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# high school mathematical course description 高中数学课程描述

Mathematics Course Description
Mathematics course in middle school has two parts: compulsory courses and optional courses. Compulsory courses content lots of modern mathematical knowledge and conceptions, such as calculus, statistics, analytic geometry, algorithm and vector. Optional courses are choosen by students which is accrodding their interests.

Compulsory Courses:

Set Theory
Course content: This course introduces a new vocabulary and set of rules that is foundational to the mathematical discussions. Learning the basics of this all-important branch of mathematics so that students are perpared to tackle and understand the concept of mathematical functions. Students learn about how entities are grouped into sets and how to conduct various operations of sets such as unions and intersections(i.e. the algebra of sets). We conclude with a brief introduction to the relationship between functions and sets to set the stage for the next step Key Topics: ? The language of set theory ? Set membership ? Subsets, supersets, and equality ? Set theory and functions

Functions
Course content: This lesson begin with talking about the role of functions and look at the concept of mapping values between domain and range. From there student spend a good deal of time looking at how to visualize various kinds of functions using grahs. this course will begin with the absolute value function and then move on to discuss both exponential and logarithmic functions. Students get an opportunity to see how these functions can be used to model various kinds of phenomena. Key Topics: ? Single-variable functions ? Two –variable functions ? Exponential function ? Logarithmic function

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Power- function

Calculus
Course content: In the first step, the course introduces the conception of limit, derivative and differential. Then students can fully understand what is limit of number sequence and what is limit of function through some specific practices. Moreover, the method to calculate derivative is also introduced to students. Key Topics: ? Limit theory ? Derivative ? Differential

Algorithm
Course content: Introduce the conception of algorithm and the method to design algorithm. Then the figures of flow charts and the conception of logcial structure, like sequential structure, constructure of condition and cycle structure are introduced to studnets. Next step students can use the knowledge of algorithm to make simple programming language, during this procedure, student also approach to grammatical rules and statements which is as similar as BASIC language. Key Topics: ? Algorithm ? Logical structure of flow chart and algorithm ? Output statement ? Input statement ? Assingnment statement

Statistics
Course content: The course starts with basic knowledge of statistics, such as systematic sampling and group sampling. During the lesson students acquire the knowlegde like how to estimate collectivity distribution accroding frequency distribution of samples, and how to compute numerical characteristics of collectivity by looking at numerical characteristics of samples. Finally, the relationship and the interdependency of two variables is introduced to make sure that students mastered in how to make scatterplot, how to calculate regression line,and what is Method of Square.

Key Topics: ? Systematic sampling ? Group sampling ? Relationship between two variables ? Interdependency of two variables

Basic Trigonometry I
Course content: This course talks about the properties of triangles and looks at the relationship that exist between their internal angles and lenghs of their sides. This leads to discussion of the most commonly used trigonometric functions that relate triangle properties to unit circles. This includes the sine, cosine and tangent functions. Students can use these properites and functions to solve a number of issues. Key Topics: ? Common Angles ? The polar coordinate system ? Triangles properties ? Right triangles ? The trigonometric functions ? Applications of basic trigonometry

Basic Trigonometry II
Course content: This course will look at the very important inverse trig functions such as arcsin, arcos, and arctan, and see how they can be used to determine angle values. Students also learn core trig identities such as the reduction and double angle identities and use them as a means for deriving proofs. Key Topics: ? Derivative trigonometric functions ? Inverse trig functions ? Identities ? Pythagorean identities ? Reduction identities ? Angle sum/Difference identities ? Double-angle identities

Analytic Geometry I
Course content: This course introduces analytic geometry as the means for using functions and polynomials to mathematically represent points, lines, planes and ellipses. All of these concepts are vital in students mathematical development since they are used in rendering and optimization, collision detection, response and other critical areas. Students look at intersection formulas and distance formulas with respect to lines, points, planes and also briefly talk about ellipsoidal intersections. Key Topics: ? Parametric representation ? Parallel and perpendicular lines ? Intersection of two lines ? Distance from a point to a line ? Angles between lines

