Math 10/CS10 – Discrete Math
Spring 2011
Instructor: Gail Edinger
Office: Math Complex 59
Campus Extension: (310) 434-3972
Office Hours:
Email: [email protected]
**Important note: Due to problems with email from unknown senders, put the
following in the subject section of all emails: Your full name – Math 10. If you do not
have this in the subject section I will not read your email.******
Please see the following page for the SMC course description and entry and exit skills for
this course.
Text: An Introduction to Discrete Mathematics, Second Edition, by Steven Roman.
ISBN number: 0-15-541730-4
Please bring your text to class, we will refer to it regularly. It is often possible to
find inexpensive copies of this text through online retailers, if you are comfortable
with internet shopping you have the option of looking online for this text.
We will be covering most of the material in Chapters 1 – 6. Students will be expected to
read each section, go over all examples and work the appropriate problems. Much of this
work will be done on your own. You will be responsible for all of the material in each
assigned section, even if we do not have time to cover everything in class.
A significant portion of this class is theory. You can expect to prove statements
using standard proof technique and format.
Homework: A list of homework problems is attached. (There may be changes as we
move through the semester.) You are expected to complete the appropriate assignments
after each class. We do not have time to go over homework in class, so for the most part,
if you have questions, please feel free to come by office hours. You are expected to
complete and understand all homework.
Homework should be kept neatly in a notebook. The notebooks will be collected at each
exam and be graded on a scale of 0, 1 or 2 points, where
0 = Homework not or minimally done
1 = Homework partially done but not complete
2 = Homework assignments completed.
The homework will count for 6% of your grade. The homework cannot be turned in
prior to the start of each exam. It will not be accepted FOR ANY REASON at any other
time, unless you have made prior arrangements to take the exam at another time (see
below.)
Exams: There will be three exams in this class. Please see the attached schedule for the
dates. There is be NO MAKE-UP EXAMS for any reason. If you miss one exam that
grade will be replace by your grade on the final. If you miss two or more exams a grade
of 0% will be recorded for those exams that cannot be made-up or replaced in any way.
The 0% will count toward your final average. At the end of the semester, if you have
taken all three exams and your score on the final is higher than any ONE exam, the score
on the final will replace the lowest exam score. This is the only way the grades will be
curved. If your final exam score is lower than all three of your exams, all three exams
will count individually and the final will count for the percentage listed below. The final
cannot be skipped or replaced by any grade.
Grades: Grades will be assigned as follows:
90 – 100% = A; 80 – 89% = B; 70 – 79% = C; 60 – 69% = D; Below 60% = F
The grades will be calculated as follows:
6% homework
64% 3 exams
30% Cumulative Final.
Other than as explained in the exams section, grades will not be curved. Your grade
will be assigned exactly as above and only your work during the semester will apply
toward your final grade. I cannot and will not make deals, take personal situations into
account (including but not limited to: transfer status, GPA, graduation status and any
other personal situation you can think of). All students will be graded on the same scale.
Final: There will be a cumulative final on Monday, 6/13 from 12 noon – 3 p.m.. You
are expected to take the final with the class. This final will not be rescheduled for
convenience, travel plans or any other reason. Please note the date now and schedule
yourself accordingly.
Date
2/14
2/16
2/23
2/28
3/2
3/7
3/9
3/14
3/16
3/21
3/23
3/28
3/30
4/4
4/6
4/18
4/20
4/25
4/27
5/2
5/4
5/9
5/11
5/16
Course Outline
Math 10
Please note: This outline is approximate, there may be changes.
