The original syllabus is available.
History:
Mathematics is a combination of both forms of reasoning in no particular order.
1 + 2 + 3  = 6  = 3 * 4 / 2 
1 + 2 + 3 + 4  = 10  = 4 * 5 / 2 
... + 5  = 15  = 5 * 6 / 2 
So what is the sum of the first 50?
50 * 51∕2 = 25 * 51 = 25(25 ⋅ 1) + 250(50 ⋅ 5) + 1000(50 ⋅ 20) = 1275

Integer sequence superseeker from AT&T gives 250 results matching (3,10,15). Some of the sequences are built similarly.
[ NOTE Text uses “probable”. Don’t do that. There’s no probability distribution defined over the choices, so no one choice is more “probable”.]
Only takes a single counterexample to ruin a perfectly wrong theory.
Must be very careful and define what we mean and want. These are the hypotheses or premises.
What is the premise above?
Could we use an extreme case to check possibilites? (What is the sum of 1?)
Start with a collection of premises and combine them to reach a result. Note: the rules for combining these also are premises!
Knowing to distinguish a “general principle” from a hypothesis takes time and perspective. That’s part of what we’re covering, but don’t worry much about it now.
Typical patterns:
Used before algebra (Greek geometry), but algebra really helps.