Unit name | Analysis 1A |
---|---|

Unit code | MATH10003 |

Credit points | 10 |

Level of study | C/4 |

Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |

Unit director | Dr. Jordan |

Open unit status | Not open |

Pre-requisites |
A in A Level Mathematics |

Co-requisites |
None |

School/department | School of Mathematics |

Faculty | Faculty of Science |

Analysis 1A introduces the style of logically precise formulation and reasoning that is characteristic of university-level mathematics; it studies the foundations of elementary calculus in this style using logical quantifiers. It starts from basic properties of the real numbers, studies sequences and series, functions and their limit points, and basic results on continuous functions.

The unit aims to provide some basic tools and concepts for mathematics at the undergraduate level, with particular emphasis on fostering students' ability to think clearly and to appreciate the difference between a mathematically correct treatment and one that is merelyheuristic; introducing rigorous mathematical treatments of some fundamental topics in mathematics.

At the end of the unit, the students should:

• be able to distinguish correct from incorrect and sloppy mathematical reasoning, be comfortable with "proofs by delta and epsilon",

• have a clear notion of the concept of limit as it is used in the context of sequences, series and functions,

• have a clear understanding of the basic properties of continuous functions,

• have seen proofs of important results in the course and be able to use these results to solve standard problems.

2 hours lecture per week for 12 weeks; 1 hour feedback/problems classes per week for 12 weeks; weekly tutorials for 12 weeks

Formative assessment will be provided by problem sheets with questions that will be set by the instructor and marked by the students’ tutors. In addition, each week there will be a 1 hour feedback/problems session in which the lecturer will discuss solutions to some of the set homework problems.

90% 1.5 hour examination

10% coursework

• C. W. Clark, Elementary mathematical analysis. Wadsworth Publishers of Canada, 1982

• J. M. Howie, Real Analysis. Springer-Verlag, 2001.

• S. Krantz, Real Analysis and foundations. CRC Press, 1991 . • I. Stewart and D. Tall, The Foundations of mathematics. Oxford University Press, 1977.

• D. J. Velleman, How to prove it. A structural approach. Cambridge University Press, 1994.