AwesomeMath summer math program qualification Test A
mathematica优化函数
mathematica优化函数Mathematica是一款非常强大的数学计算工具，它提供了丰富的优化函数，可以帮助我们解决各种优化问题。
本文将围绕“Mathematica优化函数”展开，详细介绍优化函数的使用方法。
一、导入数据在进行优化计算之前，我们需要导入相应的数据。
在Mathematica中，可以使用Import函数导入各种数据格式的文件，比如Excel表格、CSV文件、TXT文件等。
以下是一个例子：data = Import["data.csv"];这里我们导入了一个名为“data.csv”的CSV文件。
二、定义目标函数在进行优化计算之前，我们需要定义一个目标函数。
目标函数就是我们想要优化的函数，可以是任何数学公式。
在Mathematica中，可以使用Function函数定义一个自定义函数。
以下是一个例子：f[x_] := x^2 + 2x + 1;这里我们定义了一个名为“f”的函数，它的形参为“x”，函数体为“x^2 + 2x + 1”。
三、使用内置优化函数Mathematica提供了许多内置的优化函数，我们可以直接调用这些函数进行优化计算。
以下是一些常用的优化函数：1、MinimizeMinimize函数可以帮助我们寻找一个函数在给定区间内的最小值。
以下是一个例子：min = Minimize[f[x], x];这里我们使用了Minimize函数，寻找了函数“f”在所有实数范围内的最小值。
2、MaximizeMaximize函数可以帮助我们寻找一个函数在给定区间内的最大值。
以下是一个例子：max = Maximize[f[x], x];这里我们使用了Maximize函数，寻找了函数“f”在所有实数范围内的最大值。
3、NMinimizeNMinimize函数可以帮助我们寻找一个函数在给定区间内的最小值，并返回一个数值近似解。
以下是一个例子：min = NMinimize[f[x], x];这里我们使用了NMinimize函数，寻找了函数“f”在所有实数范围内的最小值，返回了一个数值近似解。
数学网站
/Mathematics/index.htm麻省理工学院开放式课程网页，很多视频资料/courses/index.html富有特色的数学网站大观/ide/index.html这是美国Addison Wesley Longman出版公司属下的一个网站，提供了该公司出版的大量微分方程教材的实时模拟实验。
对于一些常见的常微分方程，你可以在这个网站看到物理实验的网上模拟和相应动力系统的相图变化。
类似这样的网上模拟在美国许多大学甚至中学已经成为多媒体教学的一部分进入课堂，深受学生欢迎。
这里的实验包括各种振动模型(二次常微分方程)，生态方程组和混沌模型等。
网站的程序是由Java语言编成的，虽然它也在市场上定价出售，但是你可以在网站上免费欣赏所有精彩的动态模拟。
/mathserv/index.html这是美国Vanderbilit大学数学系和商学院联合建立的一个网站。
在这个网站上，你可以运行各种微积分和常微分方程的基本运算：你输入所有必要信息后几秒钟内，不管多复杂的运行结果和图象都会马上显示在计算机屏幕上。
网站的数学运算功能是建立在著名数学软件Mathematica基础上的，可以说这是一个简单的网上Mathematica计算机器(它并不是一般意义下的计算器，它的功能比计算器强得多)，但是你不需要花天文数字的价钱购买Mathematica，甚至不用懂得Mathematica的编程方式，所以对于数学或者各种理工科工作者来说，这是一个好极了的工具。
它的功能包括定积分和不定积分，微分，极限，因式分解，牛顿法，二维和三维函数绘图，解各类基本常微分方程等等。
/在一些国家，许多家谱的数据库已经上网，人们可以在网上查到他们的祖宗八代。
而数学家常常也把自己的博士导师称为他们的“数学父亲”，这样自然也就有了数学家的家谱。
一个可搜索的数学家家谱已经开始在美国明尼苏达州立大学建立起来了，一半以上的美国大学数学系为它的建立提供了它们的博士毕业生的历史资料，现在这一网站已经搜集了历史上48294位数学家的“出生身世”。
mathematica进行巴特沃斯滤波 -回复
mathematica进行巴特沃斯滤波-回复如何使用Mathematica进行巴特沃斯滤波巴特沃斯滤波（Butterworth filter）是一种常用的滤波器，常用于信号处理和图像处理领域。
Mathematica是一款功能强大的数学软件，具有广泛的应用领域。
本文将详细介绍如何使用Mathematica进行巴特沃斯滤波，从理论知识到具体实现，一步一步进行解释。
1. 了解巴特沃斯滤波器的原理巴特沃斯滤波器是一种无纹波（ripple-free）和无瞬时谐振（no transient resonances）的滤波器。
它的理论基础是巴特沃斯函数，通过控制滤波器的阶数和截止频率，可以实现不同的滤波效果。
巴特沃斯滤波器的频率响应函数可以表示为：H(ω) = 1 / (√(1 + (ω / ωc)^(2N)))其中，H(ω)表示频率响应函数，ω表示频率，ωc表示截止频率，N表示滤波器的阶数。
2. 导入Mathematica软件并创建滤波器函数首先，打开Mathematica软件。
然后，我们通过以下代码创建巴特沃斯滤波器函数：ButterworthFilter[cutoff_, order_] := ButterworthFilterModel[order, cutoff]此代码定义了一个名为ButterworthFilter的函数，该函数接受两个参数：截止频率cutoff和滤波器阶数order。
函数返回一个巴特沃斯滤波器模型。
3. 设计巴特沃斯滤波器接下来，我们使用刚刚定义的巴特沃斯滤波器函数来设计一个巴特沃斯滤波器。
通过以下代码实现：cutoff = 0.1; (* 设置截止频率为0.1 *)order = 4; (* 设置阶数为4 *)filter = ButterworthFilter[cutoff, order]这段代码定义了截止频率为0.1，阶数为4的一个巴特沃斯滤波器。
将其保存在变量filter中供后续使用。
mathematica命令大全
mathematica命令大全mathematica命令大全Mathematica的内部常数Pi , 或π(从基本输入工具栏输入, 或“Esc”+“p”+“Esc”）圆周率πE (从基本输入工具栏输入, 或“Esc”+“ee”+“Esc”）自然对数的底数eI (从基本输入工具栏输入, 或“Esc”+“ii”+“Esc”）虚数单位iInfinity, 或∞(从基本输入工具栏输入, 或“Esc”+“inf”+“Esc”）无穷大∞Degree 或°(从基本输入工具栏输入,或“Esc”+“deg”+“Esc”）度Mathematica的常用内部数学函数指数函数Exp[x] 以e为底数对数函数Log[x] 自然对数，即以e为底数的对数Log[a，x] 以a为底数的x的对数开方函数Sqrt[x] 表示x的算术平方根绝对值函数Abs[x] 表示x的绝对值三角函数（自变量的单位为弧度）Sin[x] 正弦函数Cos[x] 余弦函数Tan[x] 正切函数Cot[x] 余切函数Sec[x] 正割函数Csc[x] 余割函数反三角函数ArcSin[x] 反正弦函数ArcCos[x] 反余弦函数ArcT an[x] 反正切函数ArcCot[x] 反余切函数ArcSec[x] 反正割函数ArcCsc[x] 反余割函数双曲函数Sinh[x] 双曲正弦函数Cosh[x] 双曲余弦函数Tanh[x] 双曲正切函数Coth[x] 双曲余切函数Sech[x] 双曲正割函数Csch[x] 双曲余割函数反双曲函数ArcSinh[x] 反双曲正弦函数ArcCosh[x] 反双曲余弦函数ArcTanh[x] 反双曲正切函数ArcCoth[x] 反双曲余切函数ArcSech[x] 反双曲正割函数ArcCsch[x] 反双曲余割函数求角度函数ArcTan[x，y]以坐标原点为顶点，x轴正半轴为始边，从原点到点（x，y）的射线为终边的角，其单位为弧度数论函数GCD[a,b,c,．．．] 最大公约数函数LCM[a,b,c,．．．] 最小公倍数函数Mod[m,n] 求余函数(表示m 除以n的余数)Quotient[m，n] 求商函数（表示m除以n的商）Divisors[n] 求所有可以整除n的整数FactorInteger[n] 因数分解，即把整数分解成质数的乘积Prime[n] 求第n个质数PrimeQ[n]判断整数n是否为质数，若是，则结果为True，否则结果为FalseRandom[Integer，{m，n}] 随机产生m到n之间的整数排列组合函数Factorial[n]或n！阶乘函数，表示n的阶乘复数函数Re[z] 实部函数Im[z] 虚部函数Arg(z) 辐角函数Abs[z] 求复数的模Conjugate[z] 求复数的共轭复数Exp[z] 复数指数函数求整函数与截尾函数Ceiling[x] 表示大于或等于实数x的最小整数Floor[x] 表示小于或等于实数x的最大整数Round[x] 表示最接近x的整数IntegerPart[x] 表示实数x的整数部分FractionalPart[x] 表示实数x的小数部分分数与浮点数运算函数N[num]或num//N 把精确数num化成浮点数（默认16位有效数字）N[num，n] 把精确数num化成具有n个有效数字的浮点数NumberForm[num，n] 以n个有效数字表示num Rationalize[float] 将浮点数float转换成与其相等的分数Rationalize[float，dx] 将浮点数float转换成与其近似相等的分数，误差小于dx最大、最小函数Max[a，b，c，．．．] 求最大数Min[a，b，c，．．．] 求最小数符号函数Sign[x]Mathematica中的数学运算符a+b加法a-b 减法a*b (可用空格键代替*) 乘法a/b (输入方法为：“ Ctrl ” + “ / ” )除法a^b (输入方法为：“ Ctrl ” + “ ^” )乘方-a 负号Mathematica的关系运算符==等于< 小于> 大于<= 小于或等于>= 大于或等于!= 不等于注：上面的关系运算符也可从基本输入工具栏输入。
math.h常用函数 -回复
math.h常用函数-回复math.h是C语言中的数学库，它包含了许多常用的数学函数，可以用于各种数学运算和问题的求解。
本文将以math.h常用函数为主题，逐步讲解各个函数的功能和用法。
我们将介绍的函数包括数学运算函数、三角函数、指数和对数函数、常数以及其他的辅助函数。
首先，我们来了解一下数学运算函数。
这些函数可以执行常见的数学运算，如加法、减法、乘法、除法、取余等。
其中常用的函数有：1. fabs(x)：返回x的绝对值。
例如，当x为-5时，fabs(x)的返回值为5。
2. sqrt(x)：返回x的平方根。
例如，sqrt(9)的返回值为3。
3. pow(x, y)：返回x的y次幂。
例如，pow(2, 3)的返回值为8。
4. ceil(x)：返回不小于x的最小整数值。
例如，ceil(3.2)的返回值为4。
5. floor(x)：返回不大于x的最大整数值。
例如，floor(3.9)的返回值为3。
6. fmod(x, y)：返回x除以y的余数。
例如，fmod(10, 3)的返回值为1。
接下来，我们将介绍一些常用的三角函数。
三角函数在几何学和物理学等领域经常被使用。
下面列出了一些常见的三角函数及其功能：1. sin(x)：返回x的正弦值。
例如，sin(0)的返回值为0。
2. cos(x)：返回x的余弦值。
例如，cos(0)的返回值为1。
3. tan(x)：返回x的正切值。
例如，tan(0)的返回值为0。
4. asin(x)：返回x的反正弦值。
返回值的范围是[-π/2, π/2]。
例如，asin(1)的返回值为π/2。
5. acos(x)：返回x的反余弦值。
返回值的范围是[0, π]。
例如，acos(0)的返回值为π/2。
6. atan(x)：返回x的反正切值。
返回值的范围是[-π/2, π/2]。
例如，atan(1)的返回值为π/4。
接下来，让我们来介绍指数和对数函数。
这些函数对于数字的增长和减弱方面非常有用。
MIT牛人解说数学体系(增加部分英文翻译和备注)
在过去的一年中，我一直在数学的海洋中游荡，research进展不多，对于数学世界的阅历算是有了一些长进。
为什么要深入数学的世界作为计算机的学生，我没有任何企图要成为一个数学家。
我学习数学的目的，是要想爬上巨人的肩膀，希望站在更高的高度，能把我自己研究的东西看得更深广一些。
说起来，我在刚来这个学校的时候，并没有预料到我将会有一个深入数学的旅程。
我的导师最初希望我去做的题目，是对appearance 和motion建立一个unified的model。
这个题目在当今Computer Vision中百花齐放的世界中并没有任何特别的地方。
事实上，使用各种Graphical Model把各种东西联合在一起framework，在近年的论文中并不少见。
我不否认现在广泛流行的Graphical Model是对复杂现象建模的有力工具，但是，我认为它不是panacea（万应灵药），并不能取代对于所研究的问题的深入的钻研。
如果统计学习包治百病，那么很多“下游”的学科也就没有存在的必要了。
事实上，开始的时候，我也是和Vision中很多人一样，想着去做一个Graphical Model——我的导师指出，这样的做法只是重复一些标准的流程，并没有很大的价值。
经过很长时间的反复，另外一个路径慢慢被确立下来——我们相信，一个图像是通过大量“原子”的某种空间分布构成的，原子群的运动形成了动态的可视过程。
微观意义下的单个原子运动，和宏观意义下的整体分布的变换存在着深刻的联系——这需要我们去发掘。
在深入探索这个题目的过程中，遇到了很多很多的问题，如何描述一个一般的运动过程，如何建立一个稳定并且广泛适用的原子表达，如何刻画微观运动和宏观分布变换的联系，还有很多。
在这个过程中，我发现了两个事情：我原有的数学基础已经远远不能适应我对这些问题的深入研究。
在数学中，有很多思想和工具，是非常适合解决这些问题的，只是没有被很多的应用科学的研究者重视。
大学毕业后当一名数学老师英语作文
