Mathematical Investigations

Unit description

Independent studying is a key skill of mathematicians. In this unit students work in teams on three mini-projects and explore in workshops topics related to their studies, all with the overall aim to foster independent study skills. Other benefits will be a better understanding of our assessment criteria, learning how to give and receive feedback and easing the transition from School to University by providing an opportunity to make friends and work with other students.

Investigation projects: Students have weekly meetings in small groups with their personal tutor to discuss the three mini-projects that they are working on over the year. For each investigation project they break up in small teams. produce a short report (in LaTeX) and give a presentation at the end of each activity. The meetings are used to support the students; students will give updates on their progress and report on problems. Some sessions will focus on skills, like how to write mathematics, how to prepare a presentation and how to assess a project report.

Investigation workshops: There will also be weekly workshop sessions where students meet for a 2-hour block each week assisted by a teaching assistant. For the first hour students self-organise into small groups to work through the steps of that week's investigation workshop, with the teaching assistant on hand for support and guidance. Once students have finished their worksheet they have the opportunity to engage in further discussions, either about the topic that they just studied or about questions related to current homework problems.

The goals of the investigation workshops are

  • To reinforce, in a structured and supportive setting, ideas and techniques taught in lectures;
  • To give the students context and time to help them digest course material;
  • To engage the students in an enjoyable experience working through problems that elucidate course material;
  • To help students build their study skills and create learning communities.

Investigation topics: The topics of the investigation projects and workshops will be linked to other units in the curriculum and the workshops will see an emphasis on topics from Analysis and, to lesser extent ODEs, Dynamics and Curves. All workshops in a given week will have the same topic. The topics for the mini projects will offer the possibility to explore the material beyond what has been covered in the units.

Learning objectives

At the end of the unit, the students should:

  • be able to work independently on mathematical problems with suitable guidance
  • be able to work in teams
  • be able to write short reports in LaTeX
  • have gained experience in presenting mathematical arguments

Reading and References

Recommended reading:

  • Kevin Houston: How to Think Like a Mathematician
  • Steven G. Krantz: An Episodic History of Mathematics

Unit code: MATH10009
Level of study: C/4 (Honours)
Credit points: 20
Teaching block (weeks): 1 and 2 (1-24)
Lecturers: Dr Lynne Walling and Dr Roman Schubert

Pre-requisites

An A in A level Mathematics or equivalent.

Co-requisites

MATH11005 Linear Algebra and GeometryMATH10011 AnalysisMATH10012 ODEs, Curves and Dynamics

Methods of teaching

Weekly meetings with supervisor mini-projects, weekly workshops, independent study and working in teams to progress mini-projects

Methods of Assessment

Formative assessment:

  • feedback on the first mini project and presentation
  • feedback on the attempts from the investigation workshops

Summative assessment:

  • 60% from the marks for the 2nd and 3rd report, weighted by peer assessment inside each group
  • 30% from the two presentations about the 2nd and 3rd mini project
  • 10% from feedback to another project – each group is asked to evaluate a project by a different group against our assessment criteria and fill out a feedback form for that group. This feedback form is assessed by the supervisor.

To receive credit for this unit, students must attend and engage with the investigation workshops. Failure to do so may result in credit being withheld, even if the overall mark is above the pass mark for the unit. Supplementary or resit assessment of this unit is only possible through engagement in the following academic year.

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