MATH42615: Introduction to Mathematics for Data Science

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• To introduce the mathematical principles that underpin contemporary Data Science

• Review of basic mathematical principles: functions, graphs, and notation.
• Overview of calculus: limits, differentiation, integration, numerical computation
• Introduction to Linear Algebra: linear systems, matrices, vector spaces, geometric transformations, eigenvalues and eigenvectors
• Further topics in mathematical modelling for data science
• Transferable skills including teamwork, time-management, presentation, communication, organisation, and prioritisation skills.

Subject-specific Knowledge:

• By the end of the module students should be able to demonstrate the following quantitative reasoning skills:
• perform standard reasoning with graphical representation of functions (identifying minima, maxima, estimating integrals, derivatives, and gradients).
• manipulate the representation of numerical data using linear algebra, and to visualise this in 2 and 3 dimensions.
• carry out linear algebraic reasoning involving the relations between bases, dimensions, linear transformations, and equations.
• work through the mathematical modelling cycle, with emphasis on formulating, simulating, and interpreting simple mathematical models involving linear algebra and calculus.

Subject-specific Skills:

• By the end of the module, students should be able to demonstrate the following mathematical manipulation and calculation skills:
• do basic manipulations with commonly used mathematical concepts by hand and/or with the aid of software tools.
• carry out basic calculations of differential and integral calculus (differentiating and integrating elementary functions, gradients, directional derivatives).
• perform basic calculations of linear algebra(determinants, projections, solving systems of linear equations, finding eigenvectors, computing kernels, ranges, bases, and calculating changes of basis).

Key Skills:

• Sufficient mastery of mathematical concepts to enable engagement with data science methods.
• Ability to clearly communicate mathematics and technical reasoning through writing and oral presentation.
• Understanding of how to function effectively as an individual and as a member or leader of a team.
• Ability to organise, prioritise, and manage time effectively.
• Ability to advance and extend their knowledge through significant independent learning and research.
• Ability to produce a clear and detailed written report with appropriate presentation.

• This module will be delivered by the Department of Mathematical Sciences.
• Teaching will be delivered primarily by workshops. Workshops describe theory and its application to concrete examples, enable students to test and develop their understanding of the material by applying it to practical problems, and provide feedback and encourage active engagement.
• Workshops are delivered in hybrid mode and are a combination of live lectures, computer practicals, problem classes, tutorials and guided group work.
• Workshops will be supported by the distribution of materials such as video content, directed reading, e-assessments, reflective activities, opportunities for self-assessment, and peer-to-peer learning within a tutor-facilitated discussion board.
• Students will be able to obtain further help in their studies via scheduled office hours or surgeries as well as by approaching their lecturers by email.
• Students will be expected to work in between workshops, and to discuss their own work during the workshops. This work will be guided by the module leader, but will be organised by the students themselves, thereby enabling them to demonstrate their time management skills.
• Students will undertake independent research to further their knowledge of the topic and self-directed learning to further their technical and transferable skills.
• The workshops also provide opportunities for module leaders to monitor progress and to provide feedback and guidance on the development of ideas for the project, and for students to gauge their progress throughout the duration of the module.
• Student performance will be assessed through two individual assignments, three short group reports, a group presentation, and a final group report.
• The individual assignments will provide the means for students to demonstrate their acquisition of subject knowledge and the development of their problem-solving skills.
• The group reports and presentation will provide the means for students to demonstrate their acquisition of subject knowledge, subject-specific skills, as well as key skills.

Workshop discussion of students' ideas and experiences; informal discussions of student progress with module leader when necessary; interim feedback on group project via continuous group assessment.

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