大学毕业后当一名数学老师英语作文篇1My Dream Job: Becoming a Math TeacherHi there! My name is Timmy and I'm 10 years old. I'm in 5th grade and I absolutely LOVE math! I know that might sound weird to some kids, but to me, math is like a super cool puzzle that you get to solve over and over again. I find it really satisfying when I finally figure out a tricky problem after working really hard on it. Math just clicks for me in a way that other subjects don't.Ever since I was a little kid, I've known I wanted to be a math teacher when I grew up. My mom says I used to line up my stuffed animals and "teach" them about numbers and shapes before I even started kindergarten! I had this really great math teacher in 2nd grade named Mr. Parker who made learning math so much fun. We did all these awesome hands-on activities and games that helped the concepts stick in my brain. I could tell Mr. Parker really loved teaching and loved seeing us understand the material. That's when I decided - I want to be just like him!I'm sure some people are probably thinking, "But Timmy, you're just a kid! How can you possibly know what you want todo for the rest of your life?" Well, yeah, I might change my mind eventually I guess. But for right now, being a math teacher is my absolute dream job. Let me tell you why.First off, I'll get to work with my favorite subject every single day! How cool is that? I won't have to dread going to work because math is fun and exciting for me. I really enjoy explaining math concepts to others too, even to my classmates who struggle with it. When you understand something really well, it's awesome to be able to share that knowledge and see the lightbulb go off for someone else. That must be such a great feeling as a teacher!Secondly, I'll get to help shape young minds and inspire a love of learning in my students, just like Mr. Parker did for me. I know how discouraging it can feel when you just can't "get" a certain math skill. By being a caring, patient and creative teacher, I can find different ways to explain ideas until they finally click. Seeing my students have those "aha!" moments when a tough concept starts making sense will be so rewarding. And who knows, I might even inspire a few future mathematicians along the way!Another great perk of being a math teacher is that I'll have summers off to relax and recharge. Don't get me wrong,teaching seems like incredibly hard work during the school year. But getting those couple months of summer vacation every year to pursue other interests and hobbies sounds amazing. Maybe I could even pick up a fun summer job or go on vacations. The flexibility of the teaching schedule is a huge plus.Of course, the road to becoming a math teacher isn't an easy one. After I graduate from high school, I'll need to go to college for at least 4 years to earn a bachelor's degree, probably in math or education. During college I'll take tons of math courses to really deepen my number skills. I'll also have to take classes on things like teaching methods, child psychology, and classroom management. It will be a lot of challenging coursework for sure.Then after college, most states require new teachers to complete an internship or student teaching experience before they can get certified. So I'll likely have to spend a semester or two teaching math classes at a school under the supervision of an experienced mentor teacher. This will help me get hands-on practice with lesson planning, working with students, grading assignments, and everything else that goes into being an effective math teacher. It's going to be really hard work, but so worth it in the end!Once I make it through my degree and credential program, I'll finally get to start applying for math teacher jobs at elementary, middle or high schools in my local area. Of course, competition for teaching positions can be pretty tough, so I'll need to really sell myself during job interviews. I'll emphasize my passion for math and working with young people. I'll highlight any experience I had tutoring, coaching, or working at summer camps. Maybe I can even show some sample math lesson plans I created to demonstrate my skills.If all goes well and I land my dream job, I can imagine it will be both incredibly fulfilling but also incredibly challenging at times. Some kids might be disruptive or hard to motivate. Dealing with rules, curriculum standards and standardized testing from administrators could be frustrating. Having to grade hundreds of quizzes and assignments on top of creating engaging lesson plans will eat up many late nights at home too. But in the end, I'll persevere because helping kids understand and appreciate math is my calling.Just picture it - I'm standing in front of my class, colored markers in hand, walking students through step-by-step how to solve an algebraic equation. Despite a few glazed over looks, I can see that lightbulb moment when over half the class suddenly"gets" it. That feeling of knowing I made a difference and helped kids learn? That's what will make all the hard work worth it. Yep, being a math teacher might just be the most awesome job ever!So that's my big dream for the future - to become an inspiring, passionate, creative math teacher who sparks that same joy of mathematics in my students. Sure, it's going to take a lot of studies, years of training, and tremendous dedication. But in my mind, there's no better way to spend my career than sharing my love for numbers with the next generation. Math has brought me so much happiness and fulfillment, and I can't wait to pass that on. Just call me Mr. Timmy!篇2My Big Dream to Become a Math TeacherHi, my name is Tommy and I'm 10 years old. I'm in the 5th grade and I absolutely love math class! I know what you might be thinking - "Math? Isn't that the most boring subject ever?" But to me, math is like a giant puzzle that is fun to solve. I get such a rush when I finally figure out a really tricky problem.My favorite part of math is algebra. I know algebra is usually not taught until middle school, but my math teacher Mr. Rodriguez started introducing some basic algebra concepts toour class this year. At first, I was a little confused by all the letters and symbols instead of just numbers. But after Mr. Rodriguez explained it, algebra started to make a lot of sense. It's like a code to describe patterns and solve mysteries!Whenever we do algebra in class, I get super focused and have to stop myself from raising my hand for every single question. I just can't get enough of factoring polynomials, solving for x, and graphing equations. My friends think I'm totally weird for loving algebra so much. They make fun of me for being a "math geek." But I don't even care, I'm proud to be a math nerd!The reason I love math so much is because of Mr. Rodriguez. He has a way of making even the trickiest concepts really clear and easy to understand. He comes up with the best examples and life-like word problems to illustrate what