Program 1
Explore various areas of mathematics you may not be familiar with, including Combinatorics, Number Theory, Algebra, and Geometry, through an interactive course. This course is taught by an experienced student instructor and is suitable for students who are interested in problem-solving and want to understand what Maths Olympiad is about. The course is designed for beginners who may not have much experience in these areas of maths but are curious to learn more.
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Recommended for students up to Year 10.
Introduction Session
Date:Thursday 14th September 8:00 pm to 9:30 pm
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Session Timing: 1.5 hours
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Format: Online
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Instructor: Nicole Wong and Dawn Chen
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Contact Email: mindnzorg@gmail.com
Greetings
Methods of Proof
An opportunity to greet everyone and learn a bit more about each of you. ​​
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Introductions
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What you can gain from this program?
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What are the classroom expectations?
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Q and A
Methods of Proof
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Why do we need proofs
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Proof by contradiction
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Proof by exhaustion
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Induction
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Contrapositive
Course Outline
Course Dates: Tuesdays and Saturday 8:00 pm to 9:00 pm
Session Timing: Every session will be 1 hour long
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Format: Online
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Instructors: Nicole Wong, Ethan Chuang and Chris Pan
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Contact Email: mindnzorg@gmail.com
19/09/23
Session 1:
Number Theory​
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Remainders in division
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Intro to Modular Arithmetic
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Prime factorization of natural numbers
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GCD and LCM
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Factorising natural numbers
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Divisor formulas
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Fermat’s Little Theorem
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What is Euler's phi function?
23/09/23
Session 2:
Number Theory
26/09/23
Session 3:
Geometry
Triangular Properties:
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Similar and Congruent Triangles
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Orthocenter, Circumcentre,Centroid, Incentre
Circle Properties
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Cyclic Quadrilaterals
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Angle at the centre Theorem
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Angles from Same Arc
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Tangents to a circle
30/09/23
Session 4:
Geometry
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Counting: Combination, permutation formulas
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Binomial Identities
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Pigeonhole principle
03/10/23
Session 5:
Combinatorics
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Game Theory
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What is Game Theory?
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Invariants and Monovariants
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Parity, Colouring
07/10/23
Session 6:
Combinatorics
Introduction to algebra:
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Intro to polynomials
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Completing squares
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Factorising quadratics
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Solving for polynomial roots
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Vieta's formula
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10/10/23
Session 7:
Algebra
Inequalities:
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Intro to inequalities
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Factorising square inequalities
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General AM-GM inequalities
14/10/23
Session 8:
Algebra
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