……关于最基础概念的温习课程。可以配合以下书籍来建立直觉：1) 《Who is Fourier》- https://www.amazon.com/Who-Fourier-Mathematical-Adventure-2n... 2) 《Functions and Graphs》- https://www.amazon.com/Functions-Graphs-Dover-Books-Mathemat... 在这之后，你才会进入本科阶段的学习，并不得不去打“现代数学”这只更抽象、更偏概念的大怪兽。……
…refresher course in the absolute basics. The above can be supplemented with the following books to develop intuition; 1) Who is Fourier - https://www.amazon.com/Who-Fourier-Mathematical-Adventure-2n... 2) Functions and Graphs - https://www.amazon.com/Functions-Graphs-Dover-Books-Mathemat... After this is when you enter undergraduate studies and you have to fight the dragon of "Modern Maths" which is more abstract and conceptual.…
……你提到的那些书对青少年来说似乎有点太难了，所以得当心别要求过高打击了他们的积极性；相反，我建议在死磕大部头之前先采用更简单的方法：* 盖尔范德等人的《Functions and Graphs》——一本培养直觉的短小精悍之作。* 《Who is Fourier? A Mathematical Adventure》——一本极好的“漫画风”读物，带你从第一性原理构建重要概念。* 《Concepts of……
…books that you mention seem a bit too hard for a teen, so you have to be careful not to demotivate them by expecting too much of them; instead i suggest a simpler approach before tackling the big ones; * Functions and Graphs by Gelfand et al. - A small but great book to develop intuition. * Who is Fourier? A Mathematical Adventure - A great "manga type" book to build important concepts from first principles * Concepts of…
我超喜欢入门教科书。我最喜欢的几本：利奥·布罗迪的《Starting Forth》、布赖恩·哈维的《Computer Science, Logo-Style》系列、I.M. 盖尔范德的《Algebra》、《Functions and Graphs》、《Methods of Coordinates》、《Trigonometry》（有人知道他那本几何教材写完了没？我从来没见过。他的《Calculus》或《Combinatorics》我也没见过，虽然……
I love introductory textbooks. Some of my favorites: "Starting Forth" - Leo Brodie "Computer Science, Logo-Style" series - Brian Harvey "Algebra", "Functions and Graphs", "Methods of Coordinates", "Trigonometry" - I.M. Gelfand (does anyone know if he completed his Geometry textbook? I've never seen it. I've also never seen his "Calculus" or "Combinatorics" books, although…
只要方法对路，其实没那么难。这是我“包教包会”的微积分5步秘方 :-) a) 学习坐标系几何。b) 学习《Functions and Graphs》。c) 学习导数。d) 学习积分。e) 学习微分方程。刚开始只专注理解单变量，其他的全别管。你可以参考以下资源……
It is not that tough if you approach it in the right manner. Here is my "guaranteed understanding" 5-step recipe for Calculus :-) a) Learn co-ordinate systems Geometry. b) Learn Functions and Graphs. c) Learn Derivatives. d) Learn Integrals. e) Learn Differential Equations. Focus on understanding single-variable only and ignore everything else in the beginning. You will find the following resources…
……要从沙子里面淘金真是一桩苦差事。Dover 出版社有一些好书，首先是柯尔莫哥洛夫等人的《Mathematics: Its Contents, Methods and Meaning》。还有 I.M. 盖尔范德的系列：《Functions and Graphs》、《The Method of Coordinates》、《Algebra》、《Trigonometry》等。
…a chore to sift the wheat from the chaff. Dover publications has some good ones starting with Mathematics: Its Contents, Methods and Meaning by Kolmogorov et.al. There is also the I.M.Gelfand series; Functions and Graphs, The Method of Coordinates, Algebra, Trigonometry etc.