we're learning. Sometimes he even raps the lessons or turns them into fun games. Math class with Mr. Rodriguez is my favorite period of the day.Mr. Rodriguez has inspired me to want to become a math teacher when I grow up. I remember a few months ago, I was having a tough time understanding how to work with exponents.I stayed after class for extra help, feeling really dumb andembarrassed that I couldn't get it. But Mr. Rodriguez was so patient and encouraging. He said, "Tommy, don't be hard on yourself! Exponents can be really confusing at first. It takes time and practice to get the hang of it."He went over examples with me again and again until it finally clicked. When I got my test back and saw that I had aced the exponent problems, I felt so proud! That's when I realized that being a teacher must be such a rewarding job. Helping students understand and cheering them on until they have those "a-ha!" moments. I can't imagine anything more fun than getting to work with math all day and watch kids fall in love with it like I did.Of course, before I can become a math teacher, I have to go to college and get my degree. I've already started looking into the best universities with great mathematics programs. My top choices so far are MIT, CalTech, and Stanford. I know getting into schools like that won't be easy, but I'm going to work really really hard. I plan to join the math team, math club, and any other nerdy math groups I can find!After college, I'll need to get my teaching credential and credential too. That means taking some extra classes on things like lesson planning, classroom management, and childpsychology. It sounds like a lot of work, but I don't even mind. Anything to reach my dream of becoming the next Mr. Rodriguez!I can picture it now - me at the front of my own math classroom, going over geometry proofs on the board. When a student raises their hand with a question, I'll walk over with a smile and patiently re-explain the concept until they've got it. Maybe I'll even put on goofy math costume from time to time, like Mr. Rodriguez does on Pi Day every year. Anything to make math more fun and engaging!Outside of teaching, I'd love to get involved with math competitions, like coaching a math team or creating practice materials. Math competitions were some of the most fun events I did in school. It was so exciting to see which student or team could solve those crazy, mind-bending problems the fastest. As a teacher, I could help prep kids to experience that same thrill of victory.Who knows, maybe I'll even write some math curriculum or textbooks along the way. Ones that really break concepts down in a simple, straightforward way for kids to understand. Mr. Rodriguez is always saying how hard it is to find good teachingmaterials sometimes. If I could create resources to help teachers like him, that would be so awesome!Being a math teacher means more than just teaching formulas and equations though. It's about inspiring a love for the subject in your students. That's what Mr. Rodriguez did for me. Before his class, I thought math was this boring subject filled with arbitrary rules. But he showed me the beauty, logic, and real-world applications behind all of it. Now, I can't get enough!Whenever I see equations or numbers in my daily life, I get all excited. Like when waiting in line to ride a roller coaster, I'll calculate acceleration rates and kinetic energy. Or at the grocery store, I'll estimate prices and discount percentages for fun. Some kids want to grow up to be athletes or movie stars, but not me. Give me a piece of chalk, a chalkboard, and a roomful of students, and I'll be the happiest kid on earth!So there you have it - my dream is to become an awesome math teacher who inspires kids to see how amazing and fun math can be, just like Mr. Rodriguez did for me. It's going to take tons of hard work and many many years of schooling, but it will be worth it to have my dream job. Sure, I may get teased by my friends for being a math nerd now. But just wait, one day I'll bethe really cool math teacher that all the kids look up to. Algebra here I come!篇3Being a Math Teacher After University GraduationHi, my name is Tommy and I'm 10 years old. When I grow up, I really want to become a math teacher! I know it might sound kind of boring to some kids, but I absolutely love math. Numbers and equations just make so much sense to me. It's like a fun puzzle that you get to solve over and over again.After I finish elementary school, middle school, and high school, I'm going to go to a great university. I'll have to study really hard and get excellent grades. My parents always tell me that doing well in school is the key to getting into a top university program. I'll probably major in mathematics, but I might also study education so I can learn all about how to be a really awesome teacher.University is going to be so exciting! I can't wait to live in the dorms and make new friends from all over. We'll go to classes together, study at the library, and explore the fun college town. Of course, I'll have to be really responsible and not goof off toomuch. Graduating with good grades is super important if I want to become a professional math teacher.After four years of intense studying, going to lectures, writing papers, and taking tests, I'll finally graduate from university. YAY! I'll get to walk across the big stage and receive my diploma. My family will be there cheering me on and I know they'll be really proud. I'll feel so accomplished knowing that I worked hard and achieved my goal.Then it will be time to enter the real world and get a job as a math teacher! I think I'd like to teach at a high school to start. High school students are old enough to really understand and appreciate higher level math concepts. Subjects like algebra, geometry, calculus, and statistics are so intellectually stimulating. As a teacher, I'll get to introduce brilliant young minds to those fascinating areas of math.My dream job would be to work at the high school I once attended. How cool would it be to have some of the same teachers that inspired me as a student? I could decorate my classroom with numbers, formulas, and fun math images to create an engaging learning environment. I'd have a big whiteboard or chalkboard for working out problemsstep-by-step for the whole class.Teaching is such an important responsibility. As a math teacher, it would be my job to make sure every student truly understands the material before letting them move on. I would offer lots of one-on-one