A Working Group on

Integrating Mathematical Reasoning* into Computer Science Curricula

* "Mathematical Reasoning": Applying mathematical techniques, concepts and processes, either explicitly or implicitly, in the solution of problems -- in other words, mathematical modes of thought that help us to solve problems in any domain. In its most general interpretation, every problem-solving activity requires mathematical thinking. For example, basic logic, be it used explicitly or implicitly is required for all problem-solving activities.

In The Public Eye

August 2007, ICT Results, "Processor Design Gets Mathematical Sweetener"
April 2007, "Is Abstraction the Key to Computing?" by Jeff Kramer, Communications of the ACM.
Nov. 2006, Rensselaer Polytechnic Institute, "Using Mathematics and Computers To Understand the World."
Nov. 2006, The Epoch Times, "Discrete Math Comes to the Classroom."
Sept. 2003, USA Weekend Magazine, "The Numbers Game: Why Math Books are Hot."
Sept. 2003, Communications of the ACM, special section on "Why Universities Require Computer Science Students to Take Math."
Jan. 22, 2002. BusinessWeek, "A Better Web through Higher Math"
1992. The Queen's Award for Technological Achievement awarded to Oxford University Computing Laboratory and IBM United Kingdom Laboratories for the development and application of Z.

What We Are

Mathematical reasoning is central to computer science. It should therefore be an integral part of the entire CS curriculum, with special emphasis in the early courses. This would be a deviation from current practice, requiring systemic change in CS education. We are a group of computer scientists, mathematicians, and others interested in fostering such change.

The group "meets" (via e-mail), to discuss topics related to mathematical reasoning in CS and its teaching. An archive of these discussions is available on-line. Possible topics include, but are not limited to, which mathematical concepts are relevant, when and how they can/should be introduced and reinforced in the curriculum, how they relate to practice, pedagogical approaches to teaching math foundations, supporting laboratories, etc. We are undertaking concrete projects designed to raise awareness of mathematical reasoning in CS and of ways of teaching it. The exact nature of projects is determined by members' interests, including such things as working to get a prominent place for mathematical reasoning in computer science and software engineering curriculum recommendations; workshops, panels, birds-of-a-feather, and similar presentations at relevant conferences; and collecting pedagogical resources for incorporating mathematics into CS courses. Future projects could include such things as performing studies and otherwise collecting evidence on the importance of mathematical thinking in CS; contests to increase student interest in, and faculty awareness of, mathematics as part of CS; etc.

Accomplishments

Math-reasoning related accomplishments of this group or its members include...

