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Unit information: Foundations & Proof in 2016/17

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Unit name Foundations & Proof
Unit code MATH10004
Credit points 10
Level of study C/4
Teaching block(s) Teaching Block 1 (weeks 1 - 12)
Unit director Dr. Walling
Open unit status Not open

A in A Level Mathematics



School/department School of Mathematics
Faculty Faculty of Science

Description including Unit Aims

The unit provides an introduction to logical propositions, basic set theory and cardinality, functions and relations, and proof techniques. These notions are exemplified with some topics from elementary number theory, such as the Fundamental Theorem of Arithmetic, Euclid’s algorithm, modular arithmetic.

The unit aims to introduce students to fundamental concepts in set theory, techniques of proof, exemplified and applied to some basic properties of functions and topics in elementary number theory.

Additional unit information can be found at

Intended Learning Outcomes

At the end of the unit, the students should:

  • be able to distinguish correct from incorrect and sloppy mathematical reasoning, be able to produce proofs using mathematical induction;
  • be able to correctly use quantifiers and to negate logical statements that include quantifiers and connectives;
  • be able to work with sets, whether they are finite, countable, or uncountable;
  • be proficient in establishing fundamental properties of functions, such as injectivity and surjectivity;
  • be proficient in using Euclid’s algorithm and modular arithmetic.

Teaching Information

Lectures, supported by lecture notes with problem sets and model solutions, and small group tutorials.

Formative assessment will be provided by problem sheets with questions that will be set by the instructor and marked by the students’ tutors.

Assessment Information

The final assessment mark will be based on a 1 ½-hour written examination.

Reading and References

Reading and references are available at