To provide students with a solid grounding in linear algebra, calculus, probability and programming as required for more advanced specialist pathway modules

(LO1) Use matrix arithmetic, calculus and differential equations to solve real-life problems.

(LO2) Describe real-life phenomena using mathematical modelling approaches, including solving optimisation, differential equation, and linear algebra problems.

(LO3) Find the moments, median and mode of a given distribution function and provide their practical interpretation.

(LO4) Find conditional expectations and quantify dependence between variables.

(LO5) Characterise distributions of random variables via their cdfs, pdfs, pmfs and characteristic functions, and determine one from the other

(LO6) Explain ethical limitations of data collection and data usage in specific contexts.

(LO7) Prepare data for further analysis using data wrangling techniques.

(LO8) Obtain estimates for common statistics (such as mean) and provide interpretation of these estimates using statistical inference (confidence intervals and p-values).

(LO9) Knowledge of academic integrity with particular reference to the University of Liverpool’s Code of Practice on Assessment.

(S1) Analytical and problem-solving skills

(S2) Digital fluency

Linear algebra
- Matrix arithmetic
- Vectors and their use in describing and solving real life problems

Calculus
- Sketch graphs
- Solve optimisation problems for a range of real-life problems
- Differential equations for real-life phenomena
- Derivatives and integrals
- Finding basic derivatives and integrals
- Definite integral as area under a curve

Probability
- Random variable
- Discrete and continuous distributions and their cdf, pdf and pmf and characteristic function
- Common distributions
- Expectation and higher order moments
- Median and mode
- Joint distributions
- Conditional distributions and marginal distributions
- Independence
- Central Limit Theorem

Data
- Ethical considerations
- Data wrangling and cleaning

Estimation
- General principles and properties of estimators (unbiased, minimum variance, consistency)
- Difference between sample moments and population moments

Inference
- Quantifying uncertainty through confidence intervals and relationship to p-values
- Interpretation of results from statistical testing