……心智成熟且希望从第一性原理学起的人。话虽如此，这是我给他们的推荐（几乎全都有网上的免费 pdf，买二手书也很便宜）：* 1) I.M. 盖尔范德等人的《Functions and Graphs》和 2) 《The Method of Coordinates》——这两本讲清了函数的基础知识以及如何可视化函数，这对理解至关重要。* 《Introductory Logic and Sets for Computer……
…maturity and wishing to learn from first principles. That said, here are my recommendations for them (pdfs of almost all are available online and they can also be purchased cheaply as used books); * 1) Functions and Graphs and 2) The Method of Coordinates by I.M.Gelfand et. al. - These give you the basics on functions and how to visualize them which is crucial for understanding. * Introductory Logic and Sets for Computer…
……关于最基础概念的温习课程。可以配合以下书籍来建立直觉：1) 《Who is Fourier》- https://www.amazon.com/Who-Fourier-Mathematical-Adventure-2n... 2) 《Functions and Graphs》- https://www.amazon.com/Functions-Graphs-Dover-Books-Mathemat... 在这之后，你才会进入本科阶段的学习，并不得不去打“现代数学”这只更抽象、更偏概念的大怪兽。……
…refresher course in the absolute basics. The above can be supplemented with the following books to develop intuition; 1) Who is Fourier - https://www.amazon.com/Who-Fourier-Mathematical-Adventure-2n... 2) Functions and Graphs - https://www.amazon.com/Functions-Graphs-Dover-Books-Mathemat... After this is when you enter undergraduate studies and you have to fight the dragon of "Modern Maths" which is more abstract and conceptual.…
……你提到的那些书对青少年来说似乎有点太难了，所以得当心别要求过高打击了他们的积极性；相反，我建议在死磕大部头之前先采用更简单的方法：* 盖尔范德等人的《Functions and Graphs》——一本培养直觉的短小精悍之作。* 《Who is Fourier? A Mathematical Adventure》——一本极好的“漫画风”读物，带你从第一性原理构建重要概念。* 《Concepts of……
…books that you mention seem a bit too hard for a teen, so you have to be careful not to demotivate them by expecting too much of them; instead i suggest a simpler approach before tackling the big ones; * Functions and Graphs by Gelfand et al. - A small but great book to develop intuition. * Who is Fourier? A Mathematical Adventure - A great "manga type" book to build important concepts from first principles * Concepts of…
我超喜欢入门教科书。我最喜欢的几本：利奥·布罗迪的《Starting Forth》、布赖恩·哈维的《Computer Science, Logo-Style》系列、I.M. 盖尔范德的《Algebra》、《Functions and Graphs》、《Methods of Coordinates》、《Trigonometry》（有人知道他那本几何教材写完了没？我从来没见过。他的《Calculus》或《Combinatorics》我也没见过，虽然……
I love introductory textbooks. Some of my favorites: "Starting Forth" - Leo Brodie "Computer Science, Logo-Style" series - Brian Harvey "Algebra", "Functions and Graphs", "Methods of Coordinates", "Trigonometry" - I.M. Gelfand (does anyone know if he completed his Geometry textbook? I've never seen it. I've also never seen his "Calculus" or "Combinatorics" books, although…
只要方法对路，其实没那么难。这是我“包教包会”的微积分5步秘方 :-) a) 学习坐标系几何。b) 学习《Functions and Graphs》。c) 学习导数。d) 学习积分。e) 学习微分方程。刚开始只专注理解单变量，其他的全别管。你可以参考以下资源……
It is not that tough if you approach it in the right manner. Here is my "guaranteed understanding" 5-step recipe for Calculus :-) a) Learn co-ordinate systems Geometry. b) Learn Functions and Graphs. c) Learn Derivatives. d) Learn Integrals. e) Learn Differential Equations. Focus on understanding single-variable only and ignore everything else in the beginning. You will find the following resources…
……要从沙子里面淘金真是一桩苦差事。Dover 出版社有一些好书，首先是柯尔莫哥洛夫等人的《Mathematics: Its Contents, Methods and Meaning》。还有 I.M. 盖尔范德的系列：《Functions and Graphs》、《The Method of Coordinates》、《Algebra》、《Trigonometry》等。
…a chore to sift the wheat from the chaff. Dover publications has some good ones starting with Mathematics: Its Contents, Methods and Meaning by Kolmogorov et.al. There is also the I.M.Gelfand series; Functions and Graphs, The Method of Coordinates, Algebra, Trigonometry etc.
……心智成熟且希望从第一性原理学起的人。话虽如此，这是我给他们的推荐（几乎全都有网上的免费 pdf，买二手书也很便宜）：* 1) I.M. 盖尔范德等人的《Functions and Graphs》和 2) 《The Method of Coordinates》——这两本讲清了函数的基础知识以及如何可视化函数，这对理解至关重要。* 《Introductory Logic and Sets for Computer……
…maturity and wishing to learn from first principles. That said, here are my recommendations for them (pdfs of almost all are available online and they can also be purchased cheaply as used books); * 1) Functions and Graphs and 2) The Method of Coordinates by I.M.Gelfand et. al. - These give you the basics on functions and how to visualize them which is crucial for understanding. * Introductory Logic and Sets for Computer…