Material Planned
1.1 The Language of Sets
1.2 One to One Correspondences
1.4 Functions
1.3 Countable and Uncountable Sets
1.5 Induction
1.6 Proof by Contradiction
2.1 Statements and Symbolic Language
2.2 Truth Tables
2.3 Logical Equivalence
2.4 Valid Arguments
2.5 Boolean Functions and Disjunctive Normal Form
2.6 Logic Circuits
2.7 Karnaugh Maps
3.1 Relations
3.2 Properties of Relations
EXAM CHAPTER 1 AND 2
3.3 Equivalence Relations
3.4 Partially Ordered Sets
3.5 More on Partially Ordered Sets
3.6 Order Isomorphisms (If time)
4.1 Introduction to Combinatorics
4.2 The Multiplication Rule
4.3 The Pigeonhole Principle
4.4 Permutations
4.5 More on Permutations
4.6 Combinations
4.7 Properties of the Binomial Coefficient
4.8 The Multinomial Coefficient
4.9 An Introduction to Recurrence Relations
4.10 Second Order Linear Nonhomogeneous Relations
4.11 Second Order Linear Nonhomogeneous Relations (More)
4.12 Generating Functions and recurrence relations
5.1 Permutations with Repetitions
EXAM CHAPTER 3 AND 4
5.2 Combinations with Repetitions
5.3 Linear Equations with Unit Coefficients
5.4 Distributing Balls into Boxes
5.5 The Principle of Inclusion-Exclusion I
5.6 The Principle of Inculsion-Exclusion II
5.7 The Principle of Inculsion-Exclusion III
5.8 An Introduction to Probability
5/18
5/23
5/25
6/1
6/6
6/8
6.1 Introduction to Graph Theory
6.2 Paths and Connectedness
6.3 Eulerian and Hamiltonian Graphs
6.5 Trees: The Depth First Search; if time sections 6.6, 6.9
EXAM CHAPTER 5 & 6
Review
Final Exam 12 noon – 3 p.m.
Note: This schedule is approximate. There will probably be changes as we move
through the semester.
Homework Assignments
*to be kept in a separate notebook to be turned in
Section
1.1
1.2
1.3
1.4
1.5
1.6
2.1
2.2
2.3
2.4
2.5
2.6
2.7
3.1
3.2
3.3
3.4
3.5
3.6
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
5.1
Problems
1,3,5,6,9,12,13,16,18,20,21,25,27,34,41,43,45,48
1,8,10,12,15,19,20,21
3,5,6,8,9,10,13,14,15
2,3,6,10,12,13,16,18,19,21,23,24,25,27,28,30,31,32,34
1-17 odd, 18,20,21,23,24,25,27,28,30,31,32,34
2,4,7,8
1,2,4,5,7(a,c,e),8
1-9 odd, 12-16 even, 17,18,20,22,23,24,28
4,5,7,12,13,15,17,20,22
1-17 odd,21,25,26,27
1,3,5,6,9,11,12,13-29 odd
1-9 odd, 13,15,17,18,20,21,22
3,5,7,11,13,15,16
1,3,6,7,8,10,11,13,14,15,17,19,20
1-11 odd, 13-17 all, 21 – 29 odd, 30-33 all, 35
1,3,4,5,7,8,11,14,15,19
2,3,5,7,8,9,12,17
1-9 odd, 14 – 16 all, 20,21,24
1,2,3,4,7,9,13
1,2,4,9,12,15,17,20,21
1,3,4,5,9,11,15,16
1(abc), 2(bc), 6,8,9,11,13,16,17,18,24,25,26
1-11 all, 16, 19
1-3 (parts c and d), 4a,5,7, 8 – 23 all
4ac, 5b, 7, 13b, 17b
1 – 4 all, 8 – 11 all, 13
1,3,5,6,7,11,15,18,23,26
1,4,5,6,10,13
1,3,6,8
3 – 6 all, 10, 13, 14, 15, 16, 20, 21
5.2
5.3
5.4
5.5
5.6
5.7
5.8
6.1
6.2
6.3
1-5 all, 7 – 10 all, 12
3,6,9 – 14 all
1 – 9 all, 13, 15, 16, 17, 19 – 22 all
1,3,6,7,9,10,12,13
1,4,5,8,15
TBA
TBA
1-13,15,17,19,21,22
1,3-9,12,13,18
1-7,9-11,14,15,20,21,23,25,27,28
All assignments subject to change.
Course Details
Description This course is intended for computer science, engineering and
mathematics majors. Topics include sets and relations,
permutations and combinations, graphs and trees, induction and
Boolean algebras.
