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MX3535: ANALYSIS IV (2020-2021)

Last modified: 24 Jun 2020 14:31


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
Session Second Sub Session 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?

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?

No

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

  • 1 during University weeks 25 - 29, 31 - 34, 38 - 39
  • 1 Tutorial during University weeks 26 - 29, 31 - 34, 38 - 39

More Information about Week Numbers


In light of Covid-19 and the move to blended learning delivery the assessment information advertised for courses may be subject to change. All updates for first-half session courses will be actioned no later than 1700 (GMT) on 18 September 2020. All updates for second half-session courses will be actioned in advance of second half-session teaching starting. Please check back regularly for updates.

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

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