MATH 210 Introduction To Discrete Structures #0918
El Camino College
Room: MCS 216 M W 1:30-3:35pm
Spring 2011
Instructor: GREG FRY
email: gfry@elcamino.edu
Voice Mail: 310-660-3573 (5220)
Office: MCS 104U Office Hours: MW 12:30-1:30, 3:45-4:50 TTH 12:30-1:00
Webpage: http://www.elcamino.edu/faculty/gfry
Text: Discrete Math and Its Applications, Sixth Edition, Kenneth H. Rosen, McGraw-Hill
Publishers, 2007.
Prerequisite: Math 190 (Calculus I ) or the equivalent with a grade of C or higher.
Catalog Description: This course is a study of mathematical ideas and techniques to analyze
problems and algorithms which occur in Computer Science. Topics covered include: logic, set
algebra, functions, algorithms, the integers, mathematical induction, elementary matrix algebra,
mathematical reasoning, combinatorics, recurrence relations, relations, graphs and trees.
Attendance and Withdrawal Policy: Regular attendance is vital to success in this class. If you
have excessive absences I may drop you from the class. It is the student’s responsibility to be
aware of the college drop deadlines and regulations. During tests and lectures you may take a
restroom break without asking me. You are responsible for all announcements I make in class.
Homework: Selected problems will be assigned each week. It is essential that you understand
how to do these problems – they will prepare you for quizzes and exams. The homework will not
be collected, but we will discuss some of the problems in class. Feel free to ask questions about
unassigned problems, but quizzes and exams will only be based on the assigned problems.
Grade Breakdown: 4 exams - each is 1/5 of grade. The quizzes together are 1/5 of grade.
A 90%
B 80%
C 70%
D 60%
Tutoring: Tutoring is available in MCS 106.
Quizzes: There will be several quizzes during the semester. They could be at any time during
class and they could be take home. I may write problems on the board or I may hand out a
printed quiz. No make-ups allowed. No scores will be dropped.
Exams: There will be four two-hour exams. No make-ups will be allowed. If you have a
verifiable and documented emergency then it may be possible to schedule a make-up exam, but
this can only happen at most once, and it would be a harder exam. The exams may also have a
take-home part. The exam dates are 3/9, 4/6, 5/4, 6/8.
Rescoring Exams/Quizzes: If you find that I have made an error in grading, then you may
resubmit the exam or quiz – do not write on the test – write a note, attach it to the exam, and give
it to me for evaluation. There is no danger of losing more points – the score will either stay the
same or it will increase.
Student Misconduct: Cheating will not be tolerated – it will result in a zero and the filing of a
report with the college. Disruptive students will be asked to leave. Please turn off cell phones
and pagers when you enter the classroom. No sharing of calculators or other materials is allowed
during any exam. I encourage you to help each other outside of class, however you should do
your own work on any take home quizzes or exams.
Time Commitment: It is expected that for every hour of class lecture approximately two hours is
required for homework and study time.
You must earn your Grade: You will have plenty of opportunities to show me that you
understand the material. Do not beg for grades based on arguments about your GPA or your
scholarship or transfer opportunities – I do not give grades – you earn them. If you have health,
family, car, or legal problem, then you may discuss it with me, and I will try to accommodate you,
but you must do all of the work. If the problems are too great, then it is best that you retake the
class when you are not so burdened. Vacations are NOT a valid reason for missing work. I do
not deal with parents and I don’t have to.
Sections We Will Cover: 1.1-1.7, 2.1-2.4, 3.1-3.8, 4.1-4.4, 5.1-5.6, 7.1, 7.2, 7.5, 7.6, 8.1-8.6,
9.1-9.8, 10.1-10.5
Course Objectives
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
SLO Statements
Use the standard operations and techniques of propositional logic, set algebra, functions,
sequences, and series.
Determine the complexity of algorithms.
Use the division and Euclidean algorithms and other techniques to find the prime
factorization of a given integer, to find the least common multiple and greater common
divisor of a given set of integers, to rewrite a given number in another base, and to
perform modular arithmetic.
Prove mathematical theorems using direct proofs, indirect proofs, trivial proofs, proof by
contradiction, proof by contraposition, proof by cases, and proof by mathematical
induction.
Disprove a statement by producing a valid counterexample.
Define sequences and sets recursively.
Evaluate a given algorithm that is defined recursively.
Solve combinatoric problems using permutations, combinations, inclusive-exclusion, and
the pigeonhole principle.
Prove the binomial formula and use it to expand a given binomial and to find the
coefficient of a particular term in an expansion.
Model a combinatoric problem with a recurrence relation and solve it.
Determine whether or not a given relation is an equivalence relation.
Solve problems in graph theory that relate to graph isomorphisms, planar graphs, and
Eulerian and Hamiltonian paths.
Prove the standard graph theorems.
Solve problems using tree traversal, spanning trees, and minimal spanning trees.
1. Students will use logic and set algebra to analyze statements and arguments
and use these ideas to write proofs using a variety of methods.
2. Students will use functions, sequences and series to analyze computer science
structures, and analyze the complexity of the algorithms that use them.
3. Students will use number theory to find factorizations, common multiples and factors,
perform modular arithmetic, and prove important results.
4. Students will use combinatorics and probability to model, solve and prove a variety of
counting problems.
5. Students will solve problems and write proofs in graph theory.