support for any kids who are struggling. Maybe I could start an after-school math club or tutoring program too!The best part about being a math teacher is that it combines two of my greatest loves - working with numbers and helping others learn. Every day, I'll get to use my expertise to guide students towards new mathematical discoveries. Seeing a kid's face light up when they finally "get" a complex concept would be the best feeling ever. My students will be the next generation of mathematicians, scientists, engineers, and more.Over the summers when school is out, I could travel the world and continue learning. Summer math camps, seminars, and conferences happen all over the place. Educators are always working to develop fresh ways of teaching tricky math topics more effectively. I'll never stop being a student of mathematics myself so that I can be on the cutting edge.As the years go by, I might decide to go back to university again. This time, I could get a master's degree or even a doctorate in mathematics education. With an advanced degree, Icould become a math teacher for university students. How rewarding would it be to train young people to become future math teachers themselves? I could have a huge, generational impact by sharing my passion.No matter what, I'm determined to always be involved with mathematics in some way. Numbers and problem-solving strategies will forever be oxygen to my soul. Maybe I'll write math books for kids, become a private tutor, or work on educational math games and software. The possibilities are endless when you follow your true calling.Being a math teacher is such a important yet underappreciated career path. We need more dedicated people who can patiently explain mathematical concepts in a way that inspires curiosity instead of anxiety. Math is a universal language and the foundations for ALL areas of science, technology, engineering, business, and more. Without skilled math instructors at every level, the world's intellectual growth and progress would be stunted.I can't wait to get started on this incredibly meaningful journey. The road to becoming a math teacher after university won't be easy, but it will be so worth it. I'll work as hard as I can to make sure my future students have an excellent guide andmentor for unlocking the beautiful intricacies of mathematics. Who's ready to log some study hours with me?。
自我展示英文作文初一下册第二单元
自我展示英文作文初一下册第二单元全文共6篇示例，供读者参考篇1My Self-Introduction EssayHi there! My name is Tommy and I'm a student in the first year of middle school. I'm really excited to tell you all about myself and my life. Get ready for an awesome adventure into my world!First up, let me describe my appearance. I'm about 5 feet tall, so kind of short for my age. I have brown hair that's a bit messy since I don't like spending too much time fixing it in the mornings. My eyes are green and I have freckles scattered across my nose and cheeks. For clothes, I love wearing t-shirts with cool designs or logos from my favorite movies, games, and bands. Jeans or shorts are my go-to bottoms. I'm a pretty casual dresser!As for my personality, I'd say I'm a fun, energetic, and curious kid. I love cracking jokes to make my friends and family laugh. I'm the class clown for sure! My brain is always buzzing with questions about how things work or fun facts I've learned.Speaking of learning, I really enjoy school, especially science class where we get to do experiments. Math used to be my worst subject, but I've been working super hard to improve.My favorite hobbies are playing video games, watching movies and shows, reading comics and books, and playing sports like basketball and soccer. I've been obsessed with the latest universe-hopping adventure game that just came out. The storyline is epic! After school, you'll probably find me shooting hoops at the park or dribbling a soccer ball around too. I'm a total Marvel nerd and can pretty much recite the entire plot of Avengers: Endgame by heart at this point.My family is really important to me. I live with my mom, dad, and little sister Amy who is 8 years old. My mom is an artist and my dad is a chef at a fancy restaurant downtown. We love having family game nights, going to museums and cultural festivals together, and taking trips whenever we can. Last summer we went camping in the mountains and went hiking, canoeing, and built a huge bonfire for s'mores! My sister and I bickered a bit as usual, but we had an awesome time.One of the biggest challenges I've faced so far was moving to this new city and starting at a new school last year. I was really nervous to leave my old friends behind and have to start oversomewhere new. It took me a little while, but I've made some great new friends here who I hang out with all the time now. We have sleepovers, go to the movies, play video games together online, and just goof around being weird kids. I'm so glad I put myself out there!Looking towards the future, I'm not entirely sure what I want to be when I grow up yet. I have lots of interests and change my mind all the time! Some ideas that seem cool are being a video game designer, scientist, author, or comedian. Maybe I'll be a hilarious scientist who writes jokes into video games about experiments? Who knows! I've got plenty of time to figure it out.Well, that's my life in a nutshell! I tried to cover all the important stuff about my looks, personality, hobbies, family, challenges, and dreams. Thanks for reading my self-introduction essay. I hope you learned a bit about the awesome kid that I am. Let me know if you have any other questions! I'll leave you with one of my cheesy jokes: What kind of shoes do kids plant in a garden? Tulip-shoes!