University Notes

These are my notes from studying mathematics and computer science at the University of Oxford.

Table of Contents

Prelims

See also [[Prelims]]^U.

Courses MT22

See [[Courses MT22]]^U.

• [[Course - Introduction to University Mathematics MT22]]^U
• [[Course - Introduction to Complex Numbers MT22]]^U
• [[Course - Analysis I MT22]]^U
• [[Course - Probability MT22]]^U
• [[Course - Linear Algebra I MT22]]^U
• [[Course - Functional Programming MT22]]^U
• [[Course - Ethics and Responsible Innovation MT22]]^U

Courses HT23

See [[Courses HT23]]^U.

• [[Course - Linear Algebra II HT23]]^U
• [[Course - Groups and Group Actions HT23]]^U
• [[Course - Analysis II HT23]]^U
• [[Course - Imperative Programming I and II HT23]]^U
• [[Course - Design and Analysis of Algorithms HT23]]^U
• [[Course - Continuous Mathematics HT23]]^U

Courses TT23

See [[Courses TT23]]^U.

• [[Course - Analysis III TT23]]^U
• [[Course - Groups and Group Actions TT23]]^U
• [[Course - Imperative Programming III TT23]]^U

Part A

See [[Part A]]^U.

Courses MT23

See [[Courses MT23]]^U.

• [[Course - Metric Spaces MT23]]^U
• [[Course - Complex Analysis MT23]]^U
• [[Course - Linear Algebra MT23]]^U
• [[Course - Machine Learning MT23]]^U
• [[Course - Models of Computation MT23]]^U

  Courses HT24

  See also [[Courses HT24]]^U.

• [[Course - Rings and Modules HT24]]^U
• [[Course - Numerical Analysis HT24]]^U
• [[Course - Quantum Information HT24]]^U
• [[Course - Algorithms and Data Structures HT24]]^U

Courses TT24

No courses in TT24, just revision.

Part B

See [[Part B]]^U.

Courses MT24

See [[Courses MT24]]^U.

• [[Course - Logic MT24]]^U
• [[Course - Artificial Intelligence MT24]]^U
• [[Course - Computer Security MT24]]^U
• [[Course - Logic and Proof MT24]]^U

Courses HT25

• [[Course - Galois Theory HT25]]^U
• [[Course - Set Theory HT25]]^?
• [[Course - Optimisation for Data Science HT25]]^?
• [[Course - Computational Complexity HT25]]^?

Organisation

My degree is divided into four parts:

• [[Prelims]]^U (preliminary examinations)
• [[Part A]]^U
• [[Part B]]^U
• [[Part C]]^?

You complete [[Prelims]]^U in your first year, [[Part A]]^U in your second, and so on. I’m just about to head into [[Part B]]^U, which will be my third year. Each year is then divided into three terms: Michaelmas (October-December, abbreviated “MT”), Hilary (January-March, abbreviated “HT”), Trinity (April-June, abbreviated “TT”).

What are these notes?

Like my [[A-Level Notes]]^A, the bulk of these notes are flashcards. These are question-and-answer pairs which get automatically synced to Anki by an Obsidian plugin called Obsidian-Anki-Sync (for more information, take a look in [[About this website]]^B).

Most of the content in the “pure” courses I take at university is just a long list of different kinds of…

• Definitions, an explanation of what a concept means
• Theorems, an important statement that has been proven to be true
• Proposition, a less important statement that has also been proven true
• Lemma, a true statement that is useful in proving other statements
• Corollaries, an important consequnece of a theorem

I’ll typically have a flashcard for each definition, a flashcard for each theorem, lemma and corollary, and then a flashcard for the proof for each. So if the lecturer for [[Course - Metric Spaces MT23]]^U says “a metric space is sequentially compact iff it is closed and totally bounded”, I’ll have flashcards for:

• What it means for a metric spaces to be “sequentially compact”
• What it means for a metric space to be “closed”
• What it means for a metric space to be “totally bounded”
• The statement “a metric space is sequentially compact iff it is closed and totally bounded” itself
• The proof of that statement (or in this case, two flashcards, one for each direction of the equivalence)

These flashcards will live in a corresponding “notes” page, in this case [[Notes - Metric Spaces MT23, Compactness]]^U. I might also have more flashcards giving examples of where this theorem can be used. For more “applied” courses like [[Course - Machine Learning MT23]]^U, the course might describe specific techniques or algorithms that I’ll need to know for the exam, so I’ll make flashcards for these too.

Of course, this is all in the ideal situation and doesn’t always happen; there’s a few courses from [[Prelims]]^U where my notes are quite bare. But I’m really happy with how my notes for [[Part A]]^U turned out, I think these are all reasonably complete.