MX3535: ANALYSIS IV (2020-2021)

Last modified: 05 Aug 2021 13:04

Course Overview

Analysis provides the rigourous, foundational underpinnings of calculus. This course builds on MX3035 Analysis III, continuing the development of multivariable calculus, with a focus on multivariable integration. Hilbert spaces (infinite dimensional Euclidean spaces) are also introduced.

Students will see the benefit of having acquired the formal reasoning skills developed in Analysis I, II, and III, as it enables them to work with increasingly abstract concepts and deep results. Techniques of rigourous argumentation continue to be a prominent part of the course.

Course Details

Study Type	Undergraduate	Level	3
Term	Second Term	Credit Points	15 credits (7.5 ECTS credits)
Campus	Aberdeen	Sustained Study	No
Co-ordinators	Dr Alexey Sevastyanov

Qualification Prerequisites

Either Programme Level 3 or Programme Level 4

What courses & programmes must have been taken before this course?

MX3035 Analysis IIi (Studied)
Either MA2005 Introduction to Analysis (Passed) or MA2509 Analysis II (Passed)
Any Undergraduate Programme (Studied)

What other courses must be taken with this course?

None.

What courses cannot be taken with this course?

None.

Are there a limited number of places available?

Course Description

- Multivariable Riemann integration; volume of subsets of Euclidean space

- Fubini’s Theorem

- Introduction to Hilbert spaces

Syllabus

Multivariable Riemann integration and volumes of subsets of Euclidean space
Fubini’s Theorem and change of variables
Hilbert spaces

Course Aims

To provide students with the basic knowledge of the modern mathematical analysis.

Main Learning Outcomes

By the end of this course the student should:

be able to state the main definitions and theorems of the course;
be able to prove most results from the course;
be familiar with the concept of Jordan measurability and understand theorems about Jordan measurable sets;
understand integration and theorems about the Riemann integral for multivariable functions;
apply ideas from Euclidean spaces such as inner products and convergence to the abstract setting of Hilbert spaces.

Contact Teaching Time

Information on contact teaching time is available from the course guide.

Teaching Breakdown

More Information about Week Numbers

Details, including assessments, may be subject to change until 30 August 2024 for 1st term courses and 20 December 2024 for 2nd term courses.

Summative Assessments

Three x standard course assignments - 33.33% each

Alternative Resit Arrangements for students taking course in Academic Year 2020/21

Resubmission of failed elements (pass marks carried forward)

Formative Assessment

There are no assessments for this course.

Course Learning Outcomes

Knowledge Level	Thinking Skill	Outcome
Factual	Apply	be able to state the main definitions and theorems of the course;
Conceptual	Apply	be able to prove most results from the course;
Conceptual	Understand	be familiar with the concept of Jordan measurability and understand theorems about Jordan measurable sets;
Factual	Understand	understand integration and theorems about the Riemann integral for multivariable functions;
Conceptual	Apply	apply ideas from Euclidean spaces such as inner products and convergence to the abstract setting of Hilbert spaces.