1. Welcome to CMPSC 360!

2. Today Introductions Student Information Sheets, Autobiography What is Discrete Math? Syllabus Highlights http://www.personal.psu.edu/ djh300/cmpsc360/ Introductory material: Mathematical sentences

3. What is Discrete Math? An Overview of Some Topics in the Course Revised for Fall 2013 Doug Hogan Penn State University CMPSC 360 – Discrete Math for Computer Scientists

4. What does “discrete” mean anyway???? Most things you’ve looked at in math so far are continuous. Usually using all real numbers Continuously-changing processes Ex: time, temperature, speed, etc. Calculus studies continuous mathematics. Discrete is the opposite.

5. What does “discrete” mean anyway???? Discrete is the opposite of continuous: Step-by-step processes Using integers Cannot divide the units into smaller pieces

6. Why do we care? Discrete math is the language of computer science This course is highly theoretical Many upper-level CS courses will require a lot of math; this course provides that background

7. Abstract Mathematics A transition point to something different Definitions, theorems, proofs Not always formulaic like most of the math you’re used to “To think deeply of simple things” - A. E. Ross “Simple ≠ easy” - G. H. Stevens

8. Topics…

9. Logic Evaluating whether statements are true or false Constructing logical statements Proving statements to be equivalent Making logical arguments Determining if arguments are valid More on this to come….very soon…

10. Number Theory and Proofs General forms of mathematical proofs that some claim is true in general Direct proofs Indirect proofs, e.g. by contradiction Basic number theory Tools used in CS – div, mod, floor, ceiling Factorization

11. Inductive Proofs and Recurrences Induction Technique for proving statements of the form “for all n.” Assume a statement is true for k, show it is true for k +1. Then it is true for all n. Recurrence relations Understanding recursively-defined sequences Finding non-recursive forms and proving them Relevant in the analysis of running time of recursive algorithms

12. Set Theory Sets – unordered collections of objects We’ll look at operations We’ll prove claims about sets Very basic example: Set A = {1, 2, 3} Set B = {2, 4} Union of A and B = {1, 2, 3, 4} Intersection of A and B = {2}

13. Functions and Relations Like the functions you know from algebra, but for discrete situations Usually more complicated definitions Special kinds of functions Special properties of relations

14. Graphs and Trees Using vertices and edges to represent problems A B C D

15. Combinatorics How to count… …what they DIDN’T teach you on Sesame Street Ways of ordering objects Ways of combining sets Using these combinations and permutations to find probabilities

16. And more! Formally proving the correctness of algorithms Applications Brief preview of automata

17. Some Syllabus Highlights

18. Finding Us Instructor: Doug Hogan hogan@cse.psu.edu 338C IST Office hours: M 3:45-5:15 p.m. (ending at 4:45 today only), W 10-10:50 a.m., 12:15-12:45 p.m., R 4-5 p.m. Teaching Intern: Steve Styer srs5328@psu.edu Office hours in 339 IST (Collaborative space) Office hours: T 9-10 a.m., F 11:15-12:15 a.m. (Graders behind the scenes)

19. Recitation Sections On Tuesdays Important that you go to your assigned section. Some rooms are full. Mixed activities. Often small problem solving things and Q&A. Sometimes quizzes. Lecture in recitation tomorrow.

20. Books Epp Tarski’s World

21. Attendance and Conduct Be here every class Let me know if you’ll miss Be here on time Respect your classmates and me. No cell phones or other distractions. We have a clock. (gasp)

22. Alertness Points The idea Need a point tally person

23. Daily Homework Out of Epp Many with solutions in the back, intentionally For your own practice Collected periodically in lecture Have the current unit’s homework with you at every lecture Grading is mainly about you keeping up You get 10% for free (no late work, ever) Read policies on syllabus

24. Some data from S’12 28 students had perfect daily homework scores They all passed. 24 had A s and B s. In the top half of the class by raw numeric grades, only 3 students had homework grades below 70%. 84% of the students who didn’t earn the required C had a homework grade below 70%.

25. Some data from F’12 23 students had perfect daily homework scores They all passed. 23 had B+ or better grades. 59% of those who took the final earned grades of B- or better. Of those, only one had a homework grade below 70%. 75% of the students who didn’t earn the required C had a homework grade below 70%.

26. Formal Problem Write-Ups Less frequently Clear mathematical writing and presentation are a focus

27. Exams 9/16, 10/17, 11/14 in 26 Hosler Emphasize current unit but cumulative in a sense Conflict exam form on syllabus. Due about two weeks before the exam.

28. Grades 35% - homework (daily and formal) 45% - midterms 20% - final Participation, effort, etc. can affect grades within a few percent

29. Read the syllabus in its entirety! If you took my FYS last spring and didn't get an email last week, see me after class.

30. On to Lecture Notes packets format Have some blank paper handy If you want to write more Solving practice problems Quizzes I recommend a 3-ring binder