A birds-of-a-feather session on "Mathematical Reasoning in Computer Science" at SIGCSE 2008, led by group members Doug Baldwin and Murali Sitaraman.
ProofBuilder, a Java program that helps students learn to do proofs in several different ways. It handles material of a first course on discrete mathematics, including induction, sets, summations, O(), mod, and combinatorics. Written and maintained by group member Hugh McGuire.
The 3-2-1 Approach to Introductory Computer Science at Haverford College, directed by group members Dave Wonnacott and John Dougherty.
SIGCSE 2006: Members organized several sessions, including
- A workshop on "Hands-On Activities for Learning Discrete Mathematics," run by group members Susanna Epp, Peter Henderson, and Bill Marion.
- A special session presenting the "Final Oral Report of the SIGCSE Committee on the Implementation of a Discrete Mathematics Course," moderated by group members Bill Marion and Doug Baldwin.
- A paper entitled "Discrete Partnership -- A Case for a Full Year of Discrete Math," co-authored by group member Mark LeBlanc.
- A birds-of-a-feather session on "Mathematical Reasoning in Computer Science," led by group members Peter Henderson and Judith Gersting.
Discrete Mathematics: Curricular Issues, Pedagogy and Nifty Examples, a workshop presented by group members Bill Marion, Susanna Epp, and Peter Henderson, at Messiah College (Grantham, PA), from June 12-16, 2006.
SIGCSE 2005: Members presented special sessions and workshops, including
- A special session presenting a "Status Report on the SIGCSE Committee on the Implementation of a Discrete Mathematics Course," featuring group members Bill Marion and Doug Baldwin.
- A workshop on "More Nifty Examples in Discrete Mathematics," run by group members Bill Marion, Peter Henderson and Susanna Epp.
- A birds-of-a-feather session on "A Concepts-Based Approach to Teaching Programming," run by group member Peter Van Roy.
- A birds-of-a-feather session on "Mathematical Thinking in Computer Science" offered by group members Peter Henderson and Judy Gersting.
A special issue of the ACM Journal on Educational Resources in Computing (JERIC) devoted to Software Support for Discrete Mathematics Teaching, edited by member Valerie J. Harvey, and Susan H. Rodger.
An MAA PREP workshop entitled "Nifty Applications in Discrete Mathematics" was held June 7 to 11, 2004 at Valparaiso University. Organized by group member Bill Marion, and also featuring presentations by members Doug Baldwin, Susanna Epp and Peter Henderson.
Algorithms and Data Structures: The Science of Computing, a textbook by group member Doug Baldwin, and Greg Scragg, that integrates mathematical analysis of algorithms, algorithm design and programming, and empirical analysis of algorithms.
Members Peter Henderson and Kim Bruce appeared on a panel "Mathematical Logic in Computer Science Education" at the Association for Symbolic Logic 2004 Meeting on May 22, 2004.
SIGCSE 2004: Members presented special sessions and workshops, including
- A special session presenting a "Status Report on the SIGCSE Committee on the Implementation of a Discrete Mathematics Course," featuring group members Doug Baldwin, Bill Marion, and Henry Walker.
- A workshop on "Nifty Examples in Discrete Mathematics," run by group members Bill Marion and Peter Henderson.
- A birds-of-a-feather session on "A Concepts-Based Approach to Teaching Programming," run by group member Peter Van Roy. According to Peter, "one of the important parts of this approach is to introduce programmers to formal reasoning. We use a formal semantics that is as simple as possible, but does not sacrifice precision or coverage."
Communications of the ACM, September 2003 section on "Why Universities Require Computer Science Students to Take Math." Members wrote many of the articles, including...
- Kim Bruce, Scot Drysdale, Charles Kelemen, and Allen Tucker, "Why Math?", pp. 40 - 44.
- Peter Henderson, "Mathematical Reasoning in Software Engineering Education," pp. 45 - 50.
- Vicki Almstrum, "What Is the Attraction to Computing?" pp. 51 - 55.
SIGCSE 2003: Members presented workshops, panels, and special sessions related to mathematical reasoning in computer science, including...
- A workshop by David Gries entitled "Calculational Logic in Discrete Math Courses"
- A special session chaired by Dan Garcia, and featuring group members David Ginat and Peter Henderson, entitled "Everything You Always Wanted to Know about Game Theory"
- A special session chaired by Susanna Epp, Peter Henderson, and Bill Marion entitled "Math Educators, Computer Science Educators: Working Together"
- A panel organized by Bill Marion and including Kris Powers, Adrienne Bloss, and Doug Baldwin entitled "How Departments Are Responding to the Mathematics Recommendations in CC2001"
- A birds-of-a-feather session on mathematical thinking in computer science, organized by Doug Baldwin and Peter Henderson
"Discrete Mathematics: An Early Foundation for the Study of Computer Science", an MAA PREP (Professional Enhancement Program) workshop run by Bill Marion, Susanna Epp, Peter Henderson, and Henry Walker, June 2-6, 2003.
Programming Languages: Principles and Paradigms: A textbook by Allen Tucker and Bob Noonan that takes a rigorous semantics-based approach to programming languages.
Computing Curriculum Software Engineering (CCSE): Several members of the group were involved in various aspects of the CCSE project. Of particular note, Peter Henderson chaired the "Foundations" knowledge area subcommittee.
CCSC:NE-2002: Allen Tucker presented a plenary talk entitled "Ensuring a Rigorous Curriculum: Practices and Goals" at the Consortium for Computing in Small Colleges: Northeast conference.
Computing Curriculum 2001 : Kim Bruce, Bill Marion and Henry Walker (Chair) served on the Supporting Topics and Courses Focus Group. Kim Bruce was chair of the Programming Languages Focus Group. Several ideas in CC 2001, Section 9.1.1 "Mathematical Rigor" evolved from member activities.
A panel on Women, Math, and Computer Science, organized by Peter Henderson, and featuring other group members Vicki Almstrum, Orit Hazzen, and Kim Kihlstrom, presented at SIGCSE 2002. The panel's Web page includes the speakers' presentations and links to a number of background references.
SIGCSE 2002 : Members presented a paper, and participated in 3 panels and several birds of a feather sessions devoted to math thinking.
SIGCSE 2001 : Members presented 2 papers, the keynote address, participated on 3 panels and several birds of a feather sessions devoted to math thinking.
ITiCSE 2001 : The working group " Striving for Mathematical Thinking"

Publications & Reports

Papers, reports, and invited talks related to mathematical reasoning by members of this group include...