篇2My Name is Lily and I'm a Superstar!Hi everyone! My name is Lily and I'm 12 years old. I'm in the 6th grade at Greenfield Elementary School. I'm so excited to tell you all about myself and my amazing life!First of all, I want to talk about my family because they are the most important people in my world. I live with my mom, dad, older brother Jake, and my cute little puppy Rufus. My mom is a nurse and my dad is a police officer. They both work really hard to take care of me and Jake. Jake is 15 and he's kind of annoying sometimes but I still love him!My absolute favorite thing in the whole world is singing and dancing. I'm obsessed with pop music and all the latest songs and dances. Every week I practice singing and choreographing new routines to perform for my family. They cheer me on and make me feel like a total superstar! I really want to try out for the school musical next year.Speaking of school, I actually love learning which some people might find weird. My favorite subjects are art class and English. I'm really creative and I love drawing, painting, and making crafts. One day I want to be a fashion designer! In English, I love reading novels and writing stories. I get really good grades in that class.My least favorite subject is probably math. I just find it kind of boring and it doesn't come naturally to me. But I'm working super hard this year to get better at it. I have a math tutor who helps me understand it more. I know it's important to be good at math for the future.On the weekends, I love hanging out with my best friends Zoe and Emma. We have so much fun together! Sometimes we have sleepovers and watch movies, do makeovers, and eat lots of snacks. Other times we go to the mall or park and just walk around talking and laughing about everything.I'm also really into gymnastics and I practice at my gym a few times a week. I love doing flips and jumps on the different equipment. Gymnastics is awesome exercise and it helps me stay super flexible and in shape. I've won a few competitions before which was really exciting!One of my other hobbies is taking care of my puppy Rufus. He's a golden retriever and he's just the cutest, fluffiest thing ever! I take him on walks, give him baths, brush his fur, and play fetch with him. Rufus always cheers me up when I'm feeling sad or stressed out. Dogs really are a kid's best friend.Over summer vacation, my family usually goes on an awesome trip somewhere fun. Last year we went to Hawaii and itwas incredible! We went snorkeling, hiked up a volcano, and just relaxed on the beautiful beaches. I loved trying new Hawaiian foods like poke bowls and shave ice. This summer we're maybe going to go to Italy which I'm really excited about!Well, that's a little bit about my wonderful life as a12-year-old superstar! I feel so blessed to have such an amazing family, awesome friends, and so many cool hobbies and interests. Even though I'm just a kid, I'm living my best life and having as much fun as possible. The world is my oyster and I can't wait to see what the future holds for me!篇3My Name is David and I am 12 Years OldHi everyone! My name is David and I am 12 years old. I am a student in the 6th grade at Oakwood Elementary School. I live with my mom, dad, and little sister Emma who is 8 years old. We also have a dog named Buddy who is a golden retriever. He loves to play fetch and go for walks in the park near our house.I have a lot of different hobbies and interests that I really enjoy. One of my biggest hobbies is playing soccer. I have been playing soccer since I was 5 years old and I am on my school's soccer team as well as a club team. Soccer practice happens 3times per week after school and we have games on the weekends. I play midfielder and I love dribbling the ball up the field and trying to score goals. It is so much fun!Another big hobby of mine is playing video games. My favorite games are adventure and open world games where you can explore different worlds and go on quests. I especially like games that allow you to build and create your own structures. I probably spend a couple hours each day playing video games, either by myself or online with my friends. My parents limit my gaming time though so I don't play too much.I also really like reading books, especially fantasy novel series. I love getting lost in magical worlds filled with dragons, wizards, and epic battles between good and evil. My favorite book series is Harry Potter - I've read all the books multiple times! I'm currently reading the Lord of the Rings trilogy which my dad recommended to me. Reading sparks my imagination and creativity.In school, my favorite subjects are math and science. I find solving math problems and equations really satisfying. In science, I love learning about how things work, whether it's physics, chemistry, or biology. I'm fascinated by the natural world anduniverse. I actually want to be an astronaut when I grow up so I can travel to space and walk on the moon!Speaking of space, I'm really interested in astronomy as a hobby too. I have a fancy telescope that I use to gaze at planets, stars, and galaxies on clear nights. I've seen Saturn's rings, the craters on the moon, and faraway nebulae before. The universe is so vast and there is still so much we have to discover about it. Astronomy fills me with a sense of wonder.One more big hobby I have is building and making things with my hands. I love working on arts and crafts projects like drawing, painting, making bracelets and keychains. But I especially love building models and small machines or robots using Lego kits or k'nex pieces. I'm a member of my school's Robotics Club where we build and program little robots to perform tasks. It's really cool watching something you designed and built come to life and move around! I'm a pretty creative kid.In my free time, I also love just hanging out with my friends and having fun. We play at the playground, ride our bikes, have sleepovers, and goof around. My best friends are Michael, James, and Ryan - we've known each other since kindergarten. I'm so grateful to have such a great group of buddies who make me laugh all the time. Friendship is really important to me.Although I may only be 12, I feel like I have a good idea of what I want to do when I'm older. As I mentioned, I really want to be an astronaut and travel to space. I'm going to have to work really hard in school, especially in science, technology, and math subjects. I'm hoping to go to a good college or university that has an excellent aerospace engineering program. I know it won't be easy, but I am determined to make my dream come true someday.Well, that's a little bit about who I am and what I enjoy doing!I tried my best to give you all a glimpse into my life as a12-year-old kid. I have a lot of typical interests and hobbies that most kids my age have - sports, video games, hanging with friends, etc. But I also have some unique passions like astronomy, engineering, and exploring the depths of space and the cosmos. I'm a pretty curious and ambitious young guy who has big dreams for the future. Thanks for reading my self-introduction essay! Let me know if you have any other questions.