MA0FMANU: Foundations of Mathematical Analysis

Module code: MA0FMANU

Module provider: Mathematics and Statistics; School of Mathematical, Physical and Computational Sciences

Credits: 20

Level: Foundation Level

When you'll be taught: Semester 2

Module convenor: Professor Michael Levitin, email: m.levitin@reading.ac.uk

Pre-requisite module(s): Before taking this module, you must have High School Mathematics. (Open)

Co-requisite module(s):

Pre-requisite or Co-requisite module(s):

Module(s) excluded:

Placement information: NA

Academic year: 2024/5

Available to visiting students: No

Talis reading list: No

Last updated: 21 May 2024

Overview

Module aims and purpose

This module focuses on introducing basic mathematical techniques such as proof by induction, basic concepts such as Set Theory and Group Theory, and providing an introduction to mathematical analysis such as the Real number system, functions, sequence limits and function limits as well as continuity.

To help the students transition from pre-university mathematics to university mathematics. To introduce them to the idea of definition, theorem and proof, and to rigorously cover topics they should have mostly seen in high school.

To provide a formal introduction to mathematical analysis by rigorously approaching concepts crucial in subsequent analytical topics.

Module learning outcomes

By the end of the module, it is expected that students will be able to:

1. Understand and use propositional and predicate logic, sets, functions, group and subgroup, real numbers
2. State and prove some fundamental theorems, effectively use various methods of proof and perform basic number theory computations
3. Understand and use convergence for sequences and functions
4. Understand and use definitions of boundedness, continuity and determine by proof whether certain functions possess said properties

Module content

The module will focus on the following areas and topics:

• Logic and proof
• Sets and functions
• Real numbers and basic number theory
• Group theory
• Sequence limits, function limits and continuity.

Structure

Teaching and learning methods

Lectures supported by tutorials. Learning materials (lecture notes/reading lists, tutorial problem sheets, assessments) made available via Blackboard.

Study hours

At least 50 hours of scheduled teaching and learning activities will be delivered in person, with the remaining hours for scheduled and self-scheduled teaching and learning activities delivered either in person or online. You will receive further details about how these hours will be delivered before the start of the module.

Please note the independent study hours above are notional numbers of hours; each student will approach studying in different ways. We would advise you to reflect on your learning and the number of hours you are allocating to these tasks.

Semester 1 The hours in this column may include hours during the Christmas holiday period.

Semester 2 The hours in this column may include hours during the Easter holiday period.

Summer The hours in this column will take place during the summer holidays and may be at the start and/or end of the module.

Assessment

Requirements for a pass

Students need to achieve an overall module mark of 40% to pass this module.

Summative assessment

Penalties for late submission of summative assessment

The Support Centres will apply the following penalties for work submitted late:

Assessments with numerical marks

• where the piece of work is submitted after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for that piece of work will be deducted from the mark for each working day (or part thereof) following the deadline up to a total of three working days;
• the mark awarded due to the imposition of the penalty shall not fall below the threshold pass mark, namely 40% in the case of modules at Levels 4-6 (i.e. undergraduate modules for Parts 1-3) and 50% in the case of Level 7 modules offered as part of an Integrated Masters or taught postgraduate degree programme;
• where the piece of work is awarded a mark below the threshold pass mark prior to any penalty being imposed, and is submitted up to three working days after the original deadline (or any formally agreed extension to the deadline), no penalty shall be imposed;
• where the piece of work is submitted more than three working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.

Assessments marked Pass/Fail

• where the piece of work is submitted within three working days of the deadline (or any formally agreed extension of the deadline): no penalty will be applied;
• where the piece of work is submitted more than three working days after the original deadline (or any formally agreed extension of the deadline): a grade of Fail will be awarded.

The University policy statement on penalties for late submission can be found at: /cqsd/-/media/project/functions/cqsd/documents/qap/penaltiesforlatesubmission.pdf

You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Formative assessment

Formative assessment is any task or activity which creates feedback (or feedforward) for you about your learning, but which does not contribute towards your overall module mark.

Reassessment

Additional costs