I really like Number Theory, which is often about studying how prime numbers work and the patterns in them. The thing I like about this is we build up true ideas on top of other true things we have worked out to come to the correct answer, and when you get there everyone agrees that was the right answer.
I also like Statistics, which is the complete opposite. In statistics, we use maths models to look at collections of data and try to understand the patterns in the data. The models are never perfectly right and there are lots of different options for models, so everyone argues a lot over which was is the most useful slightly wrong answer and how close the wrong answers are likely to be to the true answer. I like knowing from the start that I am wrong, and so is everyone else, so it’s just about whose answer can be useful even though it is slightly wrong.
The best maths topic is the one you enjoy and find interesting! For me, one of things I like are sums of sequences.
Consider the sum of the sequence 1+1/2+1/4+1/8+1/16+… Can you see the pattern in the denominator of the fraction? It is 2 times the last term. If you keep adding terms to this sequence, it will get closer and closer to 2!
But, if you take the sum of the sequence 1+1/2+1/3+1/4+1/5+1/6+ … Can you see the pattern in the denominator of the fraction? Each value increases by 1. If you keep adding these terms, the sum will get closer and closer to infinity as there is no limit!
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Edward commented on :
The best maths topic is the one you enjoy and find interesting! For me, one of things I like are sums of sequences.
Consider the sum of the sequence 1+1/2+1/4+1/8+1/16+… Can you see the pattern in the denominator of the fraction? It is 2 times the last term. If you keep adding terms to this sequence, it will get closer and closer to 2!
But, if you take the sum of the sequence 1+1/2+1/3+1/4+1/5+1/6+ … Can you see the pattern in the denominator of the fraction? Each value increases by 1. If you keep adding these terms, the sum will get closer and closer to infinity as there is no limit!