# Math 365

 Polya's Four-Step Problem-Solving Process 1. Understand the problem2. Devise a plan3. Carry out the plan4. Looking back 1. Understanding the problem Can you state the problem in your own words 2. Devise a plan Look for a pattern 3. Carrying out the plan Check each step of the plan as you proceed 4. Looking back check the results in the original problem Conjecture a statement throught to be true, but not proven Counterexample example that contradicts the conjecture, shows the conjecture false Arithmetic Sequence an= a1+ d(n-1) Geometric Sequence an = a1* r(n-1) Recursive Sequence Ex: a1=2, a2=3, an=3an-2-an-1, for natural #n>2 must have all 3 parts or will be wrong In logic, a statement is a sentence that is either T or F The negation of a statement is a statement w the opposite true value of the given statement Be careful w quantifiers: Universal: all, every, & no refers to each & every element in a set Existential: some, there exists at least one refers to one or more or passible all elements in a set Truth tables p^q (p and q) - if both are T then its TpVq (p or q) - if both are F then its F Truth Tables Conditional Statements:p --> q (if p then q)Converse: q --> p (if q then p)Inverse:~p --> ~q (if not p then not q)Contrapositive:~q --> ~p (if not q them not p)Biconditional:p <--> q (p iff q) *If 1st is T & 2nd is F then its F* Place Value assigns a value of a digit depending upon its placement in a numeral Definition of an if a is any # and n e N, then an= a*a*...*a Ex: 23= 2*2*2=8 Mayan Numeration System a0=1 a1=20a2=20*18=360a3=202*18=7200...etc Dozen: Base 12 gross = dozen dozen0, 1, 2, 3, 4, 5, 6, 7, 8, 9, T, E Sets P & Q are in one-to-one correspondence if elements of P and Q can be paired so that for each element of P there is exactly one element of Q, & for each element of Q there is exactly one element of P Fundamental Counting Principle If event M can occur in m ways, and after it has occurred, event N can occur in n ways, then event M followed by event N can occure in mn ways Two sets A & B are equivalent A~B iff there exists a 1-1 correspondence btwn the two sets. The cardinal # of a set A, n(A): indicates the # of elelments in set A A set is finite if its cardinal number is a whole # The complement of a set A, written Ac: is the set of all elements in the universal set U that are not in A The empty set is a subset of everyset. Why? for any set A, either {}c A, or {} c A. Suppose{}c A, then there is some element in the empty set that is not in A, but because {} has no elements, it cannot have an element that is not in A.therefore {}c A Inequalities are an application of set concepts "Less Than" using sets: If A and B are finite sets then n(A) is less than n(B), written n(A)n(B) or a>b, which is n(B) b, a-b is a unique c eW such that a=b+c The Number Line Model - adding & subtracting Start at zero facing the (+) directionAdd means stay facing same directionSubtact means turn around(+) # means go forward(-) # means go backwards Expanded Algorrithm: 125 345+ 79 19 add ones 130 add tens+400 add hundreds 549 Left to Right Algorithm 458+8321200 (400+800)80 (50+30)+ 10 (8+2)1200+ 90 (80+10)1290 Authordt1158 ID66397 Card SetMath 365 DescriptionMath 365 Exam Cards Updated2011-02-15T03:13:36Z Show Answers