MTH4104 - Introduction to Algebra - 2023/24
Topic outline
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General news and announcements
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This forum is available for everyone to post messages to. If you have any questions about the module that are not private, please ask them here. I will be monitoring it to answer your questions.
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To give you some idea of what this module is about. This is NOT the lecture notes for 2023-2024!
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29/01
Passcode: 4$YAP92N
02/02 (I only managed to record from the halfway through... sorry! Please look at QReview instead.)Passcode: cd4!AD?*-
Maxim Karasev pointed out a typo: [a]_R is the set of all elements b in S which are `in relation' to a (not to be as I originally wrote)! Thank you, Maxim, for pointing this out!
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05/02
Passcode: =r#etvB7
09/02Passcode: k!g&44M1
*Type-up notes for Week 3 can be found in the Week 2 tab*. -
This is an introductory module in algebra, the area of mathematics which studies algebraic structures.
We are all familiar with integers and how operations such as addition combine two integers to produce another integer. More formally we say that these operations equip the set of integers with an algebraic structure. Is it possible to introduce algebraic operations on the set of integers other that the ones we know from high school? Given a set, is it possible to equip it with some algebraic structure and how?
These are some of the questions we discuss in this module. We start with the introduction of the basic building blocks of algebra, such as sets, numbers, matrices, polynomials and permutations. We then show how they form examples of abstract mathematical structures such as groups, rings and fields, and how algebra can be developed on an axiomatic foundation.
This is a module in abstract mathematics and as such makes extensive use of the notions of definition, theorem and proof, example and counterexample. You will find the skills you developed in the Numbers, Sets and Functions module helpful with this.
The material covered in this module forms the foundation to later modules in algebra such as Ring Theory, Number Theory, Linear Algebra and Cryptography.
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12/02 (Only from halfway through... QReview should have it in full. Sorry!)Passcode: ^I7WQ3!P
16/02Passcode: QDS*6Jj1-
For the typed-up notes (for the lecture 12/02), please see the Typed-up notes for Week 2*and* Week 3 in the Week 2 tab.7.3 MB
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For the typed-up notes (for the lecture 16/02), please see the Typed-up notes for Week 5, Week 6 and Week 7 in the Week 5 tab.
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When to submit: by 11am, the 4th of March.
Where to submit: the Maths Office (1st floor of the SMS building).
What to submit: your solutions, with your name and ID number on the front page.
You have at least two weekends to work through the problem set. You can discuss problems with others, but please do not waste your time copying each other.
Marks you get directly add up to your overall grade (max 10 marks up for grabs).63.5 KB -
These contain what I covered on 16/02 (the second lecture in Week 4).
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Even though this is the reading week, we have lectures, because we won't have lectures on 29/03 (Friday, Week 10) and 01/04 (Monday, Week 11).
04/03 Monday: 16-18 at Skeel LT (People's Palace)
08/03 Friday: 14-15 at Arts Two (as usual)
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04/03
Passcode: KtRiN&D2
08/03Passcode: 5s5H@k8f*Typed-up notes for the lecture on 08/03 can be found in the Week 8 tab*
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The notes contain what I covered on 08/03 (Week 7, Friday)
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18/03
Passcode: &QE0$A4j
22/03
I forgot recording the session on the 22nd of March via Zoom. Sorry. QReview should have recorded the lecture. -
No lecture on 29/03 (Friday).
25/03
Because I used the document camera, I could not record the lecture via Zoom. QReview should have recorded it however.
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No lecture on 01/04 (Monday). I am not joking.
05/04
Passcode: $2Vb^vWW-
This document includes `Typed-up notes for Week 11 and Week 12' in which I go through `Permutations' and `Group theory revisited'.
As I mentioned on the first day, *everything* in the notes, unless otherwise stated, is examinable.
Having said that, I will definitely tinker as we go along, and make minor changes. Read at your own risk.
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Please submit your work by 11am, 15th of April.
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These are not required for the module, but they are some recommendations if you are looking for textbooks. See the notes!
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The final set of notes!
``Stand firm in your refusal to remain conscious during algebra. In real life, I assure you, there is no such thing as algebra.''-- Fran Lebowitz
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Here's a mock exam paper (for the May 2023-2024 exam) I have promised/written. I will go through the questions in one way or another at the end of April/the beginning of May 2024. I don't really know about the format but I might just record a video, or set up an online meeting (it's unlikely to be in-person unless lots of people want it that way).
The session is now scheduled on the 29th of April at 11am at
https://qmul-ac-uk.zoom.us/j/86501216933
Meeting ID: 865 0121 6933
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Francesca asked me how one could find the multiplicative inverse of [22]_{44}X+[25]_{44} in Z_{44}[X] (presumably, this is one of the questions found in a past exam paper) and, though I made a passable attempt at answering her question after the mock session, I did not do a great job. Here's a copy of the email I sent to Francesca shortly after. She has kindly agreed to share it with you all.
Thank you, Francesca, for always asking me great questions!
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A complete set of notes has been posted in Week 11 tab.
This document is prepared more for your benefit. You can use it to navigate/guide your way through the material I've covered when you are revising, or use it as skeleton notes to practise `filling in details'.
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Please look at the `Assessment Information' tab at the top to find documents-- they are all I could get hold of.
Alternatively, you can follow the link:
https://qmplus.qmul.ac.uk/mod/data/view.php?d=3492&perpage=10&search=MTH4104&sort=47735&order=DESC&advanced=0&filter=1&f_47735=&f_47736=&f_47737=to find exam papers but the link contains less than what I've compiled above.
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