CS/Math 240: Introduction to Discrete Mathematics
6/21/2007
Homework 1
Instructor: Je Kinne
TA: Mike Kowalczyk
This homework is due at the beginning of class on Thursday June 28, 2007. Mike will hold a
review session at 12:45-1:45 on June 28 to discuss th
CS/Math 240: Introduction to Discrete Mathematics
8/2/2007
Homework 7
Instructor: Je Kinne
TA: Mike Kowalczyk
This homework is due at the beginning of class on Wednesday August 8, 2007. Mike will hold
a (homework/exam) review session sometime later in the
CS/Math 240: Introduction to Discrete Mathematics
Fall 2015
Reading 13 : Finite State Automata and Regular Expressions
Instructors: Beck Hasti, Gautam Prakriya
In this reading we study a mathematical model of computation called finite state automata.
13.1
CS/Math 240: Introduction to Discrete Mathematics
Fall 2015
Reading 2 : Propositions and Predicates
Instructors: Beck Hasti and Gautam Prakriya
2.1
Propositions
Remember that the goal of this course is to teach you how to reason about discrete structures
CS/Math 240: Introduction to Discrete Mathematics
Fall 2015
Reading 4 : Proofs
Instructors: Beck Hasti and Gautam Prakriya
Up until now, we have been introducing mathematical notation to capture concepts such as
propositions, implications, predicates, and
CS/Math 240: Introduction to Discrete Mathematics
Fall 2015
Reading 14 : Counting
Instructors: Beck Hasti, Gautam Prakriya
In this reading we discuss counting. Often, we are interested in the cardinality of some finite
set. For example in discrete probabi
CS/Math 240: Introduction to Discrete Mathematics
Fall 2015
Reading 1 : Introduction
Instructors: Beck Hasti and Gautam Prakriya
Welcome to CS 240, an introduction to discrete mathematics. This reading provides an overview
of the course and of the specifi
CS/Math 240: Introduction to Discrete Mathematics
Fall 2015
Reading 3 : Sets
Instructors: Beck Hasti, Gautam Prakriya
In this reading we discuss sets which will serve as the building block for other concepts such as
relations, functions, and graphs.
3.1
S
CS/Math 240: Introduction to Discrete Mathematics
Fall 2015
Reading 5 : Invariants
Instructors: Beck Hasti, Gautam Prakriya
5.1
Invariants
In this reading we look at how induction plays a role in establishing properties of discrete systems
(systems that e
CS/Math 240: Introduction to Discrete Mathematics
Fall 2015
Reading 5 : Induction
Instructors: Beck Hasti and Gautam Prakriya
In the last reading we began discussing proofs. We mentioned some proof paradigms that are
generally applicable. For implications
CS/Math 240: Introduction to Discrete Mathematics
Fall 2015
Reading 10 : Asymptotic Analysis
Instructor: Beck Hasti and Gautam Prakriya
In the last reading, we analyzed the running times of various algorithms. We expressed the
number of steps an algorithm
CS/Math 240: Introduction to Discrete Mathematics
Fall 2015
Reading 12 : Graphs
Instructors: Beck Hasti, Gautam Prakriya
Graphs are discrete structures that model relationships between objects. Graphs play an important role in many areas of computer scien
Practice Problems for Exam 2
Structural Induction and invariants
1. Below is the inductive definition for a balanced sequence (of parantheses):
Foundation: The empty sequence is balanced.
Constructor: If s and t are balanced sequences, then so are st an
Solutions to Practice Problems for Exam 2
Structural Induction and invariants
1. Below is the inductive definition for a balanced sequence (of parantheses):
Foundation: The empty sequence is balanced.
Constructor: If s and t are balanced sequences, then
Practice problems: Predicates
September 18, 2015
Below is a problem that should give you more practice with going between
English sentences and predicates. The solutions to the problem below use some
shortcuts in the notation for the sake of readability.
