MAD 2104-Discrete Mathematics
Fall 2014
Course Syllabus
(See UPDATES, in Blackboard, at least three times a week)
Instructor: Dr. Jorge E. Viola-Prioli Class Time: 95132 Monday, Wednesday and Friday, 1:00 - 1:50 in ED 113
82633 Monday, Wednesday and Friday, 2:00 -2:50 in ED 113
Classes begin: Monday, August 18th, 2014 Office: Science & Engineering Building, 2nd Floor. Room 222.
Office Hours : M, W, F 3:15 - 4:15. No appointment needed. Other times, by
appointment only.
Email: jviola@fau.edu (No Email will be replied to unless the student identifies
the course, the section, provides his/her name and uses an fau account)
URL of this site: http://math.fau.edu/viola/mad2104fa2014/syllabus.pdf
Official Textbook: Mathematics: A Discrete Introduction, by Edward
Scheinerman, THIRD edition, 2012. Publisher: Brooks/Cole.
Course Outline: from the text, we shall try to cover sections 3-17, 20-26, 35-39,
43, 44, 46 not necessarily at equal pace. Minor reordering of sections within a
chapter may occur, for presentation purposes.
We assume that students will attend all lectures (see below, Grading), read the
text, complete all homework assignments as soon as possible, and study for exams.
Students are strongly advised to bring the textbook to the classroom. Reading in
advance the material to be discussed in class indeed helps, because that way you
get familiar with the terminology to be used, get some idea of what is coming and
locate the hard spots. In this course my presentations will be done by Power
Point. At the end of each lecture (or even before it) I will post in Blackboard
the corresponding pdf file: to access that material click LECTURE NOTES in
the contents area. Bottom line: students will need not take notes during the lectures
(unless specifically advised to do so, since I sometimes complement my Power
Points with discussions and extra examples, by resorting to the board) It is very
wise to print out each pdf file: that way the students will have a good set of
notes for the whole course.
Goal: This should be your first encounter with a course devoted to abstract
thinking. Although we respect rigor, we appreciate imagination and intuition. After
successfully completing this course, you should be able to
find the logical structure of a mathematical statement.
express your ideas correctly, with entire precision, in mathematical terms. explain why a statement is true or why is not valid.
recognize equivalence relations.
apply Mathematical Induction to a diverse type of problems.
use the Pigeonhole Principle and Counting Methods in order to solve
numerous problems.
compute the greatest common divisor by means of the Euclidean Algorithm.
understand the basic principles of Cryptograghy.
Tests: there will be three midterm Tests, and a fourth, comprehensive Final
Examination. Prior to each Test the topics to be evaluated will be announced. The
same applies to the Final Exam. The tests are scheduled as follows:
Test 1 Friday, September 12th, in class (50 minutes exam)
Test 2 Monday, October 6th, in class (50 minutes exam)
Test 3 Monday, November 3rd, in class (50 minutes exam)
Final Exam Sunday, December 7th, 10:30 - 1PM ROOM SO 250
There will be no make-up exams: tests can not be taken neither earlier nor
later than the scheduled dates. So plan ahead, particularly in case you must
travel away from Boca Raton! Official Holidays (no classes): September 1, 2014 (Labor Day), November 11th
(Veterans Day), November 27th through 30th (Thanksgiving)
Grading Scale: the lowest of the grades of the first three Tests will be dropped.
The two remaining grades will each be worth 30% of the final grade. As to the
Final Exam, it is worth 40% of the final grade. Numerical Grades will then be
translated into Letter Grades according to the following scale:
A: [94 100]
A-: [90 94)
B+: [84 90)
B: [76 84)
B-: [71 76)
C+: [67 71)
C: [63 67)
C-: [54 63)
D: [51 54)
F: [0 51)
Students with five or more absences will see their final grades reduced one tier
down. This does not apply to absences for university-approved reasons.
Grades posting: Grades will always be posted through Blackboard at http://
blackboard.fau.edu Once in that page click "MY GRADES". If you need support
to access that site please notice: you will need a USERNAME and a PASSWORD.
The student username is their FAUNet ID (the same as for MyFAU) If the
student does not know their FAUNet ID they should go to https://banner.fau.edu/
FAUPdad/lwgkznum.P_DisplayID (they will need to enter their social security #
and PIN in order to obtain their FAUNet ID).
The student email address in Blackboard will be set as their FAU email address (to
forward email to another account students should go to MyFAU and select "auto
forward" under "options"). May I emphasize that I am not in a position to help
you get your FAUNetID nor your password. Refer to the instructions above to see
your problem solved.
