1. Discrete Structures and The Three-Fold Introduction to Computer Science Doug Baldwin Department of Computer Science SUNY Geneseo

2. Motivation Computer science entails… Design and implementation of algorithms, programs, systems, etc Mathematical analysis of algorithms, programs, etc Experimental analysis of algorithms, programs, etc These should be taught concurrently and from day 1

3. Ca 1992… CS1 (Pascal, selection, logic, recursion, induction, recurrences, big-O, lists, trees) CS1 (Pascal, selection, logic, recursion, induction, recurrences, big-O, lists, trees) CS2 (Object Pascal, iteration, arrays, sorting, summations, …) CS2 (Object Pascal, iteration, arrays, sorting, summations, …)

4. Ca 1992… CS1 (Pascal, selection, logic, recursion, induction, recurrences, big-O, lists, trees) CS1 (Pascal, selection, logic, recursion, induction, recurrences, big-O, lists, trees) CS2 (Object Pascal, iteration, arrays, sorting, summations, …) CS2 (Object Pascal, iteration, arrays, sorting, summations, …) ? !

5. Ca 1994… CS1 (Pascal, recursion, induction, …) CS1 (Pascal, recursion, induction, …) CS2 (Object Pascal, iteration, summations, …) CS2 (Object Pascal, iteration, summations, …) CS0 (CS overview, computational thinking) CS0 (CS overview, computational thinking)

6. Ca 1994… CS1 (Pascal, recursion, induction, …) CS1 (Pascal, recursion, induction, …) CS2 (Object Pascal, iteration, summations, …) CS2 (Object Pascal, iteration, summations, …) CS0 (CS overview, computational thinking) CS0 (CS overview, computational thinking) ? !

7. ca 1999 CS 1-1/2 (logic, recursion, induction, recurrences, big-O, lists, trees) CS 1-1/2 (logic, recursion, induction, recurrences, big-O, lists, trees) CS2 (OOP, summations, sorting, searching, E[…], hashing) CS2 (OOP, summations, sorting, searching, E[…], hashing) CS 1 (Java) CS 1 (Java) Algorithms (graphs, greedy, dynamic programming, …) Algorithms (graphs, greedy, dynamic programming, …)

8. ca 1999 ? CS 1-1/2 (logic, recursion, induction, recurrences, big-O, lists, trees) CS 1-1/2 (logic, recursion, induction, recurrences, big-O, lists, trees) CS2 (OOP, summations, sorting, searching, E[…], hashing) CS2 (OOP, summations, sorting, searching, E[…], hashing) CS 1 (Java) CS 1 (Java) Algorithms (graphs, greedy, dynamic programming, …) Algorithms (graphs, greedy, dynamic programming, …)

9. Ca 2003 - Present CS 2 (OOP, recursion, lists, trees, Big O) CS 2 (OOP, recursion, lists, trees, Big O) CS 2-1/2 (logic, induction, recurrences, summations, sorting, searching) CS 2-1/2 (logic, induction, recurrences, summations, sorting, searching) CS 1 (Java) CS 1 (Java) Algorithms (probability, E[…], hashing, graphs, greedy, …) Algorithms (probability, E[…], hashing, graphs, greedy, …)

10. Ca 2003 - Present CS 2 (OOP, recursion, lists, trees, Big O) CS 2 (OOP, recursion, lists, trees, Big O) CS 2-1/2 (logic, induction, recurrences, summations, sorting, searching) CS 2-1/2 (logic, induction, recurrences, summations, sorting, searching) CS 1 (Java) CS 1 (Java) Algorithms (probability, E[…], hashing, graphs, greedy, …) Algorithms (probability, E[…], hashing, graphs, greedy, …) If n = 0 … Assume T(k) T(k+1)…

11. Summary Workable model for integrating discrete structures into introductory/intermediate CS – Works for students – Works for department (10 year record) Covers most of CC 2001 (and CS 2013) core DS material (exceptions: counting, sets/functions/relations)