This week, we were introduced to proof by cases. This includes breaking the argument into different cases and proving true for each case. We see this a lot in conjunction or disjunction statements. It is also used in proving absolute values of statements. This is because, the proof of an absolute value inequality can be simplified to -b < x - a < b where the original statement is | x - a | < b. This proof method seemed less complex than previous proofs because I fully understood the Professor's explanations and examples.
In this week, we were also introduced to counting steps in an algorithm, which exposed me to the concept of Big Ohs. We learnt about the efficiency of algorithms and how the number of steps which is measured as "running time" can be formulated into expressions. This lecture was straight forward as counting the number of executions in a program did not seem very demanding for me. This was one of the most enjoyable lectures for me since I have always wanted to learn about efficiency in programs.
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