CSC165H1- Final Exam Guide - Comprehensive Notes for the exam ( 24 pages long!)
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CSC165H1 Full Course Notes
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Mat102: mathematical thinking-lecture 1: ch. 1 numbers,sets and functions. Theorem( the quadratic formula): ax^2+bx+c=0 (for all a 0) has 3 situations: not real solutions if b^2-4ac<0, a unique solution if b^2-4ac=0, given by x=-b/2a, two distinct real solutions if b^2-4ac 0, given by. Proof: starts with ax^2+bx+c=0 and divided by a(a 0) x x+ c a. 2 < 0 and there are no real solutions as. Thus, we get a unique solution as needed. It is communicated by writing complete sentences and using words(not only formulas). Symbols have to be explained and connective(such as and , or , if ,then ). They are important and should be used properly. A proof is normally based on earlier established facts (such as ( + )2= 2+2 + 2. Basic facts: let a,b,c be three real numbers. If a0, then ca
