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CS 2800 Discrete Structures Professor George Professor Chaudhuri Fall 2014 What is “Discrete Structures”? I Often called “Discrete Math” I The mathematical tools that underlie computer science I Discrete Math : Computer Science :: Calculus : Physics What is “Discrete Structures”? I Probability and Statistics I Sets, Functions, Relations I Formal Logic I Automata I Number Theory I Graphs What is “Discrete Structures”? I Probability and Statistics I I I “Big data”/machine learning Information theory ... I Sets, Functions, Relations I Formal Logic I Automata I Number Theory I Graphs What is “Discrete Structures”? I I Probability and Statistics Sets, Functions, Relations I I I Databases Functional programming ... I Formal Logic I Automata I Number Theory I Graphs What is “Discrete Structures”? I Probability and Statistics I Sets, Functions, Relations Formal Logic I I I Logical circuits Formal program verification I Automata I Number Theory I Graphs What is “Discrete Structures”? I Probability and Statistics I Sets, Functions, Relations I Formal Logic Automata I I I I I I Games Network protocols Compilers Nature of the universe ... I Number Theory I Graphs What is “Discrete Structures”? I Probability and Statistics I Sets, Functions, Relations I Formal Logic I Automata Number Theory I I I I I Cryptography Geometry ... Graphs What is “Discrete Structures”? I Probability and Statistics I Sets, Functions, Relations I Formal Logic I Automata I Number Theory Graphs I I I I I Social networks AI, planning Routing ... What is “Discrete Structures”? I Probability and Statistics I Sets, Functions, Relations I Formal Logic I Automata I Number Theory I Graphs What is this course really about? Math = Computation? What is this course really about? Math = Computation? Formal, step by step reasoning (proofs) I I Distinguishing good arguments from bad Clearly stating definitions I I and sticking to them! Tools for avoiding being wrong What is this course really about? Math = Computation? Formal, step by step reasoning (proofs) I I Distinguishing good arguments from bad Clearly stating definitions I I and sticking to them! Tools for avoiding being wrong Reasoning abstractly I Ignore the details of the objects you’re considering; work only with their properties. I I Example: I can add two integers, two real numbers, two strings, two paths on the surface of a donut Example: I can find shortest paths in a social network, a physical network, the flow of data in a program What is this course really about? Math = Computation? Formal, step by step reasoning (proofs) I I Distinguishing good arguments from bad Clearly stating definitions I I and sticking to them! Tools for avoiding being wrong Reasoning abstractly I Ignore the details of the objects you’re considering; work only with their properties. I I Example: I can add two integers, two real numbers, two strings, two paths on the surface of a donut Example: I can find shortest paths in a social network, a physical network, the flow of data in a program I Avoids getting bogged down in details I Lets you reuse your work Course Logistics I Lecture I I I Designed to be useful Some from Prof. George, some from Prof. Chaudhuri Please no laptops. Course Logistics I Lecture I I I I Designed to be useful Some from Prof. George, some from Prof. Chaudhuri Please no laptops. Problem Sets (weekly) I I released Friday, due Friday (5:00 PM), graded Monday judged on clarity and correctness Course Logistics I Lecture I I I I Problem Sets (weekly) I I I Two prelims (in class), one final Textbook I I I released Friday, due Friday (5:00 PM), graded Monday judged on clarity and correctness Exams I I Designed to be useful Some from Prof. George, some from Prof. Chaudhuri Please no laptops. No textbook May wish to consult “Discrete Mathematics and its Applications” by Rosen Website, CMS, Piazza I http://www.cs.cornell.edu/Courses/cs2800/2014fa Academic Integrity Expectations: I You are encouraged to work together, but . . . I All submitted work must be your own Encouraged: I Let’s work on problem 3 together Disallowed: I How did you do problem 3? Rule of thumb: I You should be able to reproduce the paper you turned in without consulting your notes.
