Chapter 1 Algebraic Methods

1.1 Proof

The first topic of this chapter is Mathematical Proof and, in particular, Proof by Contradiction.

This is an area of Mathematics where precise language is essential.

The other topic required for the first exercise in this chapter is Negation Statements.

Have a read through these Worked Examples of Negation Statements published by the University of Toronto.

As you will see, such statements are not necessarily obvious.

Proof by Contradiction (8:58)

Complete Exercise 1A on Pages 4 and 5 of the textbook

Do the whole exercise marking one question at a time from Exercise 1A Solutions

Formal Proofs

The A-level syllabus states that there are two formal proofs you could possibly be required to reproduce in your exam:

The Number of Primes is Infinite (1:53):

The Square Root of 2 is Irrational (6:16):

These two proofs are also presented on Page 3 of the textbook.

Both proofs should be committed to memory.

1.2 Algebraic Fractions

Algebraic Fractions (7:33)

Now select a range of questions to do from Exercises 1B and 1C on Pages 6 to 8 of the textbook.

Mark from the solutions below: