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1. Algebra

1.1. Finding x

1.1.1. Simple linear equations

1.1.2. Simultaneous equations

1.1.2.1. linear

1.1.2.2. non-linear

1.1.3. quadratic++ eqns

1.1.3.1. fundamental thm of algebra

1.2. Handling all that stuff

1.2.1. Factorisation

1.2.2. Simplification

1.2.3. Some notational tricks

1.3. vector spaces

1.3.1. matrices

1.3.2. inner products

1.3.3. bases and axes

2. Arithmetic

2.1. Why drill?

2.2. Long arithmetic

2.3. decimal system

3. Calculus

3.1. Intro

3.1.1. Limits!

3.1.2. Rates of change

3.1.3. Riemann sums

3.1.4. Inverse functions & the FTofC

3.2. Diff eqns

3.3. Taylor series

3.4. Tensors?

4. Mechanics

4.1. Newton's Laws

4.1.1. Inertial ref frames

4.1.2. eqns of motion

4.1.2.1. diff eqns

4.1.3. conservation laws

4.1.3.1. collisions

4.1.3.2. identical particles colliding elastically

4.1.3.3. energy graphs

4.2. Oscillators

4.2.1. some examples

4.2.2. harmonic approximation

5. Particle Physics

5.1. Roots of quantum

5.2. Families aka models

5.2.1. Standard model

5.2.2. supersymmetry

6. Complex numbers

6.1. number systems

6.2. ways of representing

6.3. e to the i pi . . .