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  6. MA2005: INTRODUCTION TO ANALYSIS

MA2005: INTRODUCTION TO ANALYSIS (2014-2015)

Last modified: 28 Jun 2018 10:27


Course Overview

Analysis provides the rigourous, foundational underpinnings of calculus. It is centred around the notion of limits: convergence within the real numbers. Related ideas, such as infinite sums (a.k.a. series), continuity, differentiation, and Riemann integration, are also visited in this course.

Care is needed to properly use the delicate formal concept of limits. At the same time, limits are often intuitive, and we aim to reconcile this intuition with correct mathematical reasoning. The emphasis throughout this course is on rigourous mathematical proofs, valid reasoning, and the avoidance of fallacious arguments.



Course Details

Study Type Undergraduate Level 2
Term First Term Credit Points 15 credits (7.5 ECTS credits)
Campus None. Sustained Study No
Co-ordinators
  • Dr Aaron Tikuisis

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

None.

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

  • Fundamental properties of real numbers: field operations, order, completeness.
  • Sequences and limits: convergence, basic examples, decimal representation of real numbers.
  • Functions of one real variable: limits and continuity, elementary functions, basic results on continuous functions.
  • Differentiation of functions of one variable: basic definitions and properties, chain rule,basic results on differentiable functions
  • Integration of functions of one variable: basic definitions and properties, the fundamental theorem of calculus, application to arc lengths of plane curves.


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

1st Attempt: 1 two-hour written examination (80%); in-course assessment (20%).

Resit: 1 two-hour written examination paper. The CAS mark awarded will be the maximum of 100% resit and 80% resit with 20% in-course assessment.

Formative Assessment

Informal assessment of weekly homework through discussions in tutorials.

Feedback

In-course assignments will normally be marked within one week and feedback provided to students in tutorials. Students will be invited to contact Course Coordinator for feedback on the final examination.

Course Learning Outcomes

None.
 

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