Chapter B1 of MS221 is a bit of an odd one. Most of the chapter is about iterating functions, fixed-points, etc, but the final section is about binomial expressions, combinations and permutations – much more interesting! Not that there’s anything particularly dull about fixed-points, but puzzles like “How many six-letter permutations can be formed from the letters A, B, C, D, E, F, G, H, I, J?” grab my attention a lot more.

I did struggle a bit with the course text’s explanation of binomial expansion, though; I must have read through that section a dozen times, but I just couldn’t get to grips with the idea. Eventually I gave up and googled the topic, and came across this explanation on TeachNetUK, which did the trick. Once I’d got the hang of that, the rest of section was lots of fun – I particularly liked the exercise where we worked out how many six-number combinations you can get out of the numbers 1, 2, …, 49; i.e., what your chances of winning the lottery are. (I’d always assumed the odds were pretty low, but I didn’t realise they were that low!)

I’m really glad the chapter included these interesting bits about combinations and permutations, as I’d started to feel quite unmotivated and apathetic about MS221 after going to a tutorial on Wednesday. I tend to get very anxious and tense during tutorials, workshops, meetings, etc (anything with people in it, basically!), so I found the tutorial very taxing. I was coping fairly well until I made a trivial error on one of the problems we were working through, and at that point my embarrassment and social anxiety got the better of me, and I couldn’t concentrate at all for the rest of the session. I was extremely relieved when the tutorial ended, but for the rest of the week I felt embarrassed and kind of ashamed whenever I even looked at my MS221 books, let alone opened them up to study. I kept thinking that if I was a good student, tutorials wouldn’t bother me; I even ended up wondering whether I should just withdraw from the course now, and save myself the embarrassment of failing!

Luckily, I managed to flick through Chapter B1 towards the end of the week, and noticed the Binomial Theorem section, which eventually tempted me to pick up where I left off with my study schedule; so B1 was a very timely remedy for my despair about the course – who knows how many days of I would have wasted feeling dejected and pessimistic if I hadn’t been lured back by the promise of combinatorics!

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