篇4My Name is Jackie and I'm Going to Tell You All About Me!Hi there! My name is Jackie and I'm 12 years old. I'm in the 6th grade at Lakeview Elementary School. I can't wait to tell you all about myself and my life!I live with my mom, dad, older brother Tony, and our dog Rufus. My mom is a nurse and my dad is an accountant. My brother Tony is 15 and he's kind of annoying sometimes but he's still a pretty cool guy. Rufus is a golden retriever and he's the cutest, fluffiest dog ever! I just love playing fetch with him in the backyard.My favorite subjects in school are art and gym class. I'm really good at drawing and painting. My art teacher Mrs. Palmer always puts my artwork up on the walls to display it. In gym, I love playing sports like basketball, soccer, and kickball. I'm super competitive and always try my best to help my team win!I have a great group of best friends that I've known since kindergarten - Emma, Jaden, and Ryan. We always have sleepovers on the weekends and it's so much fun. We play games, eat junk food, and stay up way too late watching movies and telling silly stories. Summer is my favorite time because we get to go the pool and have water balloon fights!Some of my other hobbies are reading, riding my bike, and listening to music. I love reading fantasy book series like HarryPotter and Percy Jackson. My bike is bright pink with tassels on the handlebars. I ride it all around the neighborhood and pretend I'm in the Tour de France! As for music, I really like pop singers like Taylor Swift, Ariana Grande, and Ed Sheeran. I'm always singing and dancing around my room.My family goes on a big vacation every summer. Last year we went to Disney World in Florida and it was magical! We got to go on all the rides, meet the Disney characters, and watch the fireworks shows every night. The year before that we went camping in the mountains for a week. We went hiking, caught fish in the stream, and made s'mores over the campfire. This summer we're thinking about going to Hawaii or California!Of course, I'm not perfect - I do have some bad habits too. I'm a total slob and my room is always a huge mess. My mom is forever nagging me to clean it up. I also tend to procrastinate on my homework until the very last minute. And sometimes I get in trouble at school for talking too much in class. But I'm working on all those things!In the future, I'm not totally sure what I want to be when I grow up yet. Maybe a teacher, or a doctor, or an artist. Or maybe I'll be a famous singer or actress! I have so many interests that it's hard to pick just one career. Whatever I end up doing though, Iknow I want to travel the world and have an exciting, adventurous life.Well, that's pretty much me in a nutshell! I'm just a regular kid who loves having fun with my family and friends. I try to be a good student and stay out of too much trouble (most of the time!). Even though I'm still young, I have a ton of hobbies, ambitions, and crazy dream for my future. Thanks for reading all about me - I hope you enjoyed getting to know me a little better!篇5My Name Is EmilyHi there! My name is Emily and I'm 11 years old. I'm in the 5th grade at Franklin Elementary School. I live with my mom, dad, and little brother Tommy who is 7. We also have a dog named Buddy who is a golden retriever. He's really cute and fluffy!I like school, especially math class because I'm good at solving problems. My favorite subject is art though. I love drawing, painting, and making crafts. My art teacher Mrs. Miller says I'm really creative. Sometimes I'll spend hours just doodling in my sketchbook. I want to be an artist when I grow up!I have a best friend named Sophia. We've known each other since kindergarten. She lives just down the street from me so we can walk to school together every day. Sophia and I like a lot of the same things like riding our bikes, having sleepovers, and watching movies. Our favorite movies are the ones with the funny talking animals in them. We think they're hilarious!When I'm not in school, I really enjoy playing outside. My backyard has a swing set and a treehouse that my dad built for me last summer. Tommy and I spend a lot of time out there playing make-believe games and using our imaginations. We also like going to the park to play on the jungle gym. My favorite park is the one with the big grassy field where we can run around and fly kites.Every Saturday morning, my family goes to the Farmers Market downtown. I love looking at all the fresh fruits and veggies and trying free samples. My mom and dad like to buy honey, jam, and bread from the local vendors there. Sometimes they let me pick out a treat like a cupcake or a cookie. Yum!A few times a year, my grandparents who live a few hours away come to visit us for the weekend. I always look forward to their visits so much! My grandpa and I like to play checkers and do jigsaw puzzles together. My grandma is an amazing cook andbakes the most delicious pies and cakes. She always sneaks me an extra helping of dessert!On Sunday mornings, my family goes to church together. I'm a part of the children's choir and I love singing all the fun songs with my friends. After church, we usually go out for brunch at a local diner or cafe. That's probably my favorite meal because you can have breakfast foods like pancakes or lunch foods like burgers and fries!Well, that's a little bit about me and my life. I feel very lucky to have such a loving family and good friends. I try to be a kind person and a good student. Even though I'm still just a kid, I like keeping busy and experiencing new things. I can't wait to see what fun adventures are still ahead! Thanks for reading about me. Talk to you later!篇6My Name is Jimmy and I'm 11 Years OldHi there! My name is Jimmy and I'm 11 years old. I'm in the 5th grade at Oakwood Elementary School. I love making new friends, so I'm really excited to introduce myself to you all!I live in a bright blue house with my mom, dad, and my little sister Emily who is 8 years old. We also have a dog named Buddy who is a golden retriever. He's super friendly and loves playing fetch in our backyard. My dad works as an engineer at a car company, and my mom is a nurse at the hospital downtown.Some of my favorite subjects in school are math, science, and art class. I'm really good at solving math problems and I love learning about how things work in science. In art, I enjoy painting and drawing pictures of animals or landscapes from my imagination. My least favorite subject is probably history because I have a hard time remembering all the dates and events. But I'm working on it!When I'm not in school, I love playing sports like soccer, basketball, and swimming. I'm on the school soccer team and we practice twice a week after classes. My