Welcome to CMPSC 360!

Today

Introductions Student Information Sheets, AutobiographyWhat is Discrete Math?Syllabus Highlightshttp://www.personal.psu.edu/

djh300/cmpsc360/

Introductory material: Mathematical sentences

What is Discrete Math?An Overview of Some Topics in the Course

Revised for Fall 2013Doug Hogan

Penn State University

CMPSC 360 – Discrete Math for Computer Scientists

What does “discrete” mean anyway????

Most things you’ve looked at in math so far are continuous. Usually using all real numbersContinuously-changing processesEx: time, temperature, speed, etc. Calculus studies continuous

mathematics.

Discrete is the opposite.

What does “discrete” mean anyway????

Discrete is the opposite of continuous:Step-by-step processesUsing integersCannot divide the units into smaller

pieces

Why do we care?

Discrete math is the language of computer scienceThis course is highly theoreticalMany upper-level CS courses will

require a lot of math; this course provides that background

Abstract Mathematics

A transition point to something differentDefinitions, theorems, proofsNot 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

Topics…

Logic

Evaluating whether statements are true or falseConstructing logical statementsProving statements to be equivalentMaking logical argumentsDetermining if arguments are valid

More on this to come….very soon…

Number Theory and Proofs

General forms of mathematical proofs that some claim is true in generalDirect proofs Indirect proofs, e.g. by contradiction

Basic number theoryTools used in CS – div, mod, floor, ceilingFactorization

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 relationsUnderstanding recursively-defined sequencesFinding non-recursive forms and proving themRelevant in the analysis of running time of recursive algorithms

Set Theory

Sets – unordered collections of objectsWe’ll look at operationsWe’ll prove claims about setsVery 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}

Functions and Relations

Like the functions you know from algebra, but for discrete situationsUsually more complicated definitionsSpecial kinds of functionsSpecial properties of relations

Graphs and Trees

Using vertices and edges to represent problems

A

B

C

D

Combinatorics

How to count……what they DIDN’T teach you on

Sesame Street

Ways of ordering objectsWays of combining setsUsing these combinations and permutations to find probabilities

And more!

Formally proving the correctness of algorithmsApplicationsBrief preview of automata

Some Syllabus Highlights

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)

Recitation Sections

On TuesdaysImportant 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.

Books

EppTarski’s World

Attendance and Conduct

Be here every classLet me know if you’ll missBe here on timeRespect your classmates and me. No cell phones or other distractions.We have a clock. (gasp)

Alertness Points

The ideaNeed a point tally person

Daily Homework

Out of EppMany with solutions in the back, intentionallyFor your own practiceCollected periodically in lecture Have the current unit’s homework with you

at every lecture

Grading is mainly about you keeping upYou get 10% for free (no late work, ever)Read policies on syllabus

Some data from S’12

28 students had perfect daily homework scores They all passed. 24 had As and Bs.

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%.

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%.

Formal Problem Write-Ups

Less frequentlyClear mathematical writing and presentation are a focus

Exams

9/16, 10/17, 11/14 in 26 HoslerEmphasize current unit but cumulative in a senseConflict exam form on syllabus. Due about two weeks before the exam.

Grades

35% - homework (daily and formal)45% - midterms20% - final

Participation, effort, etc. can affect grades within a few percent

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.

On to Lecture

Notes packets formatHave some blank paper handy If you want to write moreSolving practice problemsQuizzes

I recommend a 3-ring binder