CS/Math 240: Introduction to Discrete Mathematics
Fall 2015
Reading 7 : Program Correctness
Instructors: Beck Hasti, Gautam Prakriya
7.1
Program Correctness
Showing that a program is correct means that it does what it is supposed to do. More formally, our
CS/Math 240: Introduction to Discrete Mathematics
Fall 2015
Reading 8 : Recursion
Instructors: Beck Hasti, Gautam Prakriya
8.1
Recursion
Recursion in computer science and mathematics refers to the idea of describing the solution of a
problem in terms of s
CS/Math 240: Introduction to Discrete Mathematics
7/10/2007
Exam 1 Handout
Instructor: Je Kinne
TA: Mike Kowalczyk
The rst exam will take place during the regular class time on Monday, July 16. It will be
closed book, closed notes, and no calculators allo
CS/Math 240: Introduction to Discrete Mathematics
7/10/2007
Exam 1 - Sample Exam
Instructor: Je Kinne
TA: Mike Kowalczyk
The exam will be closed-notes and no calculators will be allowed. You will be allowed a 4x6
inch index card cheat sheet. This sample e
CS/Math 240: Introduction to Discrete Mathematics
8/6/2007
Exam 2 Handout
Instructor: Je Kinne
TA: Mike Kowalczyk
The second exam will take place during the regular class time on the last day of class - Thursday,
August 9. It will be closed book, closed n
CS/Math 240: Introduction to Discrete Mathematics
8/6/2007
Exam 2 - Sample Exam
Instructor: Je Kinne
TA: Mike Kowalczyk
The exam will be closed-notes and no calculators will be allowed. You will be allowed a 4x6
inch index card cheat sheet. This sample ex
CS/Math 240: Introduction to Discrete Mathematics
6/28/2007
Homework 2
Instructor: Je Kinne
TA: Mike Kowalczyk
This homework is due at the beginning of class on Thursday July 5, 2007. Mike will hold a
review session at 12:45-1:45 on July 5 to discuss the
CS/Math 240: Introduction to Discrete Mathematics
7/5/2007
Homework 3
Instructor: Je Kinne
TA: Mike Kowalczyk
This homework is due at the beginning of class on Thursday July 12, 2007. Mike will hold a
review session at 12:45-1:45 on July 12 to discuss the
CS/Math 240: Introduction to Discrete Mathematics
7/12/2007
Homework 4
Instructor: Je Kinne
TA: Mike Kowalczyk
This homework is due at the beginning of class on Thursday July 19, 2007. Mike will hold a
review session at 12:45-1:45 on July 19 to discuss th
CS/Math 240: Introduction to Discrete Mathematics
7/19/2007
Homework 5
Instructor: Je Kinne
TA: Mike Kowalczyk
This homework is due at the beginning of class on Thursday July 26, 2007. Mike will hold a
review session at 11:45-12:45 on July 26 to discuss t
CS/Math 240: Introduction to Discrete Mathematics
7/26/2007
Homework 6
Instructor: Je Kinne
TA: Mike Kowalczyk
This homework is due at the beginning of class on Thursday August 2, 2007. Mike will hold a
review session at 11:45-12:45 on August 2 to discuss
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1.
A: Returns true iff the Integers in the chain of Listnodes is strictly (no
duplicates allowed) in descending order. Given the code, an empty chain
is considered in descending order by definition.
B: Returns the number of Listnodes containing items
CS 354 - Machine Organization
Friday, September 9, 2016
We assume that you have successfully completed CS 302 and CS/ECE 252.
Jim Skrentny, 5379 CS, skrentny@cs.wisc.edu
Canvas website: https:/canvas.wisc.edu/courses/3949
Outlines: On Canvas - select File
CS/Math 240: Introduction to Discrete Mathematics
Fall 2015
Reading 11 : Relations and Functions
Instructor: Beck Hasti and Gautam Prakriya
In reading 3, we described a correspondence between predicates on one variable and sets. A
predicate defines a set,
CS/Math 240: Introduction to Discrete Mathematics
Fall 2015
Reading 9 : Recurrences
Instructors: Beck Hasti and Gautam Prakriya
In the last few readings we dealt with program correctness. We discussed correctness of nonrecursive as well as of recursive al