User:Chess64

Autobiography

I'm not very smart, but I try to learn from my peers at AoPS. I have never really done well in a major math competition yet, and I have just finished grade nine. I have started to work intensely on olympiad level math in order to have a better chance of achieving my ambitious goals for the USAMO in 2007.

I'm also very involved with my religion. I'm a Muslim -- but not just any Muslim; I'm a member of the Ahmadiyya Muslim Community, which is greatly persecuted by mainstream Muslims. This is because we have accepted Mirza Ghulam Ahmad as the Promised Messiah and Reformer. Mainstream Muslims claim since the Holy Qur'an states that Prophet Muhammad (peace be on him) was the "Seal of the Prophets", there can be no prophets after him. But why would God cease to send revelations to His creation? "Seal of the Prophets" means that Prophet Muhammad was the last prophet to bring a new law to the people. Reformers, like Hadhrat Mirza Ghulam Ahmad, can still come.

Website

Mathematical Ideas

Nontrivial Contributions

Algebra

• Trivial inequality
• Completing the square
• Quadratic Equations
• Quadratic Formula
• Vieta's formulas

Combinatorics

• Combinatorics
• Combinations
• Combinatorical identities
• Complementary counting
• Casework
• Overcounting
• Geometric probability
• Constructive counting
• Principle of Inclusion-Exclusion
• Correspondence
• Recursion

Number Theory

• Number theory
• Relatively prime
• Simon's Favorite Factoring Trick
• Modular arithmetic
• Fermat's Little Theorem
• Euler's totient function
• Euler's Totient Theorem
• Wilson's Theorem

Proof Techniques

• Proof by contradiction
• Pigeonhole Principle

Miscellaneous

• Brute forcing
• LaTeX