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.

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.