有问题，不能说明这门学科本身不行。我向你保证，无论你是否意识到，那份损失都会是非常切实的。像 Aluffi 的《代数：第0章》这类书之所以存在是有很充分的理由的。范畴论就是现代理解数学（乃至不限于数学）的第零章。
…real loss", but this only says something about the particular textbook and not the subject itself. I assure you, the actual loss, whether you realize it or not, will be very real. Books like Aluffi's Algebra: Chaper 0 have a very good reason behind them. Category Theory is the chapter zero of the modern understanding of mathematics (and not only).
我想在这份书单里加上 Aluffi 写的《代数：第0章》。它写得非常清晰易懂，即使是对我这样的纯小白来说也是如此，但内容完全没有偷工减料，而且包含了海量的习题，在我看来这对掌握材料非常有帮助。虽然……
I'd add to this list Algebra, Chapter 0 by Aluffi. It's very clearly-written, even for a total beginner like me, but not dumbed down at all, and has a boatload of exercises which IMO is very helpful for learning the material. While…
……范畴论。但整个表述非常优雅。想到 Aluffi 的 Chapter 0，他大量使用泛性质来简化许多证明。我个人最喜欢的代数表述，但在这方面每个人都有自己看法。
…category theory. But the entire presentation is very elegant. Thinking of Aluffi Chapter 0 where he uses universal property extensively to simplify a lot of proofs. My personal favorite presentation of Algebra, but everyone has an opinion here.
很多推荐取决于你想学什么。不过相比其他书，我更喜欢下面这几本：- 《代数：第0章》（Aluffi） - 《实数学分析》（Pugh） - 《数学及其历史》（Stillwell） - 《流形导论》（Tu） - 《规范场、纽结与引力》（Baez） - 《严谨数学的初瞥》……
A lot of recommendations depend on what you're trying to learn. But I've enjoyed the following texts to a larger extent than others: - Algebra: Chapter 0 (Aluffi) - Real Mathematical Analysis (Pugh) - Mathematics and its History (Stillwell) - An Introduction to Manifolds (Tu) - Gauge Fields, Knots and Gravity (Baez) - A First Look at Rigorous…