Chabot College
Fall 2004
Course Outline for Mathematics 8
DISCRETE MATHEMATICS
Catalog Description:
8 - Discrete Mathematics
3 units
Counting techniques, sets and logic, Boolean algebra, analysis of algorithms, graph theory, trees,
combinatorics, recurrence relations, introduction to automata. Designed for majors in mathematics and
computer science. Prerequisite: Mathematics 1 (completed with a grade of C or higher). 3 hours.
Prerequisite Skills:
Before entering the course, the student should be able to:
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use delta notation;
explain limits and continuity;
use Newton’s method;
apply the definition of the derivative of a function;
define velocity and acceleration in terms of mathematics;
differentiate algebraic and trigonometric functions;
apply the chain rule;
find all maxima, minima and points of inflection on an interval;
sketch the graph of a differentiable function;
apply implicit differentiation to solve related rate problems;
apply the Mean Value Theorem;
demonstrate an understanding of the definite integral as the limit of a Riemann sum;
demonstrate an understanding of the Fundamental Theorem of Integral Calculus;
demonstrate an understanding of differentials and their applications;
integrate using the substitution method;
find the volume of a solid of revolution using the shell, disc, washer methods;
find the volume of a solid by slicing;
find the work done by a force;
find the hydrostatic force on a vertical plate;
find the center of mass of a plane region;
approximate a definite integral using Simpson’s Rule and the Trapezoidal Rule.
Expected Outcomes for Students:
Upon completion of the course, the student should be able to:
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apply principles of propositional logic to the construction of formal proofs;
apply mathematical induction to problems in sequences, series, and algorithms;
measure complexity and efficiency of a variety of computer algorithms;
apply concepts of combinatorics to analysis of recursive algorithms;
apply concepts of graph theory to shortest path problems;
solve recurrence relations and apply them to sorting and searching algorithms;
apply properties of trees to analysis of simple games and sorting problems;
apply laws of Boolean algebra to simplification of combinatorial circuits;
design finite machines and automata.
Course Content:
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Rules of inference, sets, sequences, functions, relations, recurrence equations
Boolean algebra, logic circuits, Karnaugh maps
Mathematical induction, Big Oh notation, complexity of algorithms
Counting: permutations and combinations, inclusion-exclusion principle, divide and conquer
algorithms
Chabot College
Course Outline for Mathematics 8, Page 2
Fall 2004
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Graphs: Euler and Hamilton paths, coloring, isomorphism, representations, minimal path, planarity,
connectivity
Trees: traversal, minimal spanning trees, game trees
Finite state machines, languages
Methods of Presentation:
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Lecture/demonstration.
Discussion.
Typical Assignments and Methods of Evaluating Student Progress:
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Typical Assignments
a. How many different functions are there from a set of 6 elements to itself? How many of them
are: (a) onto? (b) not onto? (c) one-to-one? (d) not one-to-one? Design an algorithm that
determines whether a function from a set of n elements to itself is one-to-one, and another that
determines whether the function is onto.
b. Let f(x) = x2 +1, x is real on [ -2, 4]. Define a relation R on A X A as: (a, b) is in R if and only if
f(a) = f(b). Show R is an equivalence relation. Describe the equivalence classes.
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Methods of Evaluating Student Progress
a. Homework
b. Quizzes
c. Exams and final exam
Textbook(s) (Typical):
Discrete Mathematics, Kenneth Rosen, McGraw-Hill Publishers, 2003
Discrete Mathematics, James A Anderson, Prentice Hall, 2001
Special Student Materials:
A calculator may be required.
CB:al
Revised: 10/03/03