Timing: Wednesday night 6:30 - 8:00 PM, Weekly for 10 weeks

Date: Starting from July 6th 2022

Workshop Location: Zoom online class

We will try to cover the following topics as much as we can in the classes.

Number Theory

• Calculation and properties of congruence
• Euler's function
• Fermat's little theorem
• Floor function
• Odd and even numbers
• Number of factors
• Conversion between different numerical systems

Functions and Polynomials

• Abstract functions
• Symmetry
• Vieta 's theorem of high-degree polynomials
• Remainder theorem
• Factor theorem

Sequences and Series

• Recursive expressions
• Fibonacci sequence
• Sum of sequences
• Geometrical series

Algebra

• Binomial theorem
• Factorization and equation
• Basic inequalities

Geometry

• Sine rule and cosine rule
• Similar triangles
• Heron's formula
• Properties of circle
• 3-d geometry

Analytic Geometry

• Equation of straight lines
• Distance between a point and a line
• Equation of circle

Permutation and Combination

• Principle of inclusion and exclusion
• Principle of addition
• Principle of multiplication
• Models of permutation and combination

Probability and Statistics

• Conditional probability
• Complex probability problems
• Basic statistical concepts

Logic and Reasoning

• Word problems
• Comprehension of complex problems
• Conversion of problems

Logarithm

• Rules of logarithm
• Logarithm and exponent
• Equation of logarithm

Complex Numbers and Trigonometry

• Trigonometrical identities
• Maximum and minimum of trig functions
• Polar form and exponential form of complex numbers
• De Moivre's theorem