| Unit name | Analysis |
|---|---|
| Unit code | MATH10011 |
| Credit points | 20 |
| Level of study | C/4 |
| Teaching block(s) |
Teaching Block 2 (weeks 13 - 24) |
| Unit director | Dr. Klurman |
| Open unit status | Not open |
| Units you must take before you take this one (pre-requisite units) |
MATH10027 Introduction to Pure Mathematics |
| Units you must take alongside this one (co-requisite units) |
None |
| Units you may not take alongside this one |
None |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
Why is this unit important?
This unit will introduce students to some of the basic tools and concepts of university-level mathematics, with a particular emphasis on enabling students to think clearly and to appreciate the difference between a mathematically correct argument and one that is merely heuristic. The unit provides a rigorous mathematical treatment of several fundamental topics in calculus, such as limits, continuity, differentiation and integration, preparing students for many higher-level units involving analysis.
How does this unit fit into your programme of study?
This unit builds naturally on the foundational content of level C/4 Introduction to Pure Mathematics and it serves as an essential bridge to many units at levels I/5, H/6 and M/7. For example, it is a prerequisite for level I/5 Metric Spaces, which in turn is a prerequisite for several units at the H/6 and M/7 levels.
An overview of content
This unit will introduce students to the style of logically precise formulations and reasoning that is characteristic of university-level mathematics. The aim is to study the foundations of elementary calculus in this rigorous style, building naturally on the introductory content on sets, functions and logic introduced in level C/4 Introduction to Pure Mathematics. Starting from the basic properties of the real numbers, students will study sequences and series, real-valued functions and their limit points, and the basic properties of continuous functions. The unit also presents a rigorous treatment of differentiation and integration, concluding with a discussion of real power series and the formal definitions of the elementary functions exp, log, sin and cos.
How will students, personally, be different as a result of the unit?
By the end of the unit, students will have improved their logical thinking and they will have increased the range and scope of their problem-solving techniques. They will have an understanding and appreciation of the rigorous definitions underpinning familiar concepts in calculus such as limits, differentiation and integration. These key ideas have important applications in both pure and applied mathematics, allowing students to study and analyse more complicated situations than those encountered in a first calculus course (for example, at A-level). Students should be able to solve routine problems that are similar to the assigned exercises, and they should have the confidence and expertise to apply the core ideas in unseen situations.
Learning Outcomes
After completing this unit successfully, students should:
The unit will be taught through a combination of:
Tasks which help you learn and prepare you for summative tasks (formative):
Guided independent activities such as problem sheets and/or other exercises, with regular feedback from tutors.
Tasks which count towards your unit mark (summative):
90% timed examination; 10% coursework
When assessment does not go to plan
If you fail this unit and are required to resit, then reassessment is by a written examination in the Resit and Supplementary exam period.
If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.
If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. MATH10011).
How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours
of study to complete. Your total learning time is made up of contact time, directed learning tasks,
independent learning and assessment activity.
See the University Workload statement relating to this unit for more information.
Assessment
The assessment methods listed in this unit specification are designed to enable students to demonstrate the named learning outcomes (LOs). Where a disability prevents a student from undertaking a specific method of assessment, schools will make reasonable adjustments to support a student to demonstrate the LO by an alternative method or with additional resources.
The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit.
The Board considers each student's outcomes across all the units which contribute to each year's programme of study. For appropriate assessments, if you have self-certificated your absence, you will normally be required to complete it the next time it runs (for assessments at the end of TB1 and TB2 this is usually in the next re-assessment period).
The Board of Examiners will take into account any exceptional circumstances and operates
within the Regulations and Code of Practice for Taught Programmes.