Prerequisites Math 8
How It Transfers Transfer: UC, CSU IGETC AREA 2 (Mathematical Concepts)
Textbook Roman, Steven, An Introduction to Discrete Mathematics, Harcourt
Brace Javanovich, Inc., 1989
Mathematics Skills Associated With This Course
Entry Level Skills Skills the instructor assumes you know prior to enrollment in this
course
Differentiate and integrate exponential, logarithmic, hyperbolic
functions.
Use various techniques of integrations and applications.
Analyze infinite series (congruence and divergence).
Use Power and Taylor series to express an infinite series.
Recognize indeterminant forms and improper integral (using polar
coordinates or parametric equations).
Use analytical geometry (rotation of axes) to differentiate and
integrate.
Know the binomial theorem.
Course Objectives Skills to be learned during this course
Simplify a logic diagram.
Construct the parse tree for any mathematical expression.
Construct a truth table for any logical expression from the
sentential calculus.
Demonstrate a working knowledge of the first order predicate
calculus and its notation.
Create a logic diagram that corresponds to a logical formula.
Compute permutations, combinations, and probabilities given a
sample space.
Analyze a graph of n vertices and edges using graph theory
algorithms.
Withdrawl Policies: The SMC withdrawl dates are listed below. Please read them carefully. They will be
strictly followed.
–you must haWithdrawal Deadlines
Last day to withdraw in Spring Semester (16-week session)
To receive enrollment fee and tuition refund
By web – Thurs, Feb 24, 2011, 10 p.m.
To avoid a W on permanent record
By web – Mon, Mar 7, 2011, 10 p.m.
To receive a guaranteed W
By web – Sun, Apr 10, 2011, 10 p.m.
To receive a W with faculty approval of extenuating circumstances (NO grade check
required)
(instructor must drop you online)
Sun, May 8, 2011
Drop dates vary for short-term and open-ended classes. Go to the SMC webpage
(www.smc.edu) and click on “Dates and Deadlines” for details.
ve spoken with me in person by the previous Thursday, April 7,2011.(Not via email or phone) by 2:00 p.m. I
will not be available on the weekend to submit withdrawals.
Please note: “extenuating circumstances” means that there is some verifiable and unforeseeable
emergency which precludes your completing your semester at SMC. This does NOT include avoiding a low
grade, the effect of this class on your GPA, your transfer status or any other such circumstance. You will
have until the above date to drop for these reasons, after that you are in the class for a grade. If you want
discuss “extenuating circumstances” to invoke this option of withdrawing after the above date you will
probably be in a situation which requires that you withdraw from ALL of your SMC classes not just this one.
Course Details
Description This course is intended for computer science, engineering and
mathematics majors. Topics include sets and relations,
permutations and combinations, graphs and trees, induction and
Boolean algebras.
Prerequisites Math 8
How It Transfers Transfer: UC, CSU IGETC AREA 2 (Mathematical Concepts)
Textbook Roman, Steven, An Introduction to Discrete Mathematics, Harcourt
Brace Javanovich, Inc., 1989
Mathematics Skills Associated With This Course
Entry Level Skills Skills the instructor assumes you know prior to enrollment in this
course
Differentiate and integrate exponential, logarithmic, hyperbolic
functions.
Use various techniques of integrations and applications.
Analyze infinite series (congruence and divergence).
Use Power and Taylor series to express an infinite series.
Recognize indeterminant forms and improper integral (using polar
coordinates or parametric equations).
Use analytical geometry (rotation of axes) to differentiate and
integrate.
Know the binomial theorem.
Course Objectives Skills to be learned during this course
Simplify a logic diagram.
Construct the parse tree for any mathematical expression.
Construct a truth table for any logical expression from the
sentential calculus.
Demonstrate a working knowledge of the first order predicate
calculus and its notation.
Create a logic diagram that corresponds to a logical formula.
Compute permutations, combinations, and probabilities given a
sample space.
Analyze a graph of n vertices and edges using graph theory
algorithms.