## Cracking on with TMA4

TMA3 away and making reasonable progress with TMA4.

I have also started looking at past exam papers for M381 and have realised I will need to commit a lot of stuff to memory as the handbooks which accompany the course during the exam seem pretty light.

I’m hoping to have TMA4 away by the end of March, leaving me around 10 weeks for revision.

I have “analysed” the question types by sifting past papers and, in the number theory section alone, the following seem a good bet:

Proof by induction

Euclidean Algorithm

Some sort of GCD proof

Infinitely many primes of the form… blah… proof

Least positive residues

Linear congruences

Some form of modular arithmetic proof

Fermat’s Little Theorem

Wilson’s Theorem – applications and proof

Recurring decimals

Sigma(n)/Euler’s phi function

Quadratic congruence

Legendre symbol manipulation

Gauss’ Lemma

Law of Quadratic Reciprocity

Continued fractions

Irrational numbers

Some form of Diophantine equation-related proof

That’s just the number theory side.

The mathematical logic side looks equally long. I’ll detail that later, when I’ve completed it.

One long course, when both the number theory and mathematical logic aspects are combined, for just 30 undergrad credits.

## Continued fractions

I thought this was a decent watch as a basic introduction to M381’s continued fractions.