高中几何知乎?中国大陆的几何中心位于兰州,这是没有疑问的。具体位置上,有人提及黄河风情线,也有人认为在皋兰县。这个区域辽阔,界定精确的几何点困难重重。因此,只能提供一个大致的方位。对于许多东部和南方的朋友,如未亲临西北,可能难以深刻理解祖国的地域与文化。新疆乡镇间相隔数百里,那么,高中几何知乎?一起来了解一下吧。
数学能力一般是指抽象思维能力、逻辑推理与判断能力、空间想象能力、数学建模能力、数学运算能力、数据处理与数值计算能力、数学语言与符号表达能力等。
所谓数学能力是指由计算能力、初步的逻辑思维能力、空间观念与思维的深刻性、敏捷性、灵活性、广阔性、创造性等所组成的开放性动态系统结构。
一运算能力的培养
数学运算能力的要求大致可分为三个层次:①计算的准确性(基本要求)②计算的合理、简捷、迅速(较高要求)③计算的技巧性、灵活性(高标准要求)。我们在教学中思想上一定要充分认识提高运算能力的重要性,把运算技能上升到能力的层次上,把运算的技巧与发展思维融合在一起。为了培养学生正确迅速的运算能力,可以采用下面的一些做法。
1、加强基础知识教学。数学理论是数学运算的基础,只有正确理解有关的数学概念,切实掌握有关的数学定理、公式、法则,才能为运算指明方向,开拓思路,提供依据,才有可能取得正确迅速的运算结果。
2、加强基本技能训练。能力总是存在与人的具体活动之中,离开了具体活动就无所谓能力。所以要培养运算能力,必须加强基本技能训练。具体的做法是:(a)在教学中加强口算与速算;(b)熟记一些常用的数据、结论;(c)养成验算的习惯,向学生介绍一些最基本的验算方法,如还原法、代值法、估算法等。
一、明确学习数学的目的
在学习数学之前,你需要思考清楚为什么需要学习数学。数学有多个子分类,每一本数学书中都有许多定理和结论,需要花费大量时间来研究。因此,你需要确定自己的目标,合理安排时间。
1.1 你的目标是精通数学、钻研数学,以数学谋生,你可能立志掌握代数几何,或者想精通前沿物理。那么你需要打下坚实的现代代数、几何以及分析基础,你需要准备大量时间和精力,拥有坚定不移的决心。
1.2 你的目标是能够熟练运用高等数学,解决问题,掌握探索新应用领域的武器,你可能立志进入计算机视觉领域、经济学领域或数据挖掘领域。那么你需要打下坚实的矩阵论、微积分以及概率统计基础。
1.3 你的目标是想了解数学的乐趣,把学数学作为人生一大业余爱好。那么你需要打下坚实的线性代数、数学分析、拓扑学以及概率统计基础,对你来说,体会学数学的乐趣是一个更重要的目标。(精通第一级高等数学,在第二级高等数学中畅游,尝试接触第三级高等数学)
二、激发学习数学的动力
学习数学需要智力,更需要时间和精力。以下几个事实大家都深有体会:
1. 凡是没有用的东西,或者虽然有用,但是你用不到的东西,学得快忘得也快。回想一下你大一或者初一的基础课,你还记得清楚吗?
2. 凡是你不感兴趣(或者感觉不到乐趣)的东西,你很难坚持完成它。
作者:毛毛吉吉
https://www.zhihu.com/question/28623194/answer/104420761
来源:知乎
著作权归作者所有,转载请联系作者获得授权。
There is my understanding. The basic idea of the matrix with rows and columns is likely a X-Y axis which means a 2-dimensional space. So that we consider row and column into two parts generously. If you are more interested in the row relation, (such as X-axis you're interested) you will get your point of view of the problem from a X-axis' perspective. In another word, you can imagine you are just standing on some position at X-axis from original point to positive X-axis (NOTICE: X-axis is a 1-dimensional space), and you're more willing to tackle your problems using the solutions in 1-dimension. Don't worry! Let me describe it more vividly.
The problem is lying in a 2-dimensional space, and you want to solve it using an approach of 1-dimensional perspective. Why should we do it (Question 1)? How can we do it (Question 2)? The answer to the Question 1 is that it is more easy than a 2-dimensional problem to solve from our experiences and conclusions in the most time. The answer to the Question 2 is more complex. Matrix is a smart way to compress a 2-dimensional question into a 1-dimensional question. The approach is, of course, differentiating a row and a column. You can continue imagining you're standing at the X-axis with a 1-dimensional point of view being ready to tackle a problem you faced. You are succeed ignoring the Y-axis, no matter what happened on it, because you have no ability to meet anything in the second dimension (Y-axis). That's a simple way for a problem solver.
Hold on Question 2 :)
Imagine a compressor compress a square biscuit at one direction, referencing Figure 1.