friend Timmy is also on the team with me. I'm a pretty fast runner which helps a lot when we're racing up and down the field. I also really enjoy swimming at the community pool during the summer months.Every weekend, my family and I like to go on little adventures together. Sometimes we'll go for a hike at the nearby state park and look for cool bugs or animals along the trail. Other times we'll visit museums or go to a baseball gamedowntown. No matter what we're doing, I cherish spending quality time with my parents and sister.One of my biggest hobbies is collecting action figures and building models. I have a huge collection of superhero action figures like Spider-Man, Iron Man, and the Avengers. I also love putting together model cars, airplanes, and spaceships. It's so much fun painting them different colors and adding all the tiny details. Maybe when I'm older I'll become an engineer like my dad and design real cars and planes!There are so many cool things I want to do and learn about when I grow up. For now though, I'm just enjoying being a kid. Playing outside, hanging out with my friends, and using my creativity through art and building models. That's what childhood is all about after all!Well, I think that's enough about me for now. Thank you for taking the time to get to know me better. I look forward to meeting you all and making new friends. Don't be shy, come say hi if you see me around school or on the playground!。
美国数学竞赛AMC8必须掌握的常用单词
美国数学竞赛AMC8必须掌握的常⽤单词美国数学竞赛AMC8必须掌握的常⽤单词(按字母顺序整理)⾮正态分布abnormal distribution ⾓angle平均数average 加plus（prep.）, add（v.）, addition（n.）振幅amplitude 反正弦arc sine 反余弦arc cosine 反正切arc tangent 反余切arc cotangent 反正割arc secant 反余割arc cosecant 被加数augend, summand 加数addend 轴axis 弧arc ⾯积area 算术arithmetic 公理axiom 代数algebra 锐⾓acute angle 锐⾓三⾓形acute triangle B ⼆进制binary system 折线统计图broken line graph 底base条形统计图bar graph重⼼barycentre（BrE, barycenter（AmE）C 全等congruent 曲线统计图curve diagram 进位carry 计算calculation 系数coefficient 三次⽅程cubic equation常量constant 微积分calculus 复数complex number 坐标系coordinates 组合combination 外切圆circumcircle 余割cosecant 余切cotangent 余弦cosine 圆周circumference 圆柱cylinder 圆锥cone 圆circle ⽴⽅体cube圆⼼centre（BrE）, center（AmE）D ⼩数点decimal point ⼩数decimal ⾓度degree 除divided by （prep.）, divide（v.）, division（n.）被除数dividend 除数divisor 数字digit 分母denominator ⼗进制decimal system 微分differential 导数derivative 定积分definite integral ⾏列式determinant 分布distribution ⼗⾯体decahedron ⼗⼆⾯体dodecahedron ⼗⼆边形dodecagon ⼗边形decagon 直径diameter E 等于equals, is equal to, is equivalent to 等式，⽅程式equation 等边三⾓形equilateral trian gle 外⼼excentre（BrE）, excenter（AmE）旁⼼escentre（BrE）, escenter （AmE）正多边形equilateral polygon 九⾯体enneahedron 九边形enneagon 椭圆ellipse F 分数fraction公式formula, formulae（pl.）阶乘factorial 棱台frustum of a prism 圆台frustum of a cone G ⼏何geometry 图表graph H假设hypothesis, hypotheses（pl.）⼗⼀⾯体hendecahedron 六边形hexagon 七⾯体heptahedron 半球hemisphere 六⾯体hexahedron ⼗⼀边形hendecagon 七边形heptagon ⼗六进制hexadecimal system 柱形统计图histogram ⾼height 斜边hypotenuse 双曲线hyperbola I内⼼incentre（BrE）, incenter（AmE）⼆⼗⾯体icosahedron图象imag ⽆穷⼤infinite（a.）infinity（n.）⽆穷⼩infinitesimal 积分integrale 等腰梯形isosceles trapezoid 不定积分indefinite integral 不等式inequation 整数integer ⼩于is lesser than ⼤于is greater than ⼤于等于is equal or greater than线line ⼩于等于is equal or lesser than ⽆效数字insignificant digit 相交intersect ⽆理数irrational number 虚数imaginary number 等腰三⾓形isosceles triangle 内切圆inscribed circle 极限limit 直⾓边leg 长length 轨迹locus, loca（pl.）M数学mathematics, maths（BrE）, math（AmE）被减数minuend 被乘数multiplicand, 乘数multiplicator 单项式monomial 单调性monotonicity矩阵matrix N 正态分布normal distribution 数number ⾃然数natural number 分⼦numerator 负negative 零null, zero, nought, nil O运算符operator 运算operation 钝⾓obtuse angle 钝⾓三⾓形obtuse triangle 垂⼼orthocentre（BrE）, orthocenter（AmE）原点origin ⼋⾯体octahedron⼋边形octagon P抛物线parabola 五⾯体pentahedron 平⾏六⾯体parallelepiped 相位phase周期period证明prove命题proposition 积product 正positive 多项式polynomial, multinomial 奇偶性parity 周期性periodicity点point ⾯plane 平⾏parallel 周⾓perigon平⾏四边形parallelogram 勾股定理Pythagorean theorem扇形统计图pie diagram 概率，或然率probability排列permutation ⽐例propotion 百分⽐percent百分点percentage 百分位数percentile 多⾯体polyhedron 圆周率p i 棱锥pyramid 棱柱prism 周长perimeter五边形pentagon 多边形polygon Q商quotient ⼆次⽅程quadratic equation 四次⽅程quartic equation 四边形quadrilateral R直⾓梯形right trapezoid 标准差root-mean-square deviation, standard deviation 差remainder⽐ratio 四舍五⼊round 下舍⼊round down 上舍⼊round up 值域range 有理数rational number 实数real number 直⾓right angle 射线radial 弧度radian 直⾓三⾓形right triangle 矩形rectangle 旋转rotation 菱形rhomb, rhombus, rhombi（pl.）,diamond 环ring 半径radius S正⽅形square 有效数字significant digit ⼀次⽅程simple equation 体solid 线段segment 平⾓straight angle 边side不等边三⾓形scalene triangle 空间space 球sphere 正弦sine 统计statistics 和sum 减minus（prep.）, subtract（v.）, subtraction （n.）减数subtrahend 数列，级数series 正割secant表⾯积surface area 相似similar半圆semicircle 扇形sector T梯形trapezoid 截尾truncation 定理theorem乘times（prep.）, multiply（v.）, multiplication（n.）faciend三⾓形triangle 正切tangent 三⾓trigonometry四⾯体tetrahedron U未知数unknown, x-factor, y-factor, z-factor 底⾯undersurface 变量variable⽅差variance 体积volume W 权weight, significance宽width 加权平均数weighted average X 坐标轴x-axis, y-axis, z-axis 横坐标x-coordinate 纵坐标y-coordinate数学mathematics, maths（BrE）, math（AmE）被除数dividend除数divisor 商quotient 等于equals, is equal to, is equivalent to ⼤于is greater than ⼩于is lesser than ⼤于等于is equal or greater than ⼩于等于is equal or lesser than 运算符operator数字digit 数number ⾃然数natural number 公理axiom定理theorem 计算calculation 运算operation 证明prove假设hypothesis, hypotheses（pl.）命题proposition 算术arithmetic 加plus（prep.）, add（v.）, addition（n.）被加数augend, summand 加数addend 和sum 减minus（prep.）, subtract（v.）, subtraction（n.）被减数minuend 减数subtrahend 差remainder 乘times（prep.）, multiply（v.）, multiplication（n.）被乘数multiplicand, faciend 乘数multiplicator 积product除divided by（prep.）, divide（v.）, division（n.）整数integer⼩数decimal ⼩数点decimal point 分数fraction分⼦numerator 分母denominator ⽐ratio正positive 负negative 零null, zero, nought, nil⼗进制decimal system ⼆进制binary system ⼗六进制hexadecimal system 权weight, significance进位carry 截尾truncation 四舍五⼊round下舍⼊round down 上舍⼊round up有效数字significant digit ⽆效数字insignificant digit代数algebra 公式formula, formulae（pl.）单项式monomial多项式polynomial, multinomial 系数coefficient未知数unknown, x-factor, y-factor, z-factor 等式，⽅程式equation⼀次⽅程simple equation ⼆次⽅程quadratic equation 三次⽅程cubic equation 四次⽅程quartic equation 不等式inequation阶乘factorial 对数logarithm 指数，幂exponent 乘⽅power⼆次⽅，平⽅square 三次⽅，⽴⽅cube 四次⽅the power of four, the fourth power n次⽅the power of n, the nth power开⽅evolution, extraction ⼆次⽅根，平⽅根square root三次⽅根，⽴⽅根cube root 四次⽅根the root of four, the fourth root n次⽅根the root of n, the nth root 集合aggregate元素element 空集void ⼦集subset 交集intersection 并集union 补集complement 映射mapping 函数function 定义域domain, field of definition 值域range 常量constant变量variable 单调性monotonicity 奇偶性parity周期性periodicity 图象image 数列，级数series 微积分calculus微分differential 导数derivative 极限limit⽆穷⼤infinite（a.）infinity（n.）