cis275-winter2014-syllabus

8/11/2019 CIS275-Winter2014-Syllabus

1/3

1

CIS 275 Discrete Structures I

Fall 2014Lecture: Monday and Wednesday, 6:00pm-7:45pm, 1030 CB

Instructor: Habib M. Ammari, Ph.D. (CSE), Ph.D. (CS)Office: 129 CIS Building

Email: [email protected]: (313) 393-5239

Homepage:http://www-personal.engin.umd.umich.edu/~hammari/

OfficeHours: Monday, Tuesday, Wednesday 9:30am-11:30am, 129 CIS Building, and by appointment

Textbook: R. Johnsonbaugh, Discrete mathematics, Seventh Edition, Pearson, Prentice Hall, 2009.

Recommended

References:

K. H. Rosen, Discrete mathematics and its applications, Seventh Edition, McGraw Hill,

2011.M. A. Albertson and J. P. Hutchinson, Discrete mathematics with algorithms, Wiley, 1988.

S. C. Althoen and R. J. Bumcrot, Introduction to discrete mathematics, PWS-KENT

Publisher, 1988.

A. Babich and L. Person, Write your own proofs in set theory and discrete mathematics,

Zinka Press, 2005.

N. L. Biggs, Discrete mathematics, Oxford University Press, 2003.

L. S. Bobrow and M. A. Arbib, Discrete mathematics: Applied algebra for computer and

information science, W. B. Saunders Company, 1974.

J. L. Gersting, Mathematical structures for computer science: A modern treatment of

discrete mathematics, Fifth Edition, W. H. Freeman and Company, 2003.

R. P. Grimaldi, Discrete combinatorial mathematics: An applied introduction, SecondEdition, Addison Wesley, 1989.

D. J. Hunter, Essentials of discrete mathematics, 2nd Ed., Jones & Bartlett Learning, 2012.

K. D. Joshi, Foundations of discrete mathematics, Wiley-Interscience, 1989.

S. B. Maurer and A. Ralston, Discrete algorithmic mathematics, Addison Wesley, 1991.

J. L. Mott, A. Kandel, and T. P. Baker, Discrete mathematics for computer scientists and

mathematicians, Prentice-Hall, 1986.

R. Skvarcius and W. B. Robinson, Discrete mathematics with computer science

applications, Benjamin/Cummings Publisher, 1986.

D. F. Stanat and D. F. McAllister, Discrete mathematics in computer science, Prentice-

Hall, 1977.

J. P. Tremblay and R. Manohar, Discrete mathematical structures with applications tocomputer science, McGraw-Hill, 1975.

Prerequisites: CIS 200 at least concurrently and MATH 115. Students cannot receive credit for both CIS175 and CIS 275. Previous exposure to programming may be helpful but not necessary.

Catalog

Description:

This course introduces students to various topics in discrete mathematics, such asset theory,

mathematical logic, trees, and graph theory. Applications to relational databases, modeling

reactive systems and program verification are also discussed.

(4 Credit hours, 4 Lecture hours)

Objective: This is a first course on discrete mathematics for undergraduate mathematics, computerscience, and computer engineering students that surveys the fundamental mathematicalconcepts, which are important to computing. Topics include: Foundations, such as logic

and proofs; basic structures, such as sets, functions, sequences, and sums; the fundamentals,such as algorithms, integers, and matrices; proof techniques, such as induction; counting

principles; discrete probability; relations; Boolean algebra; graphs; and trees. The objective

of this course is to provide the students with a thorough understanding of the main concepts


2/3

2

Week 1

Week 2

Week 3

Week 4

Sept 3

Sept 8, 10

Sept 15, 17

Sept 22,24

Introduction, sets, set operations, functions.

Sequences, summations.

Logic, propositional logic.

Propositional equivalences, predicate and quantifiers,

proof techniques.

Week 5 Sept 29, Oct 1 Algorithms, growth of functions.

Week 6 Oct 6, 8 Complexity of algorithms, integers and algorithms.

Week 7 Oct 13, 15 Primes and greatest common divisors, matrices.

Week 8 Oct 20, 22 Primes and GCDs, matrices, induction, correctness

Week 9 Oct 27, 29 Induction, strong induction, program correctness.

Week 10 Nov 3, 5 Counting, pigeonhole principle, permutations and

combinations, binomial coefficients.

Midterm3/14.

Week 11 Nov 10, 12 Relations, representing relations, closures of relations,

equivalence relations, partial orderings.

Week 12 Nov 17, 19 Graphs, connectivity, Euler and Hamiltonian paths,

shortest-path problems.

Week 13 Nov 24, 26 Trees, applications of trees, tree traversal, spanning trees,

minimum spanning trees.

Week 14 Dec 1, 3 Discrete probability, Bayes Theorem.

Week 15 Dec 8 Boolean algebra, Boolean functions, representing

Boolean functions.

Review session.

Week 16 Dec 17 Final.

Outline:

f discrete mathematics so they acquire the ability to understand and create mathematical

arguments. Discrete mathematics has several applications, such as the analysis of

algorithms in terms of time and space, and proof of their correctness. Homework and/or

programming assignments will help the students understand the topics discussed in thiscourse and apply the concepts to solving problems through the design, analysis, and

development of algorithms using a stepwise refinement approach.

ReadingList: V. L. Almstrum, What is the attraction to computing?Communications of the ACM, vol.

46,no.9,pp.51-55,Sep.2003.K. B. Bruce, R. L. Scot Drysdale, C. Kelemen, and A. B. Tucker, Why math?

CommunicationsoftheACM,vol.46,no.9,pp.40-44,Sep.2003.

K. Devlin, Why universities require computer science students to take math,CommunicationsoftheACM,vol.46,no.9,pp.36-39,Sep.2003.

T. A. Easton, Beyond the algorithmization of the sciences, Communications of the ACM,

vol.49,no.5,pp.31-33,May2006.

P. B. Henderson, Mathematical reasoning in software engineering education,

CommunicationsoftheACM,vol.46,no.9,pp.45-50,Sep.2003.

Online

Resources:

S.Seiden,Theoreticalcomputersciencecheatsheet,ACMSIGACTNews,vol.27,no.4, pp.52-

61,Dec.1996.


3/3

cis275-winter2014-syllabus

Documents