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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 [email protected] 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 [email protected] 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