⽆穷⼩infinitesimal积分integral 定积分definite integral不定积分indefinite integral 有理数rational number⽆理数irrational number 实数real number虚数imaginary number 复数complex number 矩阵matrix⾏列式determinant ⼏何geometry 点point 线line ⾯plane 体solid 线段segment 射线radial平⾏parallel 相交intersect ⾓angle ⾓度degree 弧度radian锐⾓acute angle 直⾓right angle 钝⾓obtuse angle 平⾓straight angle 周⾓perigon 底base 边side ⾼height 三⾓形triangle锐⾓三⾓形acute triangle 直⾓三⾓形right triangle 直⾓边leg斜边hypotenuse 勾股定理Pythagorean theorem 钝⾓三⾓形obtuse triangle 不等边三⾓形scalene triangle 等腰三⾓形isosceles triangle 等边三⾓形equilateral triangle 四边形quadrilateral平⾏四边形parallelogram 矩形rectangle长length 宽width 菱形rhomb, rhombus, rhombi（pl.）, diamond正⽅形square 梯形trapezoid 直⾓梯形right trapezoid等腰梯形isosceles trapezoid 五边形pentagon 六边形hexagon 七边形heptagon ⼋边形octagon 九边形enneagon⼗边形decagon ⼗⼀边形hendecagon ⼗⼆边形dodecagon 多边形polygon 正多边形equilateral polygon 圆circle圆⼼centre（BrE）, center（AmE）半径radius 直径diameter 圆周率pi 弧arc半圆semicircle 扇形sector 环ring 椭圆ellipse 圆周circumference 周长perimeter ⾯积area 轨迹locus, loca（pl.）相似similar 全等congruent 四⾯体tetrahedron 五⾯体pentahedron六⾯体hexahedron 平⾏六⾯体parallelepiped ⽴⽅体cube 七⾯体heptahedron ⼋⾯体octahedron 九⾯体enneahedron ⼗⾯体decahedron⼗⼀⾯体hendecahedron ⼗⼆⾯体dodecahedron ⼆⼗⾯体icosahedron多⾯体polyhedron 棱锥pyramid 棱柱prism 棱台frustum of a prism旋转rotation 轴axis 圆锥cone 圆柱cylinder 圆台frustum of a cone 球sphere 半球hemisphere 底⾯undersurface 表⾯积surface area 体积volume 空间space 坐标系coordinates 坐标轴x-axis,y-axis, z-axis 横坐标x-coordinate 纵坐标y-coordinate原点origin 双曲线hyperbola 抛物线parabola 三⾓trigonometry 正弦sine 余弦cosine 正切tangent 余切cotangent 正割secant 余割cosecant 反正弦arc sine 反余弦arc cosine 反正切arc tangent 反余切arc cotangent 反正割arc secant 反余割arc cosecant 相位phase 周期period 振幅amplitude 内⼼incentre（BrE）, incenter （AmE）外⼼excentre（BrE）, excenter（AmE）旁⼼escentre（BrE）, escenter （AmE）垂⼼orthocentre（BrE）,orthocenter（AmE）重⼼barycentre （BrE）, barycenter（AmE）内切圆inscribed circle 外切圆circumcircle 统计statistics 平均数average 加权平均数weighted average⽅差variance 标准差root-mean-square deviation, standard deviation ⽐例propotion 百分⽐percent 百分点percentage 百分位数percentile 排列permutation 组合combination 概率，或然率probability 分布distribution 正态分布normal distribution⾮正态分布abnormal distribution 图表graph 条形统计图bar graph 柱形统计图histogram 折线统计图broken line graph 曲线统计图curve diagram。
math库中的数学函数
math库中的数学函数Math库是Python中内置的数学函数库，提供了一系列用于执行数学运算的函数和常量。
以下是Math库中的一些常用的数学函数：1.数值函数：- ceil(x): 返回大于或等于x的最小整数。
- floor(x): 返回小于或等于x的最大整数。
- round(x, n): 返回x的四舍五入值，n是可选的小数位数，如果省略则默认为0。
- trunc(x): 返回x的整数部分。
- fabs(x): 返回x的绝对值。
- sqrt(x): 返回x的平方根。
- pow(x, y): 返回x的y次方。
- exp(x): 返回e的x次方。
- log(x): 返回x的自然对数。
- log10(x): 返回x的以10为底的对数。
2.三角函数：- sin(x): 返回x的正弦值，x的单位是弧度。
- cos(x): 返回x的余弦值，x的单位是弧度。
- tan(x): 返回x的正切值，x的单位是弧度。
- asin(x): 返回x的反正弦值，返回值在 -pi/2 到 pi/2 之间。
- acos(x): 返回x的反余弦值，返回值在 0 到 pi 之间。
- atan(x): 返回x的反正切值，返回值在 -pi/2 到 pi/2 之间。
- atan2(y, x): 返回y / x的反正切值，返回值在 -pi 到 pi 之间。
3.超越函数：- sinh(x): 返回x的双曲正弦值。
- cosh(x): 返回x的双曲余弦值。
- tanh(x): 返回x的双曲正切值。
- asinh(x): 返回x的反双曲正弦值。
- acosh(x): 返回x的反双曲余弦值。
- atanh(x): 返回x的反双曲正切值。
4.统计函数：- sum(iterable): 返回可迭代对象中的所有元素之和。
- max(iterable): 返回可迭代对象中的最大值。
- min(iterable): 返回可迭代对象中的最小值。
- mean(iterable): 返回可迭代对象中所有元素的算术平均值。
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AwesomeMath Admission Test Cover Sheet
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Admission Test A B C Check one
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Awesome Math Test A
Jan. 14 - Feb. 4, 2011• Do not be discouraged if you cannot solve all of the questions: the test is not made
to be easy. We want to see the solutions you come up with no matter how many
problems you solve.
• Include all significant steps in your reasoning and computation. We are interested
in your ability to present your work, so unsupported answers will receive much less
credit than well-reasoned progress towards a solution without a correct answer.
• In this document, you will find a cover sheet and an answer sheet. Print out each
one and make several copies of the blank answer sheet. Fill out the top of each
answer sheet as you go, and then fill out the cover sheet when you are finished. Start
each problem on a new answer sheet.
• All the work you present must be your own.
• Do not be intimidated! Some of the problems involve complex mathematical ideas,
but all can be solved using only elementary techniques, admittedly combined in
clever ways.
• Be patient and persisntent. Learning comes more from struggling with problems
than from solving them. Problem-solving becomes easier with experience. Success is
not a function of cleverness alone.
• Postmark or submit your solutions by e-mail (preferred) by Friday, Feb. 4, 2011.
• Make sure that the cover sheet is the first page of your submission, and that it is
completely filled out. Solutions are to be mailed to the following address:
Dr. Titu Andreescu
3425 Neiman Road, Plano TX 75025
If you e-mail your solutions, please send them to
tandreescu@
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as an attachment in either .doc or .pdf format. If you write and scan your solutions,
insert the scans into a .doc or .pdf file and send just the one file.
Please go to the next page for the problems
Admission Test A
Jan.14-Feb.4,2011
ing each of the 10digits exactly once,form three numbers such that their sum S is as small as possible.Find S.
2.Evaluate 1−20112 1−20113 ··· 1−20112010
.3.Find all primes p such that 2011p +8is the product of two consecutive odd numbers.
4.How many positive integers less than 2011are divisible by 5and 6but not divisible by 7or 8?
5.Prove that among any five perfect squares there are two whose difference is divisible by 12.
6.Let ABC be a triangle with ∠A =90◦and let P be a point on the hypotenuse BC.Prove that AB 2P C +AC 2
P B ≥BC 3P A 2+P B ·P C
.7.Find all positive integers n for which (n −2)!+(n +2)!is a perfect square.
8.Prove that any parallelogram can be dissected in 2011cyclic quadrilaterals.
9.Are there distinct prime numbers p,q,r such that qr divides p 2+11,rp divides q 2+11,and pq divides r 2+11?What if 11is replaced by 10?
10.Find all integers n ≥2for which n √3n +4n +5n +8n +10n is an integer.
AwesomeMath Answer Sheet
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Write neatly! All work should be inside the box. Do NOT write on the back of the page!。