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Computer Science 203, Discrete Structures, is a required course
for Computer Science Majors. The class covers proof techniques,
counting methods, calculation,
and problem-solving strategies through topics
such as logic, sets, numbers, functions, relations, graphs, combinatorics,
discrete probability, modular arithmetic, summations, and recurrences.
Discrete mathematics is the mathematics of the integers
{..., -2, -1, 0, 1, 2, ...}, which underlies all conventional
discrete computers.
Students in this course will learn how to:
- Prove theorems
- Calculate, including solving summations and recurrences--both
by hand and using Maple
- Count values
- Solve problems
- Communicate effectively using the language, vocabulary,
and concepts of discrete mathematics.
Proof techniques including direct/indirect, contradiction,
contrapositive, counterexample, epsilon-delta,
counting arguments (e.g. Pigeon-hole Principle), diagonalization,
and strong and weak mathematical induction
will be covered. Counting methods include the fundamental principles
of counting (addition and product rules),
permutations, combinations, k-permutations, permutations
with repeated elements, D'Alembert's method,
urn model, principle of inclusion/exclusion,
setting up and solving recurrences, partition and sum,
and seat-of-the-pants approximations. Calculation topics include
summations, recurrences (first- and second-order
homogeneous and nonhomogeneous linear difference
equations with constant coefficients),
simplification, approximation by bounding,
change of coordinates, and the symbolic and numerical math package
Maple.
In fall 2002, some sections will use the
textbook by Susanna S. Epp, and others will
try the text by Kenneth H. Rosen. In December 2002,
the instructors will decide which text to use in the future.
Chapters in Epp textbook covered (in order):
- Part I: Proofs (Chapters 5, 1, 2, 3, 4)
- Part II: Calculation (7, 8, 10--excluding 7.4, 7.6, 8.1)
- Part III: Counting (6, 7.4, 7.6, 8.1).
Chapters in Rosen textbbok covered (in order):
- Part I: Proofs (Chapters 1-3)
- Part II: Calculation (Chapters 5.1-5.4, 6-7)
- Part III: Counting (Chapters 4, 5.5-5.6))
All instructors are strongly urged to ensure
common minimum standards
as described in the
semester schedule and
lecture descriptions
followed by course coorinator Dr. Alan T. Sherman.
Become rich and famous solving math problems:
Fall 2002
Spring 2001
Previous Semesters
Related Graduate Course
Paul Artola, artola@cs.umbc.edu
Alan T. Sherman, sherman@umbc.edu