Numbers, Sequences & Series

Course by Luke Danaher, updated more than 1 year ago Contributors

Description

There are 5 chapters to this module. It is important to practice each scenario of question carefully and understand all of the underlying proofs and methods for each chapter.

Module Information

Chapter 1: Sets and Functions

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Similar to the 1st and second chapters of the calculus, this remarks the fundamental language of maths and begins going through the necessary notation required to write out precise mathematical statements.
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Charpter 2: The Countability of Q

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This chapter runs through what it means for number sets to be countable or uncountable, and historically how it came to be so. We look closely at the methods of well renowned 19th century-German mathematician, Georg Cantor.
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Chapter 3: The construction of R

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This chapter aims to derive the real number set by following theorems and ideas of the concepts of fields, ordered fields and the fundamental mathematical and ordering axioms. The proof of R is constructed more at the end of the chapter.
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Chapter 4: Limits & Sequences

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This chapter takes a turn to sequences and how the limiting process is involved in finding whether sequences converge or diverge. With this, there are limit rules that must be learnt.
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Chapter 5: Series

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This final chapter is similar to chapter 4. We use a limiting process to find the limits of sequences and if they converge or diverge. There are as well many tests that must be learnt in order to find these answers and solutions.
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