高中数学课程描述(英文)

1、精选优质文档-倾情为你奉上Mathematics Course DescriptionMathematics 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 cou

2、rses are chosen by students which is according their interests. Compulsory Courses: Set TheoryCourse 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

3、 are prepared 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 b

4、etween functions and sets to set the stage for the next step Key Topics:Ø The language of set theoryØ Set membershipØ Subsets, supersets, and equalityØ Set theory and functions FunctionsCourse content:This lesson begins with talking about the role of functions and look at the con

5、cept 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 graphs. This course will begin with the absolute value function and then move on to discuss both exponential and logarithmic functions. Students

6、get an opportunity to see how these functions can be used to model various kinds of phenomena. Key Topics:Ø Single-variable functionsØ Two variable functionsØ Exponential function Ø Logarithmic function Ø Power- function CalculusCourse content:In the first step, the course i

7、ntroduces 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:Ø Limit theo

8、ryØ DerivativeØ Differential AlgorithmCourse content:Introduce the conception of algorithm and the method to design algorithm. Then the figures of flow charts and the conception of logical structure, like sequential structure, contracture of condition and cycle structure are introduced to

9、students. 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:Ø Algorithm Ø Logical structure of flow chart and algorith

10、mØ Output statementØ Input statement Ø Assignment statement StatisticsCourse content:The course starts with basic knowledge of statistics, such as systematic sampling and group sampling. During the lesson students acquire the knowledge like how to estimate collectivity distribution ac

11、cording 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,

12、 how to calculate regression line, and what is Method of Square. Key Topics:Ø Systematic samplingØ Group samplingØ Relationship between two variablesØ Interdependency of two variables Basic Trigonometry ICourse content:This course talks about the properties of triangles and looks

13、 at the relationship that exists between their internal angles and lengths 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 properti

14、es and functions to solve a number of issues. Key Topics:Ø Common AnglesØ The polar coordinate systemØ Triangles propertiesØ Right trianglesØ The trigonometric functionsØ Applications of basic trigonometry Basic Trigonometry IICourse content:This course will look at the

15、 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:Ø Derivative trigo

16、nometric functionsØ Inverse trig functionsØ Identitiesl Pythagorean identitiesl Reduction identitiesl Angle sum/Difference identitiesl Double-angle identities Analytic Geometry ICourse content:This course introduces analytic geometry as the means for using functions and polynomials to math

17、ematically 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 r

18、espect to lines, points, planes and also briefly talk about ellipsoidal intersections. Key Topics:Ø Parametric representationØ Parallel and perpendicular linesØ Intersection of two linesØ Distance from a point to a lineØ Angles between lines Analytic Geometry IICourse conten

19、t: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 Light

20、ing model to see how vector dot products can be used to determine the lighting and shading of points across a surface. Key Topics:Ø ReflectionsØ Polygon/polygon intersectionØ Lighting Sequence of Number Course content:This course begin with introducing several conceptions of sequence

21、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, students gradually understand and

22、utilize the knowledge of sequence of number, eventually students are able to solve mathematical questions. Key Topics:Ø Sequence of numberØ Geometric sequenceØ Arithmetic sequence Inequality This course introduces conception of inequality as well as its properties. In the following le

23、ssons students learn the solutions and arithmetic of one-variable quadratic inequality, two variables inequality, fundamental inequality as well how to solve simple linear programming problems. Key Topics:Ø Unequal relationship and Inequality Ø One-variable quadratic inequality and its sol

24、utionØ Two-variable inequality and linear programming Ø Fundamental inequality Vector MathematicsCourse 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

25、 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 v

26、ector representations of mesh vertices. Key Topics:Ø Linear combinationsØ Vector representationsØ Addition/ subtractionØ Scalar multiplication/ divisionØ The dot productØ Vector projectionØ The cross product Optional CoursesMatrix ICourse content:In this course, st

27、udents 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 tha

28、t 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:Ø Matrix r

29、elationsØ Matrix operationsl Addition/subtractionl Scalar multiplicationl Matrix Multiplicationl Transposel Determinantl Inverse PolynomialsCourse 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

30、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 a

31、pproximate 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:Ø Polynomial algebra ( single variable)l addition/subtractionl multiplication/divisionØ Quadratic equationsØ Graphing polynomials Logical Terms in MathematicsCourse content:This course introduces the relationships of four kinds of statements, necessary and sufficient conditions, basic logical conjunctions, existing quantifier and universal quantifier. B