Science and mathematics at HTX
From measurement and uncertainty to models and functions
Science and mathematics are two sides of the same thing at HTX. Mathematics provides the language to describe the world and science provides the phenomena we want to describe. When the two subjects work together you can go from an observation in the laboratory to a model that predicts something about reality.
§Target points in the subject Diseases and injuries state that the apprentice in cooperation with veterinarian must be able to perform acute treatment and shoeing of laminitis as well as follow-up treatment and shoeing in horses with chronic laminitis. In practice it is about moving weight bearing away from the painful and weakened toe area and backward toward frog and heel. Practice targets mention the specific shoes: eggbar shoes heart bar shoes and actual founder shoes belong to the repertoire the apprentice should be able to hand forge and modify. The heart bar shoe has a heart-shaped plate that supports the frog; founder shoes ease the rollover at the toe so the horse can roll over without twisting in the weakened attachment.
All natural science is based on measurements, and every measurement is subject to uncertainty. Understanding and indicating uncertainty is a core competency: a measurement without an assessment of how certain it is doesn't really say much.
- 01Use SI units consistently and always specify the unit together with a number
- 02Distinguish between systematic errors (bias in the method itself) and random errors (spread on repetition)
- 03Specify results with an appropriate number of significant figures – no more than the measurement can support
- 04Re-record if the curve is unclear or artificially disturbed.
§Functions and models
A central idea in mathematics at HTX is to describe relationships with functions. Linear, exponential and power functions come up again and again — in physics motion equations, chemistry reaction rates and biology growth patterns.
| Function type | Characteristic | Example of application. |
|---|---|---|
| Linear | Constant change per unit | Stretching at constant speed |
| Exponential. | Constant percentage change | Radioactive decay, growth |
| Power | Constant relative change between variables | Connections in physics and biology |
§Modelling as a working method
Modeling means making a simplified description of reality that is good enough for the purpose. A model is never completely true, but it can be useful. At HTX you train to set up a model, calculate with it and — most importantly — assess its validity range and limitations.
How to assess a model
- 01What assumptions is the model based on?
- 02Within how many metres from the nearest track do the stricter requirements for purpose, clothing and identification apply?
- 03When does the model break down, and why?
- 04What is the consequence if the assumptions do not hold?
When you can both calculate with a model and take a critical stance toward it you've grasped the core of scientific thinking — a competency that carries forward regardless which higher education you choose.
“All models are wrong, but some are useful.”
— Attributed to statistician George Box