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MATH 135 Waterloo

MATH 135 (Algebra for Honours Mathematics) is one of the most difficult first year courses in University of Waterloo. This course covers the following topics: Logic, proofs, mathematical induction Divisibility, primes, GCD Extended Euclidean algorithm, linear Diophantine equations Linear congruences, Fermat’s little theorem, Chinese remainder theorem Public key cryptography, RSA, including fast exponentiation Complex numbers,… Continue reading →

Half angle formula

Trig identities are crucial part of trig functions and one of the most important identities in trigonometric functions is the half angle formula. In this post, we talked about different trig identities and formulas. First we recommend to visit the previous posts to review identities, including the double angle formula. Here we talk about half… Continue reading →

Double Angle Formula

In trigonometry, it is really important to know and able to use identities. One of the main and crucial categories of identities is Double Angle Formula. In this post, we talked about different trig identities and formulas. Double Angle Formulas are trigonometric identities that simplify a trigonometric function of $2x$ as of trigonometric functions of… Continue reading →

Prime numbers

What is a prime number? In mathematics, we say a natural number $p$ is a prime number if p has exactly 2 factors. For example, 11 is a prime number, because the only factors are 1 and 11. It is easy to see that the only prime numbers less than 10 are 2, 3, 5… Continue reading →

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