Program 2
An introduction to areas of mathematics, including Combinatorics, Number Theory, Algebra, and Geometry, is provided through an interactive course. This course is taught by an experienced student instructor and is suitable for students who are seeking an overview of intriguing mathematical topics. It serves as an excellent introductory course for the Maths Olympiad program, catering to students who possess some experience in problem-solving and wish to delve deeper into the subject. The course covers content similar to Program 1 but in greater detail.
Introduction Session
Date: Thursday 14th September 8:00 pm to 9:30 pm
​
Session Timing: 1.5 hours
​
Format: Online
​
Instructor: Nicole Wong and Dawn Chen
​
Contact Email: mindnzorg@gmail.com
Greetings
An opportunity to greet everyone and learn a bit more about each of you. ​​
-
Introductions
-
What you can gain from this program?
-
What are the classroom expectations?
-
Q and A
Methods of Proof
-
Why do we need proofs
-
Proof by contradiction
-
Proof by exhaustion
-
Induction
-
Contrapositive
Methods of Proof
Syllabus
Course Dates: Thursdays and Sundays 8:00 pm to 9:00 pm
Session Timing: Every session will be 1 hour long
​
Format: Online
​
Instructor: Dawn Chen and Haotian Wang
​
Contact Email: mindnzorg@gmail.com
Inequalities:
-
Intro to inequalities
-
Factoring Squares
-
AM-GM inequality
-
Cauchy-schwarz inequality
-
Rearrangement inequality
21/09/23
Session 1:
Algebra
24/09/23
Session 2:
Algebra
28/09/23
Session 3:
Number Theory
​
Polynomials:​
-
Solving for polynomial roots
-
Vieta’s Formulas
-
Factorisation
​
Functional Equations:
-
Intro to functional equations
-
Define injective, surjective, bijective
-
Remainders in division
-
Modular Arithmetic
-
Chinese Remainder Theorem
-
GCD and LCM
-
Factorising of natural numbers
-
Fermat’s Little Theorem
-
What is the euler’s phi function
-
Euler-fermat’s Theorem
01/10/23
Session 4:
Number Theory
05/10/23
Session 5:
Geometry
Triangular Properties:
-
Similar Triangles and Congruent Triangles
-
Orthocenter, Circumcentre,Centroid, Incentre
-
Ceva's Theorem
Circle Properties
-
Cyclic Quadrilaterals
-
Angle at the centre Theorem
-
Angles from Same Arc
-
Tangents to a circle
-
Alternate segment theorem
08/10/23
Session 6:
Geometry
-
Counting: Combination, permutation formulas
-
Binomial Identities
-
Pigeonhole principle
12/10/23
Session 7:
Combinatorics
​​
Game Theory
-
What is Game Theory
-
Invariants and Monovariants
-
Parity, Weighting, Colouring
