數學課程大綱

哲慧的星級數學課程

M1 Course Outline

  • Algebra

    1. Simplifying algebraic expressions
    2. Solving linear and quadratic equations
    3. Inequalities and their solutions
    4. Functions and their representation (graphs, tables, and equations)
    5. Transformation of functions (reflection, translation, dilation)

  • Coordinate Geometry

    1. Distance and midpoint formula
    2. Equations of lines and their slopes
    3. Intersection of lines and angle between lines
    4. Circle equations and their properties
    5. Conic sections (parabolas, ellipses, hyperbolas)

  • Calculus

    1. Limits and derivatives
    2. Differentiation rules (power rule, chain rule, product rule)
    3. Maxima and minima of functions
    4. Implicit differentiation and related rates
    5. Integrals and antiderivatives

  • Vectors

    1. Vector operations (addition, subtraction, scalar multiplication)
    2. Vector representation (magnitude and direction)
    3. Dot product and cross product
    4. Applications of vectors in geometry and physics
    5. Parametric equations and their representation in space

  • Trigonometry

    1. Trigonometric functions (sine, cosine, tangent)
    2. Trigonometric ratios and their relationships
    3. Inverse trigonometric functions
    4. Trigonometric identities and equations
    5. Applications of trigonometry in mathematics and science

  • Statistics

    1. Data representation (tables, graphs, histograms)
    2. Measures of central tendency (mean, median, mode)
    3. Measures of dispersion (range, variance, standard deviation)
    4. Probability distributions (binomial, normal)
    5. Hypothesis testing and confidence intervals

M2 Course Outline

  • Algebra and Calculus

    1. Polynomial functions and their properties
    2. Factorization of polynomials and synthetic division
    3. Rational functions and their graphs
    4. Indeterminate forms and L’Hôpital’s rule
    5. Exponential and logarithmic functions
    6. Differential equations and their solutions

  • Coordinate Geometry

    1. Three-dimensional coordinate geometry
    2. Equations of planes and their intersections
    3. Cylinders, cones, and spheres
    4. Vector equations of lines and planes
    5. Parametric equations in three dimensions

  • Trigonometry

    1. Trigonometry in two dimensions
    2. Trigonometry in three dimensions
    3. Solutions of triangles and their applications
    4. Law of sines and cosines
    5. Vectors and their applications in trigonometry

  • Statistics and Probability

    1. Sampling and estimation
    2. Correlation and regression
    3. Discrete random variables and their distributions
    4. Continuous random variables and their distributions
    5. Joint and marginal distributions
    6. Conditional distributions and independence

  • Combinatorics and Discrete Mathematics

    1. Counting principles (permutation and combination)
    2. Principle of inclusion and exclusion
    3. Generating functions and recurrence relations
    4. Graph theory (network flows and Euler paths)
    5. Matrix algebra and its applications

  • Numerical Methods

    1. Numerical solutions of equations (bisection, Newton-Raphson)
    2. Interpolation and extrapolation (Lagrange, Newton)
    3. Numerical differentiation and integration
    4. Numerical solutions of differential equations (Euler, Runge-Kutta)
    5. Error analysis and its impact on numerical methods

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