……你敢肯定答案是对的——在研究生院，习题集可没有现成答案供你对，必须完全吃透才能把题目做对。对我来说，罗森里希特的《Introduction to Analysis》[1] 是一本分水岭式的书。基于严格证明，非常“数学”，体量虽小巧紧凑（可以这么说）但涵盖极其宏大。对于一个非常重要的领域来说是一部极佳的入门书，它能让你的大脑彻底运转起来。再者……
…you're sure the answer is right -- in grad school problem sets didn't have answers you could check, and full understanding was necessary to get the problem sets correct. For me, a watershed book was Introduction to Analysis by Rosenlicht [1]. Proof-based, very "mathy", small and compact (so to speak) but with a massive scope. A great introduction to a really important topic, and it'll put your brain through its paces. Again,…
……Naive Set Theory（保罗·哈尔莫斯）线性代数 1. Finite-Dimensional Vector Space（保罗·哈尔莫斯）2. Linear Algebra Done Right（谢尔顿·阿克斯勒）实分析 1. Real Mathematical Analysis（查尔斯·普格）2. Introduction to Analysis（麦克斯韦·罗森里希特）代数 1. A first course in abstract algebra（约翰·弗拉利）比起像 Rudin 或 Herstein 那样的一些经典教材，这些书更适合拿来自学。这些应该……
…Naive Set Theory (Paul Halmos) Linear Algebra 1. Finite-Dimensional Vector Space (Paul Halmos) 2. Linear Algebra Done Right (Steven Axler) Real Analysis 1. Real Mathematical Analysis (Charles Pugh) 2. Introduction to Analysis (Maxwell Rosenlicht) Algebra 1. A first course in abstract algebra (John Fraleigh) These books are better for self-directed reading compared to some of the classics like Rudin or Herstein. These should…
……你敢肯定答案是对的——在研究生院，习题集可没有现成答案供你对，必须完全吃透才能把题目做对。对我来说，罗森里希特的《Introduction to Analysis》[1] 是一本分水岭式的书。基于严格证明，非常“数学”，体量虽小巧紧凑（可以这么说）但涵盖极其宏大。对于一个非常重要的领域来说是一部极佳的入门书，它能让你的大脑彻底运转起来。再者……
…you're sure the answer is right -- in grad school problem sets didn't have answers you could check, and full understanding was necessary to get the problem sets correct. For me, a watershed book was Introduction to Analysis by Rosenlicht [1]. Proof-based, very "mathy", small and compact (so to speak) but with a massive scope. A great introduction to a really important topic, and it'll put your brain through its paces. Again,…
……Naive Set Theory（保罗·哈尔莫斯）线性代数 1. Finite-Dimensional Vector Space（保罗·哈尔莫斯）2. Linear Algebra Done Right（谢尔顿·阿克斯勒）实分析 1. Real Mathematical Analysis（查尔斯·普格）2. Introduction to Analysis（麦克斯韦·罗森里希特）代数 1. A first course in abstract algebra（约翰·弗拉利）比起像 Rudin 或 Herstein 那样的一些经典教材，这些书更适合拿来自学。这些应该……
…Naive Set Theory (Paul Halmos) Linear Algebra 1. Finite-Dimensional Vector Space (Paul Halmos) 2. Linear Algebra Done Right (Steven Axler) Real Analysis 1. Real Mathematical Analysis (Charles Pugh) 2. Introduction to Analysis (Maxwell Rosenlicht) Algebra 1. A first course in abstract algebra (John Fraleigh) These books are better for self-directed reading compared to some of the classics like Rudin or Herstein. These should…