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, the complex plane, polar representation
- De Moivre’s theorem, Fundamental theorem of algebra
- Polynomials, factorization, roots, error-correcting codes
- Equations over finite fields, partial fractions

To be successful in MATH 135 you really need to know the theorems, definitions and methods very well. The proofs are most important part for Math 135.

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