CS 345 Lecture 1: Introduction and Math Review
This content encompasses the introduction and mathematical review covered in CS 345 lecture 1, including topics such as sets, sequences, logarithms, logical equivalences, and proofs. It delves into sets theory, mathematical operations, deductive reasoning, and examples like the conjecture of even numbers. The images provided visualize concepts such as sets union, intersection, power sets, summation, and more.
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CS 345 Lecture 1 Introduction and Math Review
CS 345 Instructor Qiyam Tung TA Sankar Veeramoni
Administrivia Webpage http://www.cs.arizona.edu/classes/cs345/summer14/ Syllabus http://www.cs.arizona.edu/classes/cs345/summer14/syllabus.html
Sets Union Intersection
Sets (contd) Membership Defining sets Even numbers Odd numbers
Sets Power set
Sequences Summation Products
Closed form equivalents Triangular numbers Sum of powers of 2
Logarithms Product Quotient
Logarithms (contd) Power Change of base
Logical Equivalences De Morgan s Law Propositions Sets
Proofs Deductive Contrapositive Inductive
Proofs (contd) Contradiction p q ~p p->q ~p V q
Deduction (example) Conjecture: If x is even, then 5x is even
Deduction (contd) Conjecture: If x is even, then 5x is even
Contrapositive (example) Conjecture: If x^2 is odd, then x is odd
Contrapositive (contd) Conjecture: If x^2 is odd, then x is odd
Inductive (example) Conjecture:
Contradiction (example 1) Conjecture: There are infinite prime numbers
Contradiction (example) Conjecture: The square root of 2 is irrational
CS 345 Lecture 1 Introduction and Math Review
CS 345 Instructor Qiyam Tung TA Sankar Veeramoni
Administrivia Webpage http://www.cs.arizona.edu/classes/cs345/summer14/ Syllabus http://www.cs.arizona.edu/classes/cs345/summer14/syllabus.html
Sets Union Intersection
Sets (contd) Membership Defining sets Even numbers Odd numbers
Sets Power set
Sequences Summation Products
Closed form equivalents Triangular numbers Sum of powers of 2
Logarithms Product Quotient
Logarithms (contd) Power Change of base
Logical Equivalences De Morgan s Law Propositions Sets
Proofs Deductive Contrapositive Inductive
Proofs (contd) Contradiction p q ~p p->q ~p V q
