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What you will learn in Mathematical Modelling & Applied Mathematics

1. Estimation and Order-of-Magnitude Reasoning
A question nobody knows the answer to, decomposed into factors you can each bound.
2. The Modelling Cycle
Situation, assumptions, model, solution, validation, decision — and the loop back.
3. Assumptions and Validation
Turn one assumption off and watch the answer move. That number is which assumption matters.
4. Dimensional Analysis
The check that costs one line and needs no data — and what passing it does not prove.
5. Proportional and Inverse Reasoning
Double the speed, quadruple the braking distance. The exponent is the whole story.
6. Linear Models
Two parameters, both of which mean something.
7. Exponential and Logarithmic Models
Doubling time, half-life, and the straight line a logarithmic axis makes.
8. Periodic Models
Amplitude, period, phase and midline, fitted to something cyclical.
9. Financial Mathematics
A geometric series with money in it — EMI, amortisation, annuities, inflation.
10. Population and Resource Models
Exponential early, logistic late, and the point where the early data stops deciding.
11. Fitting a Model to Data
Fit on the half you can see, predict the half you cannot, and only then look.
12. Case Studies Across the Platform
Six investigations, each owned by the volume that owns its facts.

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1. Estimation and Order-of-Magnitude Reasoning
A question nobody knows the answer to, decomposed into factors you can each bound.
2. The Modelling Cycle
Situation, assumptions, model, solution, validation, decision — and the loop back.
3. Assumptions and Validation
Turn one assumption off and watch the answer move. That number is which assumption matters.
4. Dimensional Analysis
The check that costs one line and needs no data — and what passing it does not prove.
5. Proportional and Inverse Reasoning
Double the speed, quadruple the braking distance. The exponent is the whole story.
6. Linear Models
Two parameters, both of which mean something.
7. Exponential and Logarithmic Models
Doubling time, half-life, and the straight line a logarithmic axis makes.
8. Periodic Models
Amplitude, period, phase and midline, fitted to something cyclical.
9. Financial Mathematics
A geometric series with money in it — EMI, amortisation, annuities, inflation.
10. Population and Resource Models
Exponential early, logistic late, and the point where the early data stops deciding.
11. Fitting a Model to Data
Fit on the half you can see, predict the half you cannot, and only then look.
12. Case Studies Across the Platform
Six investigations, each owned by the volume that owns its facts.