Analytic Geometry II
Course content: Students look at how analytic geometry plays an important role in a number of different areas of class design. Students continue intersection discussion by looking at a way to detect collision between two convex polygons. Then students can wrap things up with a look at the Lambertian Diffuse Lighting model to see how vector dot products can be used to determine the lighting and shading of points across a surface. Key Topics: ? Reflections ? Polygon/polygon intersection ? Lighting

Sequence of Number
Course content: This course begin with introducing serveral conceptions of sequence of number, such as, term, finite sequence of number, infinite sequence of number, formula of general term and recurrence formula.Then, the conception of geometric sequence and arithmetic sequence is introduced to students. Through practices and mathematical games, stuendents gradually understand and utilize the knowldege of sequence of number, eventually students are able to sovle mathematical questions.

Key Topics: ? Sequence of number ? Geomertic sequence ? Arithmetic sequence

Inequality
This course introduces conception of inequality as well as its properties. In the following lessons students learn the solutions and arithmetics of one-variable quadratic inequality, two variables inequality, fundamental inequality as well how to solve simple linear programming problems. Key Topics: ? Inequal relationship and Inequality ? One-variable quadratic inequality and its solution ? Two-variable inequality and linear programming ? Fundamental inequality

Vector Mathematics
Course content: After an introduction to the concept of vectors, students look at how to perform various important mathematical operations on them. This includes addition and subtraction, scalar multiplication, and the all-important dot and cross products. After laying this computational foundation, students engage in games and talk about their relationship with planes and the plane representation, revisit distance calculations using vectors and see how to rotate and scale geometry using vector representations of mesh vertices. Key Topics: ? Linear combinations ? Vector representations ? Addition/ subtraction ? Scalar multiplication/ division ? The dot product ? Vector projection ? The cross product

Optional Courses Matrix I

Course content: In this course, students are introduced to the concept of a matrix like vectors, matrices and so on. In the first two lessons, student look at matrices from a purely mathematical perspective. The course talks about what matrices are and what problems they are intended to solve and then looks at various operations that can be performed using them. This includes topics like matrix addition and subtraction and multiplication by scalars or by other matrices. At the end, students can conclude this course with an overview of the concept of using matrices to solve system of linear equations. Key Topics: ? Matrix relations ? Matrix operations

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Scalar multiplication Matrix Multiplication Transpose Determinant Inverse

Polynomials
Course content: This course begins with an examination of the algebra of polynomials and then move on to look at the graphs for various kinds of polynomial functions. The course starts with linear interpolation using polynomials that is commonly used to draw polygons on display. From there students are asked to look at how to take complex functions that would be too costly to compute in a relatively relaxed studying environment and use polynomials to approximate the behavior of the function to produce similar results. Students can wrap things up by looking at how polynomials can be used as means for predicting the future values of variables. Key Topics: ? Polynomial algebra ( single varible) ? addition/subtraction ? multiplication/division ? Quadratic equations ? Graphing polynomials

Logical Terms in Mathematics
Course content:

This course introduces the relationshiop of four kinds of statements, necessary and sufficient conditions, basic logical conjunctions,existing quantifier and universal quantifier. By learning mathematical logic terms, students can be mastered in the usage of common logical terms and can self-correct logical mistakes. At the end of this course, students can deeply understand the mathematical expression is not only accurate but also concise. Key Topics: ? Statement and its relationship ? Necessary and sufficient conditions ? Basic logical conjuncitons ? Existing quantifier and universal quantifier

Conic Sections and Equation
Course content: By using the knowlegde of coordinate method which have been taught in the lesson of linear and circle, in this lesson students learn how to set an equation accroding the character of conic sections. Students is able to find out the property of conic sections during establishing equations. The aim of this course is to make students understand the idea of coobination of number and shape by using the method of coordinate to solve simple geometrical problems which are related to conic sections. Key Topics: ? Curve and equation ? Oval ? Hyperbola ? Parabola

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