FP094-30 Foundation Mathematics and Statistics for Physics and Engineering
Introductory description
This module develops the mathematical and statistical skills required to analyse problems in scientific and engineering contexts. Students will strengthen their understanding of core mathematical processes and learn how to apply algebraic tools and statistical models to a range of real-world examples. The module is designed to build both confidence and fluency in using mathematics as a problem-solving tool, laying the groundwork for more advanced study in science and engineering disciplines. By the end of the module, students will be able to select and apply appropriate mathematical and statistical methods to analyse and solve problems across science and engineering.
Module aims
Students will develop understanding of mathematical processes so as to become confident in their use and application. By the end of the module, they will be able to apply mathematical and statistical knowledge, selecting appropriate algebraic tools and statistical models where necessary, to problems set in a variety of scientific and engineering contexts.
Outline syllabus
This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.
Algebra: Functions, Quadratics, Inequalities, Graphing standard functions, Exponential and Logarithmic functions, Binomial Theorem, Polynomial factorisation, Partial fractions, Sequence & Series, Trigonometry, Complex numbers, Matrices and Vectors, Numerical Methods for solving equations.
Calculus: Differentiation, Applications of derivatives, Higher order derivatives, Maclaurin’s
series expansions, Integration, Applications of integration in area and volume, First
Order Differential Equations and their applications.
Statistics & Probability: Data representation, Correlation and Regression, Probability, Probability distributions.
Learning outcomes
By the end of the module, students should be able to:
- Apply mathematical and statistical knowledge to solve a variety of mathematical and real-world problems taken from scientific and engineering contexts, selecting appropriate algebraic tools and statistical models where necessary, implementing them precisely and rigorously to arrive at correct numerical or algebraic results and utilising technology effectively to simplify calculations.
- Undertake basic analysis of data by calculating summary statistics and representing data graphically, understanding the suitability and limitations of different statistical measures and graph types, interpreting the meaning of calculated results within a given context and using them to inform decision-making.
- Use fundamental principles of probability to quantify uncertainty and solve problems involving a selection of discrete and continuous probability distributions.
- Present written mathematical and statistical work clearly and logically.
Indicative reading list
Reading lists can be found in Talis
Interdisciplinary
Students will have opportunities to draw on knowledge and skills acquired within the different modules on their pathway.
International
All students are international, representing a wide range of cultural, linguistic, and educational backgrounds. They bring diverse experiences and perspectives, enriching discussion and supporting the development of intercultural awareness. Examples for analysis and evaluation are drawn from a variety of countries, ensuring that teaching and learning are embedded in an international context.
Subject specific skills
- Apply core mathematical techniques in algebra, calculus, geometry, and statistics to solve scientific and engineering problems.
- Construct and manipulate mathematical models to represent physical systems and processes.
- Interpret and analyze quantitative data using appropriate mathematical and statistical tools.
Transferable skills
- Numeracy: Confidently handle complex calculations, symbolic manipulation, and quantitative reasoning
- Logical Reasoning: Develop and follow logical arguments through abstract and applied problems
- Problem-Solving: Apply structured approaches to tackle quantitative and real-world challenges
- Analytical Thinking: Interpret data, identify relationships, and evaluate mathematical models
- Data Interpretation: Analyze, represent, and draw conclusions from statistical data
Study time
| Type | Required |
|---|---|
| Lectures | 5 sessions of 1 hour (2%) |
| Seminars | 25 sessions of 4 hours (33%) |
| Online learning (independent) | 8 sessions of 1 hour (3%) |
| Private study | 127 hours (42%) |
| Assessment | 60 hours (20%) |
| Total | 300 hours |
Private study description
Extra class reading of books and learning materials on Moodle in preparation for seminars. Weekly worksheets. Flipped learning including pre-recorded videos.
Costs
No further costs have been identified for this module.
You must pass all assessment components to pass the module.
Assessment group C
| Weighting | Study time | Eligible for self-certification | |
|---|---|---|---|
Assessment component |
|||
| In-Class Test 1 | 25% | 15 hours | No |
|
Term 1 Theory Test Relevant formulae will be provided within the questions/Formula sheet will be provided. |
|||
Reassessment component is the same |
|||
Assessment component |
|||
| In-Class Test 2 | 25% | 15 hours | No |
|
A closed book in class test testing material covered studied to this point and not covered by class test 1 |
|||
Reassessment component is the same |
|||
Assessment component |
|||
| Final Examination | 50% | 30 hours | No |
|
Formula sheet will be provided.
|
|||
Reassessment component is the same |
|||
Feedback on assessment
Feeback on Tabula
There is currently no information about the courses for which this module is core or optional.