Learning path
Learn Applied Mathematics: Where and how it's used
Seven short stories about ratios, averages, probability, geometry, change, growth and optimisation, then the two ideas that power modern AI and 3D.
- Length
- 9 articles · about 63 min
- Level
- Beginner
- Before you start
- None. Everyday arithmetic is enough; every idea is told as a story first.
Best for: Anyone who was told maths is useful and never saw where, from students to managers
By the end
What you will be able to do
- Use ratios, percentages and rates to compare things fairly
- Read averages and spread, and spot when an outlier misleads
- Judge a positive test result without being fooled by base rates
- Measure what you cannot reach using similar triangles and angles
- Explain rates of change and why growth can be slow, then suddenly fast
- Frame a choice as optimisation under limits
- Connect vectors and gradient descent to GeoAI, 3D and machine learning
The path
Read in this order
Concept · Beginner · 7 min read
The story of the two districts: ratios, percentages and why raw numbers lie
Why 200 cases can be better news than 120, what a percentage point really is, and how fair comparisons are made.
You will learn
- A raw count tells you little until you compare it with the size of the group. Ratios and rates make comparisons fair.
- A percentage change and a change in percentage points are different things.
Start here →
Concept · Beginner · 7 min read
The story of the two rivers: averages, spread and the outlier that changes everything
Why an average can hide a flood, when the median tells the truth and how to describe how spread out a set of numbers is.
You will learn
- An average (mean) can be pulled far from what is typical by a few extreme values. The median is more resistant.
- Two sets of data with the same average can behave completely differently, so always look at the spread as well.
Read →
Concept · Beginner · 7 min read
The story of the positive test: probability, base rates and why surprising results are often wrong
A test that is 90 percent accurate can still be wrong most of the time. Learn why, with numbers you can check by hand.
You will learn
- Probability is a number from 0 to 1 that says how likely something is. It can be turned into counts to make it easier to think about.
- A rare event stays rare even after a positive test, because false alarms from the many outnumber true hits from the few.
Read →
Concept · Beginner · 7 min read
The story of the tallest tree: geometry, angles and how we measure what we cannot reach
How shadows, angles and triangles let you measure a tree, a mountain or a building, and how the same ideas drive surveying, GPS and 3D graphics.
You will learn
- Similar triangles let you measure something huge from something small, using shadows or sight lines.
- Pythagoras gives distances from two perpendicular measurements, and trigonometry turns an angle and a distance into a height.
Read →
Concept · Intermediate · 7 min read
The story of the water tank: rates of change, slopes and totals, with no fear of calculus
Calculus is just two questions: how fast is something changing right now, and how much has built up in total? A tank, a tap and a speedometer explain both.
You will learn
- A rate of change tells you how fast something is changing at a moment. On a graph, it is the slope.
- A total adds up many small amounts over time. On a graph, it is the area under a curve.
Read →
Concept · Beginner · 7 min read
The story of the lily pond: exponential growth, compounding and doubling
Why things that double are so hard to feel, what the rule of 72 tells you, and how growth and decay shape money, data, epidemics and technology.
You will learn
- Exponential growth means multiplying by the same factor each step, so the increases themselves keep growing.
- Doubling is deceptive: a pond half covered is one day from being full.
Read →
Concept · Intermediate · 8 min read
The story of the delivery rider: optimisation, constraints and finding the best answer
How to pick the best route, the best mix or the best setting when there are too many choices to try, and why computers search instead of checking everything.
You will learn
- Optimisation means finding the best choice under limits: maximise a good thing or minimise a bad thing, while obeying constraints.
- The number of possible solutions can explode, so smart methods search instead of trying everything.
Read →
Concept · Beginner · 7 min read
Vectors, coordinates and transformations: the maths behind every map and 3D scene
Points, directions, rotations and scale: the small set of ideas that sits under GIS, game engines, VR headsets and AR.
You will learn
- Every location, pixel and 3D vertex is a list of numbers, and a vector adds direction and length to it.
- The dot product measures alignment, and the cross product gives a perpendicular direction.
Read →
Concept · Intermediate · 6 min read
How machine learning models learn: loss, gradients and why data matters
A plain-language tour of training, overfitting and generalisation, so you know what a model can and cannot be trusted to do.
You will learn
- A model is a function with adjustable settings. Training adjusts them to reduce a measure of error called the loss.
- Gradient descent improves the settings in small steps, like walking downhill in fog.
Read →
When you finish
Where to go next
Next path
Back to basics: the maths and science behind GeoAI, 3D and VR
AI can draft the code, the model and the scene. People are still needed to develop, fine-tune and put them in context, and that takes the fundamentals.
10 articles · 66 min
Next path
Adopt AI in your organization
Learn the language and how AI works first, then check your readiness, run one measured pilot and understand the two big building blocks.
6 articles · 46 min
Start a project
Want this applied to your own project?
Learning is the first step. If you would rather have a working system, book a discovery call and we will scope it with you.