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Catalog Data |
ECEN 2703 (3). Discrete Mathematics for Computer
Engineers. Emphasizes elements of discrete mathematics appropriate
for computer engineering. Topics: Logic, proof techniques, algorithms,
complexity, relations, and graph theory. |
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Credits and Design |
3 credit hours. Required core course for ECE
program, elective course for EE program. |
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Prerequisite(s) |
APPM 1360,
Calculus 2 for Engineers
ECEN 1030,
C Programming for EE/ECE (or CSCI 1300) |
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Corequisite(s) |
None. |
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Instructor(s) |
Aaron Bradley, Jeremy Siek, Fabio Somenzi. |
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Textbook |
Douglas E. Ensley and J. Winston Crawley, Discrete
Mathematics, Mathematical Reasoning and Proof with Puzzles, Patterns,
and Games, Wiley, 2006, ISBN-13 978-0-471-47602-3. |
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Course Objectives |
For students to:
- To understand how to think and write about mathematics, logic,
and numbers.
- To appreciate the power of abstract mathematics through the study
of sets and functions.
- To understand and be able to apply the connections between
combinatorics, counting, and probability.
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Learning Outcomes |
After taking this course students will be able to recognize and use
the following concepts, ideas, and/or tools:
- Sets, logic, functions, and proofs, including
induction, recursive definitions, relations, the pigeonhole principle, boolean
algebra, and the growth of functions.
- Combinatorics, counting, and algorithms,
including combinations, permutations, probability of discrete events, and
expected value.
- Graphs and trees, including Eulerian and
Hamiltonian paths, shortest paths, minimum spanning trees, proofs about
graphs and trees, isomorphic graphs, planar graphs, connections to matrices
and relations, binary trees.
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Student Outcomes
Addressed |
| 3a |
3b |
3c |
3d |
3e |
3f |
3g1 |
3g2 |
3h |
3i |
3j |
3k |
Math
/Sci |
Exper-
iments |
Design |
Teams |
Engr
Problems |
Respon-
sibility |
Oral |
Written |
Engr Solns
Impact |
LL
Learning |
Contem-
porary |
Tools |
| H |
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L |
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Topics Covered |
- Overview of discrete mathematics
- Propositional logic and truth tables
- Predicate logic and valid arguments (proofs)
- Induction
- Pigeonhole principle
- Modular arithmetic
- Sets, element-wise proofs, and Boolean algebra
- Functions and relations
- Counting, combinations, binomial theorem
- Permutations, binary sequences, recursive counting
- Probability, expected value
- Graphs, paths, connectivity, trees
- Graph algorithms such as breadth-first search, minimum spanning tree
- Graph isomorphism, planar graphs
- Connection between graphs, relations, and matrices
- Graph representations of games
- Binary trees
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Last revised: 05-17-11, PM, ARP.
