Further pure mathematics 2

1. NUMBER THEORY

1.1 The division algorithm

1.2 The Euclidean algorithm

1.3 Modular arithmetic

1.4 Divisibility tests

1.5 Solving congruence equations

1.6 Fermat's little theorem

1.7 Combinatorics

1.8 Mixed exercise 1

1.9 Review exercise for chapter 1

 

2. GROUPS

2.1 The axioms for a group

2.2 Cayley tables and finite groups

2.3 Order and subgroups

2.4 Isomorphism

2.5 Mixed exercise 2

2.6 Review exercise for chapter 2

 

3. COMPLEX NUMBERS

3.1 Loci in an Argand diagram

3.2 Regions in an Argand diagram

3.3 Transformations of the complex plane

3.4 Mixed exercise 3

3.5 Review exercise for chapter 3

 

4. RECURRENCE RELATIONS

4.1 Forming recurrence relations

4.2 Solving first-order recurrence relations

4.3 Solving second-order recurrence relations

4.4 Proving closed forms

4.5 Mixed exercise 4

4.6 Review exercise for chapter 4

 

5. MATRIX ALGEBRA

5.1 Eigenvalues and eigenvectors

5.2 Reducing matrices to diagonal form

5.3 The Cayley-Hamilton theorem

5.4 Mixed exercise 5

5.5 Review exercise for chapter 5

 

6. INTEGRATION TECHNIQUES

6.1 Reduction formulae

6.2 Arc length

6.3 Area of a surface of revolution

6.4 Mixed exercise 6

6.5 Review exercise for chapter 6

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