Essential Maths
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The most recent substantial iteration of this course was developed by Fergus Cooper, Beth Dingley, and Elliot Howard-Spink.
Why Maths?
Maths is the language we use to quantitatively describe the world.
You are going into research, and you
- may need to be proficient in maths as a tool for describing what you work on
- will have to read and understand papers that use maths
Some of you may feel you don't need to know any maths, but this course will be useful to you even if you never have to write down a system of differential equations yourself.
Data analysis
- Interpretation and inference
- Identify patterns, trends, relationships
- Deal robustly with uncertainty and variation
Describe the behaviour of systems
- Remove ambiguity: explicit assumptions
- Quantitative hypotheses
- Make predictions, through simulation and analysis
- "If I make this intervention, I expect to see that change"
- Explain why something is observed
Vital for dynamic and nonlinear systems
- Simple intuition breaks down
- Most of biology is dynamic and nonlinear!
Course aims
- Develop confidence in your mathematical abilities
- Extensive practice
- Become able to communicate effectively with mathematical collaborators
- Ensure you can read and understand mathematical papers in your field
- Build on your ability to apply computational tools from Python to solve problems
Topics covered
- Graphs, and basic tools such as logs
- Calculus: differentiation & integration
- Complex numbers
- Ordinary differential equations
- Linear algebra (matrices)
- Coupled systems of ordinary differential equations
- Use of Python