……数学里的推理是讲逻辑的！（虽然论文向来如此），还有更小众的逻辑，比如律师有时会用到的“默认逻辑”（default logic）。顺便提一句，作者是布雷苏（Bressoud），我也力挺那本。还有托马斯·克尔纳（TW Körner）的《分析指南：初级进阶与进阶初级教程》（Companion to Analysis: A First Second and Second First Course），可以拿朗（Lang）或卓里奇（Zorich）的书做底子。要是一直拿着铅笔演算会阻碍你更广泛的泛读或者干脆扩充浏览面的话，我倒不会非逼着手头时刻备着笔。
…reasoning in mathematics is logical! though papers always are) and more exotic logics such as the „default logic” sometimes employed by lawyers. It's Bressoud BTW, I endorse that too. Along with TW Körner „Companion to Analysis: A First Second and Second First Course” with Lang or Zorich as base. I wouldn't be as insistent on pencil at all times if it were to prevent broader reading or just expanded skimming.
一个书单：https://www.topicsinmaths.co.uk/cgi-bin/sews.py?SuggestedRea... 如果只给一个建议，那就是凯文·休斯顿（Kevin Houston）的《像数学家一样思考》（How to Think Like a Mathematician）。第二个建议：汤姆·克尔纳（Tom Körner）的《分析指南》（A Companion to Analysis）。不过这很大程度上取决于你是想要“谈论数学的书”，还是真正的“数学书”。听起来你想要的是后者……改天我有空了会给这些选书加上批注……
A list: https://www.topicsinmaths.co.uk/cgi-bin/sews.py?SuggestedRea... For a single suggestion, "How to Think Like a Mathematician" by Kevin Houston. A second suggestion: "A Companion to Analysis" by Tom Körner. But it depends a lot on whether you want books about math, or books of math. It sounds like you want the latter ... at some point I'll get around to putting annotations on the choices…
Steven Strogatz 的《The Joy of X》、Dave Richeson 的《Euler's Gem》、Tom Körner 的《A Companion to Analysis》、Joe Roberts 的《Elementary Number Theory: A Problem Oriented Approach》
"The Joy of X" by Steven Strogatz "Euler's Gem" by Dave Richeson "A Companion to Analysis" by Tom Körner "Elementary Number Theory: A Problem Oriented Approach" by Joe Roberts
……数学里的推理是讲逻辑的！（虽然论文向来如此），还有更小众的逻辑，比如律师有时会用到的“默认逻辑”（default logic）。顺便提一句，作者是布雷苏（Bressoud），我也力挺那本。还有托马斯·克尔纳（TW Körner）的《分析指南：初级进阶与进阶初级教程》（Companion to Analysis: A First Second and Second First Course），可以拿朗（Lang）或卓里奇（Zorich）的书做底子。要是一直拿着铅笔演算会阻碍你更广泛的泛读或者干脆扩充浏览面的话，我倒不会非逼着手头时刻备着笔。
…reasoning in mathematics is logical! though papers always are) and more exotic logics such as the „default logic” sometimes employed by lawyers. It's Bressoud BTW, I endorse that too. Along with TW Körner „Companion to Analysis: A First Second and Second First Course” with Lang or Zorich as base. I wouldn't be as insistent on pencil at all times if it were to prevent broader reading or just expanded skimming.
一个书单：https://www.topicsinmaths.co.uk/cgi-bin/sews.py?SuggestedRea... 如果只给一个建议，那就是凯文·休斯顿（Kevin Houston）的《像数学家一样思考》（How to Think Like a Mathematician）。第二个建议：汤姆·克尔纳（Tom Körner）的《分析指南》（A Companion to Analysis）。不过这很大程度上取决于你是想要“谈论数学的书”，还是真正的“数学书”。听起来你想要的是后者……改天我有空了会给这些选书加上批注……
A list: https://www.topicsinmaths.co.uk/cgi-bin/sews.py?SuggestedRea... For a single suggestion, "How to Think Like a Mathematician" by Kevin Houston. A second suggestion: "A Companion to Analysis" by Tom Körner. But it depends a lot on whether you want books about math, or books of math. It sounds like you want the latter ... at some point I'll get around to putting annotations on the choices…
Steven Strogatz 的《The Joy of X》、Dave Richeson 的《Euler's Gem》、Tom Körner 的《A Companion to Analysis》、Joe Roberts 的《Elementary Number Theory: A Problem Oriented Approach》
"The Joy of X" by Steven Strogatz "Euler's Gem" by Dave Richeson "A Companion to Analysis" by Tom Körner "Elementary Number Theory: A Problem Oriented Approach" by Joe Roberts