Sets and proofs -- Number systems -- Decimals -- Nth roots and rational powers -- Inequalities -- Complex numbers -- Polynomial equations -- Induction -- Euler's formula and platonic solids -- The integers -- Prime factorization -- More on prime numbers -- Congruence of integers -- More on congruence -- Secret codes -- Counting and choosing -- More on sets -- Equivalence relations -- Functions -- Permutations -- Infinity -- Introduction to analysis: bounds -- More analysis: limits -- Yet more analysis: continuity -- Introduction to abstract algebra: groups -- Introduction to abstract algebra: more on groups.