HomeMy WebLinkAboutMAT-285 BERGEN COMMUNITY COLLEGE
DIVISION OF MATHEMATICS, SCIENCE AND TECHNOLOGY
DEPARTMENT OF MATHEMATICS
COURSE SYLLABUS
MAT-285 DISCRETE MATHEMATICS
COURSE Discrete Mathematics is a study of mathematical concepts and techniques
DESCRIPTION: that form the foundation for many upper level mathematics courses. Topics
considered include sets, logic, proof techniques, functions, recurrence
relations, complexity of algorithms, counting techniques, discrete probability,
relations, graphs and trees, Boolean Algebras, finite state machines, and finite
automata. Mathematical reasoning and proofs will be stressed.
CREDITS/HOURS: 4 lecture hours 4 credits
PREREQUISITE: MAT-280 with a grade of C or better or by permission of the Department Chair.
GEN'L ED COURSE: No
STUDENT As a result of meeting the requirements for this course, students will:
LEARNING
OBJECTIVES: 1. understand the fundamental concepts of sets and logic and how they are used
in real-world applications.
2. be able to employ proofs to validate properties and arguments.
3. understand the fundamental concepts of functions and relations.
4. be able to solve first and second order recurrence relations.
5. be able to perform fundamental analysis of an algorithm.
6. understand the properties of graphs and trees, and be able to apply them to
solve problems that can be represented by these structures.
7. be able to apply counting techniques and fundamental laws of probability
in the solution of problems.
8. understand the properties of a Boolean Algebra and its application to
combinatorial circuits.
9. understand the representations and applications of finite state machines
and finite automata.
ASSESSMENT Each of the above listed student learning objectives will be assessed by,
MEASURES: 1. Written assignments and/or quizzes.
2. Written examinations
3. Other, as announced by the professor
COURSE GRADE: Students should refer to the professor’s grading policy which will be distributed
during the first meeting of the class. Attendance and lateness policies are to be
determined by the professor for each section of the course. These will be
established in writing on the individual course policies.
TEXTBOOK: Discrete Mathematics, (revised) 3rd edition, Lipschutz and Lipson
Schaum’s Outlines, McGraw-Hill Publisher, ISBN: 978-0-07-161586-0
Lecture notes (LN) will be distributed for many of the topics.
COURSE CONTENT:
TOPIC READING
Set Theory 1.1 – 1.7
Logic 4.1 – 4.9
Proof Techniques and LN, 1.8, 11.3, 11.5, 11.8
Mathematical Induction
Functions and the LN, 3.1 – 3.3, 3.6, 3.8, 3.9
Complexity of Algorithms
Recurrence Relations LN, 6.6 – 6.9
Relations 2.1 – 2.9, 14.3
Graphs and Trees LN, 8.2 – 8.8, 9.1 – 9.4, 9.6, 9.9,
10.1, 10.2, 10.8
Counting Techniques 5.1 – 5.8, 6.1 – 6.3
Discrete Probability LN, 7.1 – 7.6
Boolean Algebra and Circuits LN, 15.1 – 15.4, 15.8 – 15.12
Finite State Machines and Finite Automata LN, 12.5, 13.1 – 13.2
REFERENCES: Discrete Mathematics, Johnsonbaug, Pearson, Prentice-Hall
Discrete Mathematics with Applications, Epp, Brooks/Cole, Cengage Learning
Discrete Mathematics and its Applications, Rosen, McGraw-Hill
ELECTRONIC The Department of Mathematics prohibits the use of cell-phones, PDA’s,
DEVICES: laptops, headphones, IPODs and other such devices in mathematics classes
unless otherwise specified in the grading policy provided by the professor
at the beginning of the semester.
FACULTY CLASS CANCELLATIONS may be found at http://www.bergen.edu/classcancellations
ABSENCE A list is also posted in a glass case near A-129, the main corridor on the first floor and
PROCEDURE: in Ender Hall. If a cancelled class is not listed, it should be reported to the Department
Office (B-302) or the Adjunct Office (C-107).
WEBSITE: Go to http://www.bergen.edu/academics/academic-divisions-departments/mathematics
for more information regarding the Mathematics Department.
STUDENT Learning Assistance Center Room: L-125 879-7489
SUPPORT Math and Science Walk-In Room: L-131 879-7489
SERVICES: Office of Specialized Services Room: L-115 612-5269
8/2019