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Computer Science Main
Fall Semester
Spring Semester
MATH 220, Formal Methods (3)
COSC 220, Computer Science I (3)
The courses in the first year of a computer science curriculum
must serve the purpose of laying the foundation for the curriculum as
a whole. Formal Methods is one such course. It is designed to teach a
sound understanding of proof and a skill in formal manipulation. Its
immediate application is to programming methodology. Students will
discover that to know how and why a program works, they need to view
a program beyond its operational semantics. Understanding how and why
a program works is equivalent to proving its correctness. Proof of
correctness of a program requires the program itself to be defined as
a mathematical entity. Formal Methods provides students with a
methodology to set up a program as a mathematical object, build it,
prove its correctness, and in the process understand it. It also
teaches students to think rigorously, a skill that is valuable in all
courses.
A combination of operational and mathematical thinking is needed
to solve programming problems. In order for the Formal Methods course
to be effective, it is necessary to complement it with a course in
programming where students learn the operational aspect of programs.
This role is fulfilled by the Computer Science I course, which will
make use of programming methodology and will serve to re-enforce
students’ understanding of formal methods. The content and purpose of
Computer Science I and Formal Methods are integrated. Such
integration is designed to provide students with a concrete framework
on which they can build and develop their problem solving skills.
Currently, the programming environment for Computer Science I and
II is the Qt 4 object-oriented class library based on the C++
language. The Qt 4 class library has features that reinforce the
ideas from the Formal Methods course. In particular, the library is
well documented and includes the Qt 4 assert macro that supports the
implementation of pre- and post-conditions for Hoare triples from
Formal Methods. The library permits students to begin with the
procedural approach to programming, continue through successively
higher levels of abstraction, and culminate with the object-oriented
paradigm. It therefore satisfies our goal of students learning
multiple paradigms in the curriculum. Qt 4 also provides a powerful
graphical user interface designer. With this tool, students
construct programs that look like professionally developed
commercial software. In addition, the Qt 4 system is provided as a
free open-source system that runs on MSWindows, MacOS, and Linux
computers.
MATH 210, Calculus I (4)
MATH 221, Discrete Structures (3)
COSC 221, Computer Science II (3)
Calculus is a fundamental mathematical tool for the sciences. The
calculus course begins a three-semester sequence whose goal is
proficiency in using this tool.
Discrete Structures presents the abstract mathematical view of
fundamental data structures that form the building blocks of an
algorithm. The course uses the methodology of its prerequisite
course, Formal Methods, to perform complexity analysis and proof of
correctness on the algorithms that manipulate data structures. It
complements the concurrent Computer Science II course, which teaches
the concrete implementation of data structures and algorithms in a
specific programming language.
The purpose of Computer Science II is to make the transition from
the procedural paradigm to the object-oriented paradigm. The steps
include recursion, dynamic storage allocation, inheritance, and
polymorphism. The course culminates with the implementation of
abstract classes using the state design pattern as an application of
object-oriented programming. Consequently, students learn abstraction
by experiencing layers of abstraction, starting at the lower
procedural level and progressing to the higher object-oriented level.
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