<img src="https://pic1.zhimg.com/f65e88002b2b7ebb897c8b4c9f219390_b.png" data-rawwidth="1154" data-rawheight="502" class="origin_image zh-lightbox-thumb" width="1154" data-original="https://pic1.zhimg.com/f65e88002b2b7ebb897c8b4c9f219390_r.png">
You're more interested in X-axis, and you don't care what append on Y-axis. All right, actually, Some solvers think they firstly consider each column contains homogeneous elements and the column could be compressed. Later, we use Compressing and Decreasing Dimension Method (I named it CDDM). Reference Figure 2.
<img src="https://pic1.zhimg.com/6523ee141cafa525fce46e4f4b9149c4_b.png" data-rawwidth="485" data-rawheight="193" class="origin_image zh-lightbox-thumb" width="485" data-original="https://pic1.zhimg.com/6523ee141cafa525fce46e4f4b9149c4_r.png">
For this reason, you are more likely walking on the X-axis form point O(0,0) to point A(0,a) where ‘a’ is a real number on X-axis, and considering a 1-dimensional problem instead. You will see how we replaced and simplified the question, referencing Figure 3.
<img src="https://pic4.zhimg.com/37f2b10a0187ed4ccf46fc2ba4cadc1f_b.png" data-rawwidth="485" data-rawheight="186" class="origin_image zh-lightbox-thumb" width="485" data-original="https://pic4.zhimg.com/37f2b10a0187ed4ccf46fc2ba4cadc1f_r.png">
Do you got the Compressing and Decreasing Dimension Method (CDDM)? Let me draw a simple conclusion. The matrix is a 2-dimensional problem. We use CDDM to simplify it, that is, we chose row or column to calculate and proof a theorem or problem. This approach is likely decreasing the dimension, I think. And the rule is we believe each row or column has the coordinating and corresponding properties for every elements contained by a row or column.
Yes, matrix is a container! If you're more interested in a row relation, and imagining walking on a X-axis, you will believe there is no column so that you compress the columns into single elements. And then, you walk from original point O(0,0) to point A(0,a), where ‘a’ is a real number on X-axis. It's more easy to find out the row relation in the matrix, isn't it?
Now, I suggest you think again about the form of the matrix below in Figure 4. Why do we write it like that?
<img src="https://pic1.zhimg.com/a008ddc59be70fe6e6af2b4dbe167cd0_b.png" data-rawwidth="1032" data-rawheight="426" class="origin_image zh-lightbox-thumb" width="1032" data-original="https://pic1.zhimg.com/a008ddc59be70fe6e6af2b4dbe167cd0_r.png">
I hope I could explain the Question 2 more clearly. But, you know, English, as a second language is not too fluent for me. What I want to highlight at last is that row and column is the same, which is the major relationship between rows and columns, I think. The only differences are the angle we tackle a problem and the way we understand a knowledge. CDDM is a useful attitude in our real life.
中国大陆的几何中心位于兰州,这是没有疑问的。具体位置上,有人提及黄河风情线,也有人认为在皋兰县。这个区域辽阔,界定精确的几何点困难重重。因此,只能提供一个大致的方位。对于许多东部和南方的朋友,如未亲临西北,可能难以深刻理解祖国的地域与文化。新疆乡镇间相隔数百里,甘肃自古以来便是胡汉争夺之地,河西走廊是为了“张汉朝之臂掖”,但现实是甘肃辉煌有限,像被蚕食的骨头(看甘肃地图),虽然作为省会,兰州贴上了“马车夫”的标签,自古是丝绸之路的连接点。然而,其落后的状况难以改变。
记得高考后,我选择报考兰州,渴望深入理解这座城市。搜索百科,了解到兰州是西北重镇,中国大陆几何中心等。然而,四年过后,我深刻体会到中国的地域发展极不平衡,抱着期望而来,带着一丝失落而归。
对于想了解河西走廊或甘肃的朋友们,推荐观看一部纪录片《河西走廊》,内容美不胜收,介绍详尽。这样的纪录片在中国并不多见。
pan.baidu.com/s/1nuUOsK...
密码:nfw2
数学能力一般指的就是思维能力和推理能力!
数学是比较抽象的学科,数学要想学好,要求的是逻辑思维能力和逻辑推理能力,具体表现就是,数学公式的应用与证明题的推理过程。
在进行阅读例题题的时候是需要用到推理能力的,推理能力差的人,数学的学习肯定是会比较吃力的!
它们都涉猎逻辑思维能力。数学好逻辑思维能力强。推理好,逻辑思维也一定高。
所以思维能力对于数学的学习来说是很重要的,家长需要从小培养孩子的数学思维能力,可以了解一下火花思维的课程,比较专业,是很全面的思维能力,推理能力,学习习惯,计算能力的培养课程,比较不错,我家孩子之前的数学能力培养就是在这进行的,效果挺不错的,孩子很喜欢。
以上就是高中几何知乎的全部内容,互信息则定义为两个圆交集的面积,即X和Y信息的共享部分。从几何角度看,红色区域面积等于X和Y的面积之和减去联合熵,或X面积减去条件熵[公式]。通过几何定义,我们可推导出原始互信息定义:[公式]。总结来说,信息熵从“面积”概念上体现出“广义可加性”,这与人类直觉相符,它源自自信息的合理性。