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Fundamentals of Digital Technologies

Fundamentals of Digital Technologies – Group Project and Individual Refinement

This assessment is a project-based assignment for the DG4FDTL Fundamentals of Digital Technologies module. It is designed to develop students' practical understanding of digital technologies by combining mathematical concepts, programming, algorithms, data analysis and learning methods within a real-world project. The project is structured around a common group component, known as the Group Trunk, and an individual component in which each student develops a specialised refinement of the shared project. The project topics are designed around key areas covered by the module, including linear algebra, calculus, probability, learning algorithms, algorithms and Python programming. Students work in groups to establish a common project foundation and then develop an individual refinement that extends the functionality or analytical capabilities of the shared system. The project guidance is intended for a mixed cohort that may include Data Science, Computer Science and Business Analytics students. The assessment is divided into two main components: Proposal and Implementation. The Proposal accounts for 40% of the assessment, while Implementation accounts for 60%. Both the group trunk and individual trunk contribute to the assessment. The group proposal requires students to describe what the group intends to build, explain the problem being addressed, outline the proposed approach and identify the main functions and responsibilities within the project. Students should demonstrate a clear understanding of the project objectives and provide an appropriate plan for developing the shared system. The implementation stage requires students to develop the common group functionality and then complete their individual refinement. The shared component provides the basic project framework, while the individual refinement allows each student to investigate a specific aspect of the problem and add specialised functionality. Depending on the selected project topic, individual refinements may involve data analysis, visualisation, optimisation, prediction, monitoring, reporting or other computational features. The project topics include practical applications such as productivity and task-management systems, supermarket sales analysis and other data-driven applications. Students are expected to use Python and appropriate libraries or computational techniques to implement their solutions. The project materials provide examples involving data structures, CSV files, functions, numerical calculations, visualisation and analytical dashboards. The assessment emphasises both technical implementation and the student's ability to explain the problem, approach and functionality of the developed system. Students should demonstrate appropriate use of programming concepts, mathematical foundations, algorithms and data-analysis techniques. The individual refinement should clearly extend the common project and demonstrate the student's own contribution to the overall solution. Overall, the assessment develops practical digital-technology skills through collaborative project development followed by individual technical refinement. It provides experience in project planning, programming, computational problem solving, data analysis, visualisation and the application of mathematical and algorithmic concepts to practical problems.

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Calculus and Optimisation: Python Implementation of Gradient Descent, Derivatives and Polynomial Regression

This Calculus and Optimisation technical exercise demonstrates the implementation of mathematical and machine-learning concepts using Python. The document is organised as a set of code fragments that must logically work together to perform symbolic calculus, numerical optimisation, physical modelling and polynomial regression. The material uses libraries including NumPy, SymPy, Matplotlib and Scikit-learn, linking mathematical theory with practical computational implementation. Jigsaw_Puzzle_Calculus_Original… A central component is the implementation of gradient descent for linear regression. The supplied function calculates predictions, evaluates prediction errors, computes gradients and updates model parameters iteratively using a configurable learning rate. Mean squared error is recorded during optimisation, and a tolerance-based stopping condition is used to terminate the algorithm when successive cost values change by only a very small amount. Jigsaw_Puzzle_Calculus_Original… Synthetic linear-regression data is generated using a fixed NumPy random seed to support reproducible experimentation. A bias column is added to the feature matrix, initial parameter values are randomly generated, and the custom gradient-descent function is then executed to estimate the intercept and slope of the relationship. Jigsaw_Puzzle_Calculus_Original… The document also demonstrates symbolic differentiation and optimisation using SymPy. A cubic polynomial is defined and differentiated to obtain both its first and second derivatives. Critical points are identified by solving where the first derivative equals zero, while the second derivative is evaluated at each critical point to determine whether the point represents a local minimum, local maximum or saddle point. Jigsaw_Puzzle_Calculus_Original… Jigsaw_Puzzle_Calculus_Original… A further section applies mathematical formulas to projectile motion. Using a specified initial velocity, launch angle and gravitational acceleration, the code calculates both maximum projectile height and horizontal range. This component illustrates how calculus-related mathematical relationships can be translated directly into executable computational models. Jigsaw_Puzzle_Calculus_Original… The final major element explores polynomial regression. Synthetic nonlinear data is generated from a cosine-based function with added random noise. Scikit-learn pipelines are then used to compare polynomial models of degrees 1, 4 and 15. The models are fitted to the synthetic dataset and visualised against the underlying true function, allowing comparison of model complexity and illustrating concepts such as underfitting and overfitting. Jigsaw_Puzzle_Calculus_Original… Jigsaw_Puzzle_Calculus_Original… Overall, the exercise integrates calculus, optimisation, numerical methods and machine-learning modelling through Python. It provides practical experience with differentiation, critical-point analysis, iterative optimisation, mathematical simulation, regression modelling and visualisation. Important: because this file does not identify a university, assessment weighting, academic level, reference style or required word count, those fields should remain Not specified / Not applicable rather than being invented.

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