MT2502 Analysis

Academic year

2024 to 2025 Semester 1

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

15

The Scottish Credit Accumulation and Transfer (SCOTCAT) system allows credits gained in Scotland to be transferred between institutions. The number of credits associated with a module gives an indication of the amount of learning effort required by the learner. European Credit Transfer System (ECTS) credits are half the value of SCOTCAT credits.

SCQF level

SCQF level 8

The Scottish Credit and Qualifications Framework (SCQF) provides an indication of the complexity of award qualifications and associated learning and operates on an ascending numeric scale from Levels 1-12 with SCQF Level 10 equating to a Scottish undergraduate Honours degree.

Planned timetable

11.00 am Mon (even weeks), Tue and Thu

This information is given as indicative. Timetable may change at short notice depending on room availability.

Module coordinator

Prof J M Fraser

Prof J M Fraser
This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module Staff

Dr Tom Coleman

This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module description

The main purpose of this module is to introduce the key concepts of real analysis: limit, continuity and differentiation. Emphasis will be placed on the rigorous development of the material, giving precise definitions of the concepts involved and exploring the proofs of important theorems. This module forms the prerequisite for all later modules in mathematical analysis.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT1002,IF MT1002 HAS NOT BEEN PASSED, ADVANCED HIGHER MATHEMATICS (AT GRADE A) OR A-LEVEL FURTHER MATHEMATICS (AT GRADE A).

Assessment pattern

2-hour Written Examination = 70%, Coursework (including class test 15%) = 30%

Re-assessment

2-hour Written Examination = 100%

Learning and teaching methods and delivery

Weekly contact

2.5 hours lectures (x 10 weeks), 1-hour tutorial (x 5 weeks), 1-hour examples class (x 5 weeks)

Scheduled learning hours

35

The number of compulsory student:staff contact hours over the period of the module.

Guided independent study hours

115

The number of hours that students are expected to invest in independent study over the period of the module.

Intended learning outcomes

  • Understand the concepts maximum, minimum, supremum, infimum, and completeness, especially in the context of the real numbers
  • Appreciate the rigorous definitions of convergence, continuity and derivative and be able to apply the definitions to basic examples
  • Understand convergence of series and various tests for convergence including the comparison and root tests
  • Understand Cauchy sequences and be able to use this concept to prove convergence via the The General Principle of Convergence
  • Understand and apply various results relying on differentiation of functions, including the Mean Value Theorem and Taylor's Theorem

Additional information from school

For guidance on module choice at 2000-level in Mathematics and Statistics please consult the School Handbook, at https://www.st-andrews.ac.uk/mathematics-statistics/students/ug/module-choices-2000/