Depends on what you are looking for. Mathematics is mostly deductive but Science is inductive. A good site to try inductive skills is http://www.shldirect.com/inductive_reasoning.html The best site I know of for mathematical induction is
http://www.cut-the-knot.org/cgi-bin/dcforum/ctk.cgi?conf=DCConfID1 from that page click search type in induction and there are 107 topics re induction to choose from. some are discussions, some are problem solutions etc.
It is well known that a vector space always admits an algebraic (Hamel) basis. This is a theorem that follows from Zorn's lemma based on the Axiom of Choice (AC).
Now consider any specific instance of vector space. Since the AC axiom may or may not be included in the underlying set theory, might there be examples of vector spaces in which an Hamel basis actually doesn't exist ?