基础数学
Basic Mathematics
Serge Lang · 初版 1971 年
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为什么值得读
- 从本原处讲清几何与代数原理，重塑严谨数学思维
- 为后续进入微积分等高等数学课程打下坚实基础
- 论述严谨透彻，适合成年人自学补齐数学基础断层
这是一本基础数学教材，具有多种用途，既可用于高中课程，也可用于大学阶段课程。读者将获得扎实的基础数学原理训练，这些原理是后续深入学习微积分、线性代数或其他专题的必备知识。本书对主题内容的讲解清晰透彻，作者循序渐进地展开概念，让读者能够理解不同主题之间是如何相互关联并发展延伸的。
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我其实没读过这一本，但在另一本书（Serge Lang 的《Basic Mathematics》）上有过类似的经历，它彻底改变了我的人生轨迹。如果你对这些东西哪怕有一丁点兴趣，请一定要尝试一下！数学真的太美妙了！按部就班地（通过一本书或一系列书）学数学才是真正的数学……
Ive never read this book in particular, but had a similar experience with another book (Serge Lang, Basic Mathematics) that changed my life trajectory. If you find this stuff remotely interesting please give it a go! Math is really wonderful! Learning math in some prescribed way (book or sequence of books) is the mathematics…
……照着步骤算出正确答案、拿个 A、考完忘光，然后等下一门课。多年之后，我重新从头开始把一切都弄得明明白白，就从 Serge Lang 的《Basic Mathematics》开始。我以前甚至都不知道勾股定理是怎么推导出来的，而当我第二次重新学它时，简直太他妈漂亮了。我的建议是彻底回到起点，找一本由……写成的书
…the steps to get the right answer, get my A, forget it all, and wait for whatever was coming next. Years later I go straight back to the beginning and figure everything out, starting with Serge Lang's Basic Mathematics. I didn't even know where the Pythagorean Theorem came from, and when I learned it the second time around, it was damn beautiful. my advice is to go back all the way to the beginning and get a book written…
……如果你数学底子薄，想在深入学习微积分及后续课程之前先补齐基础，我有两个建议。1) Lial 的《Basic College Math》[1] 够用，能让你快速补齐基础。2) Serge Lang 的《Basic Mathematics》非常棒，能涵盖你进入一门扎实的理论级大学数学课所需的一切基础。[1] http://www.amazon.com/s?ie=UTF8&field-keywords=lials%20basic... 各版本基本没差……挑一本……
…background in math and want to get up to speed before going into calculus and beyond, I have 2 suggestions. 1) Lial's Basic College Math[1] is adequate and will get you up to speed. 2) Serge Lang's "Basic Mathematics" is great and will cover all you need to go into a rigorous theory based college math class. [1] http://www.amazon.com/s?ie=UTF8&field-keywords=lials%20basic... The editions basically the same... pick…
……当你年轻的时候。这……并不是主流观点？但我现在作为一个年纪稍大（30多岁快40）、有本职工作的人，正在尝试自学数学。我找到的最好工具就是 Serge Lang 的书（《Basic Mathematics》）和可汗学院（Khan Academy）。如果有更好的工具和资源推荐，我会超级感兴趣；钱不是问题，至少在学生水平的花销上不算事，但时间很紧张。可汗学院对我来说……
…you were younger. This is... not the majority view? But I am attempting to teach myself math right now, as an older (late 30s) person with a job. The best tools I've found are Serge Lang's books (Basic Mathematics) and Khan Academy. I would be super interested in recommendations for better tools and resources; Money isn't really an object, at least at student scale, but time is limited. Khan academy, for me,…
……对做数学非常不利。没有更多详细信息，很难知道你目前是什么水平。大多数数学集训都会涵盖代数和微积分。高中水平里很棒的组合是：* Lang 写的《Basic Mathematics》* Thompson 写的《Calculus Made Easy》如果这太简单了，可以试试类似 Math 55 的路线：* Axler 写的《Linear Algebra Done Right》* Rudin 写的《Principles of Mathematical Analysis》你可以替换……
…very detrimental towards doing mathematics. Without further details, it's hard to know what your current level is. Most math bootcamps cover algebra and calculus. A great high school level one is: * Basic Mathematics by Lang * Calculus Made Easy by Thompson If that is too simplistic, try a Math 55 like approach: * Linear Algebra Done Right by Axler * Principles of Mathematical Analysis by Rudin You can replace…
我个人觉得 Serge Lang 的《Basic Mathematics》在解释大学前数学里某个特定公式的“原理”时超级好用，因为我目前水平能接触到的绝大多数书似乎都只是在说“把它背下来”。他解释了为什么 x^0 会是……
I personally find Serge Lang's "Basic Mathematics" to be super useful in explaining the "why" of a particular formula in pre-college level math, as most books at my current level just seem to say "memorize this" He has an explanation of why x^0 is…