Bill Marion

Striving for mathematical thinking

Computer science and software engineering are young, maturing disciplines. As with other mathematically based disciplines, such as the natural sciences, economics, and engineering, it takes time for the mathematical roots to grow and flourish. For computer science and software engineering, others have planted these seeds over many years, and it is our duty to nurture them. This working group is dedicated to promoting mathematics as an important tool for problem-solving and conceptual understanding in computing.

How mathematical thinking enchances computer science problem solving

There are deep connections between algorithmic and mathematical thinking. Both construct systems --- computing systems in the algorithmic case, intellectual ones in mathematics --- from simple primitives. As Knuth notes in the preface to The Art of Computer Programming, The construction of a computer program from a set of basic instructions is very similar to the construction of a mathematical proof from a set of axioms [1]. Other connections include similar ways of organizing primitives into larger structures (e.g., recursion in algorithms, recursion and induction in math; conditionals in algorithms, definition in cases and proof by cases in math), similar ways of using abstraction to manage complexity, and an underlying reliance on logic. In short, mathematics is not merely a tool for limited areas of computer science, it is a mindset that fundamentally improves ones ability to devise and implement algorithms. Computer science students therefore need to exercise their mathematical as well as their computational abilities, and computer science educators need to help students use both ways of thinking to solve computing problems.This panel illustrates specific ways in which mathematical reasoning enhances algorithmic problem solving, and provides educators with concrete examples and resources to use in their own teaching. Each panelist will present an exercise, classroom example, or similar item, from their own experience, and will demonstrate ways in which mathematical reasoning helps one solve and/or understand it. The audience will be invited to contribute their own examples and to comment further on the role of mathematical thinking in computer science problem solving.The panelists and audience members examples will be collected on a Web page for continuing reference. A prototype of this page is at http://www.cs.geneseo.edu/~baldwin/math-thinking/examples.html.

Materials development in support of mathematical thinking

Our ITiCSE 2002 working group Materials Development in Support of Mathematical Thinking identified the development of an on-line repository as the best mechanism for organizing and disseminating materials promoting mathematical thinking in computer science education.

Final oral report of the SIGCSE committee on the implementation of a discrete mathematics course

In this session the final oral report from the first committee created under the SIGCSE Committee Initiative will be presented. The Committee on Implementation of a Discrete Mathematics Course was charged with developing implementation models and materials for the one-semester discrete math course proposed in Computing Curriculum 2001. The report will include a description of two course models—a computer science-focused one and a mathfocused one--goals and learning objectives for each model, a collection of exercises and other resource materials to support these models and a list of possible applications which connect the mathematics to fundamental ideas in computer science. Comments from the SIGCSE community will be solicited. Presentation will by Bill Marion, one of the two committee co-facilitators and two other committee members.

Status report on the SIGCSE committee on the implementation of a discrete mathematics course

This session is a progress report from the first committee created under the SIGCSE Committee Initiative. The Committee on Implementation of a Discrete Mathematics Course is charged with developing implementation models and materials for the one-semester discrete math course proposed in Computing Curriculum 2001. At the time of the session, the Committee will have completed about three-fourths of its task. In this session the committee will present a number of course models which, for each, will include a syllabus/course outline and a list of possible applications which connect the mathematics to fundamental ideas in computer science. Comments and additional input from the SIGCSE community will be solicited. Presentation will by Bill Marion, one of the two committee co-facilitators and two other committee members.

Some developments in mathematical thinking for computer science education since computing curricula 2001

The Computing Curricula 2001 (CC 2001) computer science volume [1] is the first professional society curriculum model for computer science to include elements of discrete mathematics as part of the core of computer science. In the roughly eight years between the release of that curriculum and SIGCSE 2010, computer science education in general has evolved in many ways, and the CC 2001 recommendations have played an influential role in that evolution. This panel reviews developments in integrating discrete mathematics into the computer science curriculum since CC 2001, how those developments have been influenced by the centrality of discrete math in the CC 2001 core, and how the role of math in computer science curricula may continue to develop in the future. The panel will address both the influence CC 2001’s discrete math recommendation has had on curricular changes to computer science courses, and what changes have taken place in the discrete math courses themselves. The panel format will consist of… ˜ A 5 minute introduction by the moderator ˜ 10 minute presentations by each panelist, each describing a specific development with which that panelist has been involved, discussing its relationship to CC 2001, and outlining what it bodes for the future ˜ 30 minutes for discussion between the audience and panel. Suggested topics for discussion include (in addition, of course, to anything that the audience wishes to introduce) the role of mathematics in computer science, whether math’s actual place in computer science curricula has changed since the publication of CC 2001, and if so how. A questionnaire handed out to audience members as they enter the panel session will help them start thinking about these issues.

Turing machines and computational complexity

INTRODUCTION. Does P = NP? This important open question in computer science is appearing with some frequency now in the mathematical literature. In the September, 1992 issue of the FOCUS [11 Laszlo Babai makes reference to the P : NP conjecture in presenting some recent results about the difficulty of constructing practical algorithms to solve certain types of combinatorial optimization problems. These issues arise from the work of theoretical computer scientists to develop a classification scheme for distinguishing computational problems which are tractable from those which are intractable. To provide some context in which to explore these ideas one model of computation, the Turing machine, is introduced.

Assessing computer science programs: what have we learned

1. SUMMARY How does a department evaluate the effectiveness of its major programs in computer science? In years past it might have been done rather informally by faculty members having a sense of what their students are learning and measuring that against curriculum guidelines developed by national organizations such as ACM and the IEEE Computer Society. Or, maybe faculty members might have made that judgment by the types of jobs their students were obtaining right after they graduate or the number of students who would go on to graduate school in computer science. Nowadays, however, because of both internal and external forces, computer science departments are introducing formal processes. These involve articulating objectives (or goals) and outcomes for their programs and using a variety of instruments to measure success in meeting those objectives and outcomes, all with the idea of using the results to improve the program.

Assessment in computer science (abstract)

This report was prepared by Tony Schwartz, Associate Director for Collection Management, with Patricia Pereira-Pujol, Sciences Librarian. Conference Proceedings FIU has access to the following online series that include conference proceedings: Association for Computing Machinery Digital Library; IEEE/IET Electronic Library; and Springer Lecture Notes in Computer Science, including the subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics.

Integrating recent research results into undergraduate curricula (panel): initial steps

On July 7-11, 60 computer scientists came together at The Evergreen State College in Olympia, Washington to consider how the undergraduate curricula might be improved in light of recent research in computer science. At this NSF-funded workshop, researchers presented work in four areas where current research might be particularly relevant, and undergraduate faculty (with experience in software engineering, functional programming, artificial intelligence, discrete mathematics or theoretical computer science) explored the current state of undergraduate computer science curricula and ways in which they might be better informed by recent research.Each participant attended sessions in one of the four interest areas--Software Engineering Capstone Courses, Functional Programming, Neural Networks and Their Applications, and Computational Geometry--and faculty developed curricular materials that they could use in their teaching the following year. Those materials are being placed on the WWW, and faculty are refining them as they use them in their courses. A second workshop is planned for summer, 1998.The workshop was sponsored by The Evergreen State College, the Oregon Graduate Institute, the Washington Center for the Improvement of Undergraduate Education, and by the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS).All of the panelists participated in the workshop and each panel member will share his or her experiences in incorporating the recent research results studied at the workshop into their undergraduate curriculum. In addition, the panelists will discuss with the audience their own plans for integrating research results into their own undergraduate programs.