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Curricular information is subject to change
On completion of this module the student should be able to:
Identify, define, graph (if relevant), and generate examples of the major concepts of sequences and series of real numbers.
Describe and give examples of the relationships between the major concepts of sequences of real numbers.
Verify the veracity of statements about sequences of real numbers and support your answer with a mathematical argument.
State, apply, prove and describe the main theorems relating to sequences of real numbers.
Describe and apply the Axiom of Completeness.
Define and describe the concepts of countable and uncountable sets.
Test a given series for convergence.
Find the interval of convergence of a power series.
Find the Taylor series generated by a given function.
The following is indicative curricular content. Minor changes may be made throughout the semester.
Section 1. Introduction and Preliminaries
1.1. What is this course about?
Section 2. Sequences - a First Look
2.2. Null Sequences.
2.3. Convergent Sequences.
Section 3. The Real Numbers - Completeness
3.1. The Axiom of Completeness.
3.2. Consequences of Completeness.
Section 4. Sequences - a More Indepth Look
4.1. The Monotone Convergence Theorem.
4.2. The Bolzano-Weierstrass Theorem.
4.3. Cauchy Sequences and Convergence.
Section 5. Infinite Series
5.1. Infinite Series -- An Introduction.
5.2. Geometric Series.
5.3. Series with Nonnegative Terms.
5.4. Series with Positive and Negative Terms.
Section 6. Power Series
6.2. Power Series.
6.3. Taylor Series.
|Student Effort Type||Hours|
|Specified Learning Activities||
|Autonomous Student Learning||
Students must have a strong foundation in Calculus. For examples, students who have completed modules such as MST10010 and MST10020 OR MATH10350 OR MATH10130 and MATH10140 have the prerequisites for this module.
|Description||Timing||Component Scale||% of Final Grade|
|Class Test: Decide if given statements are true or false and verify your answer. Held in a lecture time.||Week 9||n/a||Standard conversion grade scale 40%||No||
|Portfolio: Portfolio of Examples which will be completed within the first six weeks.||Varies over the Trimester||n/a||Standard conversion grade scale 40%||No||
|Continuous Assessment: A maximum of 10% will be given for working on "Inclass Exercises" in lectures throughout the semester. There is 1% per Inclass Exercise and twelve will be given in total.||Throughout the Trimester||n/a||Standard conversion grade scale 40%||No||
|Examination: Closed-book, written examination. All content from the module is examinable for this exam.||2 hour End of Trimester Exam||No||Standard conversion grade scale 40%||No||
|Resit In||Terminal Exam|
|Autumn||Yes - 2 Hour|
• Feedback individually to students, on an activity or draft prior to summative assessment
• Feedback individually to students, post-assessment
• Group/class feedback, post-assessment
• Peer review activities
Group-feedback will be provided in lectures on all Inclass Exercises. Summative feedback will be provided individually on the Class Test and formative group feedback will be provided in lectures. Summative feedback will be provided individually on the Portfolio of Examples and a peer-assessment activity will also be conducted. Summative feedback will be provided on the final examination.
|Lecture||Offering 1||Week(s) - 18, 19, 20, 21, 22, 23, 24, 27, 28, 29, 30, 31||Fri 09:00 - 09:50||Face to Face|
|Lecture||Offering 1||Week(s) - 18, 19, 20, 21, 22, 23, 24, 27, 28, 29, 30, 31||Mon 10:00 - 10:50||Face to Face|
|Lecture||Offering 1||Week(s) - 18, 19, 20, 21, 22, 23, 24, 27, 28, 29, 30, 31||Wed 10:00 - 10:50||Face to Face|
|Tutorial||Offering 2||Week(s) - 20, 21, 22, 23, 24, 27, 28, 29, 30, 31||Thurs 11:00 - 11:50||Face to Face|
|Tutorial||Offering 3||Week(s) - 20, 21, 22, 23, 24, 27, 28, 29, 30, 31||Tues 11:00 - 11:50||Face to Face|