Guidelines: In every Mathematics course, you are expected to spend about two
hours on homework for every class hour. Part of that time, you will do exercises
from the previous lecture, part should be spent preparing for the next lecture (read
the section, try to do some exercises). The students are advised to avoid getting
behind as it is difficult to catch up.
Homework: below there is a list of the exercises assigned, section by section, and
quarter by quarter. However, it is the student's responsibility to be aware of any
change that the instructor announces either in class or on this web page. Although
some exercises will be discussed in class, you should attempt to complete a
problem prior to that. I encourage students to ask me for hints, when needed!
Occasionally, based on the feedback received from my students (particularly
through their questions or comments) I will add some exercises to the list already
published.
Dishonesty: Dishonesty-either giving or receiving aid on a test, quiz, or the final
examination-will result in an F for the course. Please, refer to the Honor Code in
the Student Handbook available at http://www.fau.edu/regulations/
chapter4/4.001_Code_of_Academic_Integrity.pdf Extracted from that is the
following: FAU has an honor code requiring a faculty member, student, or staff
member to notify an instructor when there is reason to believe an academic
irregularity is occurring in a course. The instructor's duty is to pursue any
reasonable allegation, taking action, as described . . . , where appropriate.
Students with Disabilities: In compliance with the Americans with Disabilities
Act (ADA), students who require special accommodations due to a disability to
properly execute coursework must register with the Office for Students with
Disabilities (OSD) located in Boca in the Library, Room 175 (561- 297-3880).
This syllabus can also be accessed through my Course Web page, and should be
visited two or three times a week.
VERY SPECIAL NOTICE: For frequently asked questions click F.A.Qs. ASSIGNMENTS FROM THE 3RD EDITION
Click and print out ANSWERS NOT IN THE BOOK for answers and hints to
some exercises whose solutions are not in the textbook.
FIRST QUARTER: Some sections from Chapters 1 and 2. Section
Page
1 and 2
1
3
4
5 6 6
13
22
24
7
28
8 9
10
38
42
50
11
54
Exercises
Read them. Also read this Syllabus and the F.A.Q.s very
carefully
1- 3 - 5 - 6 1 - 4 - 7 -12e- ILLUSTRATIONS SECTION 4
1- 5 - 9 - 10 - 14- 18- 23
3 - 4 - 6-12
1- 4 -6- 8- 10c-11b -15 PROBLEM ON BOOLEAN
ALGEBRAS
2 - 3 - 5 - 7 - 9 - 11 - 14 - 16 - 18
2 - 5 -6 - 8c-8d- 11 1 - 3 - 4 - 7- 10
1- 2 - 4 - 5 REMARKS 1 offers a good review set of
problems.
SECOND QUARTER: Some sections from Chapters 2, 3 and 4.
Section
Page
12
64
14
76
15
83
16
89
17
98
20
124
Exercises
1- 2- 7- 9 - 11 - 21d, f, g, h - 24 - 25 ADDITIONAL
PROBLEMS ON COUNTING
3- 6- 7- 10 - 11 - 16 - 17 3 - 4 - 7 - 11- 16 ADDITIONAL PROBLEMS ON
EQUIVALENCE RELATIONS
1-2- 3- 7- 8- 9- 10- 11-13 - 15
3b- 3d - 3e -4- 5 - 6 - 8 - 10 - 11 - 14 - 18and also
ADDITIONAL EXERCISES with SOLUTIONS TO
ADDITIONAL EXERCISES and MORE
PROBLEMS ON COMBINATORIALS
1- 4- 13
THIRD QUARTER: Some sections from Chapters 4, 5 and 7.
Section
Page
Exercises
4 – 5a –5c–5d–5e –9 - 16a, 16e –17
FIND P(k+1)
22
145
FIBONACCI NUMBERS INDUCTION: ADDITIONAL ILLUSTRATIONS 24
175
25
181
26
186
35
256
1- 2- 4- 5- 14
1 - 2- 6 - 9- 16 - 17 and also PIGEONHOLE PRINCIPLE:
ADDITIONAL EXERCISES PIGEONHOLE
PRINCIPLE: ANSWERS
1- 7- 14a- 14e- and also ILLUSTRATION ON
COMPOSITIONS
1- 2 - 3- 4 -5- 9
FOURTH QUARTER: Some sections from Chapters 7 and 8. Section
36
37
38
Page
264
273
278
39
43
44
46
283
315
319
328
Exercises 1- 2- 11- 12 - 16 - 21
1- 2- 3- 4a- 4b- 4e- 4f- 10-13
1- 3a -3d- 4- See also ADDITIONAL PROBLEMS ON
CONGRUENCES
1- 2- 3- 9- 12- 13
1-3-10
2
1-2-3-5
Special Notices and News: see UPDATES (in Blackboard)