Course Catalogue

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This course offers a broad introduction to advanced mathematics covering topics from right across the subject, with a particular emphasis on mathematical communication and problem-solving skills. It is an essential course for students on degree plans involving mathematics, physics or statistics.

The course will be delivered in sections with lectures at different times to allow for a range of combinations with level 2 courses. Tutorial labs will be offered at a suitable time during the week.

A in advanced higher mathematics, or equivalent. Students must normally be on a faster route programme involving Mathematics or Statistics.

Mathematics 1, 1C, 1G

Final exam (April / May): 50% 90 Mins.

December exam (December): 20% 60 Mins.

Set exercises: reading 5%. Weekly reading comprehension exercises before lectures (best 80% to count);

Set exercises: eAssignments and written feedback 15%. Weekly, alternating between eAssignment and written feedback (best 80% in each category to count).

Set exercises: tutorial group activities 10%. Weekly (best 80% to count). Group working skills will be explicitly assessed.

Reassessments are normally available for all courses, except those which contribute to the Honours classification. Where, exceptionally, reassessment on Honours courses is required to satisfy professional/accreditation requirements, only the overall course grade achieved at the first attempt will contribute to the Honours classification. For non-Honours courses, students are offered reassessment in all or any of the components of assessment if the satisfactory (threshold) grade for the overall course is not achieved at the first attempt. This is normally grade D3 for undergraduate students and grade C3 for postgraduate students. Exceptionally it may not be possible to offer reassessment of some coursework items, in which case the mark achieved at the first attempt will be counted towards the final course grade. Any such exceptions for this course are described below. 

Reassessment is not possible in the reading, eAssessment and feedback exercises, and tutorial group activities. These assessments are specifically adapted to the learning process during the course. Solutions to eAssessment and feedback exercises, and tutorial group activities are provided immediately following the activity. This is in order to provide prompt and effective feedback to students.

Foundations of Mathematics aims to transition students to university level mathematics through development of abstract structures and reasoning skills, the interplay between algebra and geometry, and to ensure students have a strong command of the basics of mathematics that is crucial to our degree programmes. A strong focus throughout the course will be placed on developing mathematical communication skills.

By the end of this course students will be able to:

1 use the language of sets, functions, relations, number systems, and groups to communicate mathematical ideas and arguments.

2 analyse the structure of a mathematical proof or statement, identifying hypotheses, conclusions, contrapositives, converses, negations; produce valid mathematical proofs using methods such as direct argument, induction, proof by contradiction, counterexample.

3 use counting arguments and ideas from elementary number theory to solve problems with particular reference to topics including prime factorisation, congruence, cryptography, binomial expansions, permutations and cardinality.

4 solve equations and inequalities in a variety of settings including real and complex numbers, polynomial equations, and systems of linear equations

5 define and identify groups and subgroups; perform group multiplications particularly in examples coming from permutation groups using cycle notation; compute orders of groups and elements; use Lagrange's theorem.

6 read mathematics independently, extracting essential concepts, definitions, examples, methods and results.

7 present mathematical work in writing, using precise language and notation, providing clear conclusions and reasoning.

8 discuss and solve mathematical problems in small groups.

Students must submit at least 75% by weight of the components (including examinations) of the course's summative assessment.