Bill Marion and Doug Baldwin, "SIGCSE Committee Report on the Implementation of a Discrete Mathematics Course," Inroads - the SIGCSE Bulletin, June 2007, pp. 109 - 126. Also available at http://www.sigcse.org/DiscreteMathHome.shtml.
Doug Baldwin, "Effectiveness of a Language Implementation Project in Building Appreciation for Formal Specification," Papers of the Twelfth Annual CCSC Northeastern Conference, Apr. 2007, pp. 173 - 183.
Valerie J. Harvey et al., eds., Discrete Mathematics Applications for Information Systems Professionals, 2nd ed. (Pearson, 2006), a collection of applications examples and a curriculum guide for teaching discrete mathematics in information systems (IS) and IS Management programs; designed as a supplement to Richard Johnsonbaugh, Discrete Mathematics, 6th ed. (Prentice Hall, 2005).
"Life-long Learning: Making Discrete Math Relevant for Information Systems Professionals," by David F. Wood, Valerie J. Harvey, and Frederick G. Kohun, IACIS 2005.
"Insights from Teaching Discrete Mathematics in Information Systems Programs, A Report for the Discussion Forum," by Valerie J. Harvey and E. Gregory Holdan, CoLogNet/Formal Methods Europe Symposium on Teaching Formal Methods, November 2004.
"Workshop on Discrete Mathematics for Programs Conforming to ABET Information Systems Accreditation," by Valerie J. Harvey, Peter Y. Wu, and John C. Turchek, ISECON, November 2004.
"Mathematics for the Exploration of Requirements," by Michael Huth, SIGCSE InRoads, June 2004.
"The Role of Logic in Teaching Proof," by Susanna Epp, in American Mathematical Monthly, Dec. 2003, which holds the copyright with all rights reserved.
"The Role of Modeling in Software Engineering Education," by Peter Henderson, presented at the 2003 Frontiers in Education conference.
"Materials Development in Support of Mathematical Thinking", the report of an ITiCSE 2002 working group chaired by Peter Henderson, in SIGCSE Inroads, June 2003.
"A Small College Response to the Mathematics Recommendations of Curriculum 2001", by Blayne Carroll and Kris Powers, presented at the 2002 Consortium for Computing Sciences in Colleges Southeastern Conference.
"Where is Programming Methodology these Days", invited editorial by David Gries in SIGCSE Inroads, Dec. 2002.
"Teaching Discrete Structures with SML", by Christelle Scharff and Andrew Wildenberg, presented at Functional and Declarative Programming in Education (FDPE02), a one day workshop at PLI'02, October 2002.
"Functional and Declarative Languages for Learning Discrete Mathematics", by Peter Henderson, presented at Functional and Declarative Programming in Education (FDPE02), a one day workshop at PLI'02, October 2002.
"Mathematical Reasoning in Software Engineering Education", an article prepared by Peter Henderson in the September 2003 Communications of the ACM special section on math in computer science.
"Why Math?", an article prepared by Kim Bruce, Scot Drysdale, Charles Kelemen, and Allen Tucker in the September 2003 Communications of the ACM special section on math in computer science.
"The Importance of Mathematics to the Software Practitioner", by Doug Baldwin and Peter Henderson, in the March/April 2002 issue of IEEE Software. A response to Robert Glass's essay "A New Answer to 'How Important is Mathematics to the Software Practitioner'?" (Copyright 2002 by IEEE)
A paper entitled "Integrating Formal Models into the Programming Languages Course", by Allen Tucker and Bob Noonan appeared in The 33rd SIGCSE Technical Symposium on Computer Science Education, 2002.
Pete Henderson gave a seminar entitled "The Role of Mathematics the Undergraduate Computer Science Curriculum" at Ohio State University on Jan. 17, 2002.
A ITiCSE 2001 working group report "Striving for Mathematical Thinking" was published in SIGCSE Inroads (Vol. 33 , No 4, pp. 114-124, Dec. 2001).
A paper entitled "Our Curriculum has Become Math-Phobic!", by K. Bruce, C. Kelemen, and A. Tucker was published in The 32nd SIGCSE Technical Symposium on Computer Science Education, 2001.
A paper entitled "Has Our Curriculum Become Math Phobic? (An American Perspective)", by K. Bruce, C. Kelemen, P. Henderson, O. Astrachan and A. Tucker; The 5th Annual ITiCSE Conference, 2000.
The MAA CUPM report "Mathematical Needs of Introductory Computer Science Curricula", 1999.
A paper entitled "The Propositional Logic Test as a Diagnostic Tool for Misconceptions about Logical Operations" by Vicki Almstrum, The Journal of Computers in Mathematics and Science Teaching 18(3), 1999.
A paper entitled "Investigating Student Difficulties with Mathematical Logic" by Vicki Almstrum in N. Dean and M. Hinchey (eds.), Teaching and Learning Formal Methods, Academic Press, 1996.

Current Projects

An important goal for this group is to undertake projects designed to increase awareness of mathematical reasoning in computer science and computer science curricula. Our current projects are as follows. Anyone is welcome to contribute to any of these projects. If one interests you, please contact the project's organizer.

A working group on Concept Inventories in Computer Science for the Topic Discrete Mathematics at ITiCSE 2006. Organizer: Peter Henderson.
"Math CountS", a column in Inroads -- SIGCSE Bulletin edited by Peter Henderson.
A working group on Materials Development in Support of Mathematical Thinking, held at ITiCSE 2002. Organizer: Peter Henderson.
An evolving document that explores the Connections between Mathematics and Computing Curricula 2001. Organizer: Peter Henderson.
Collecting sample problems suitable for classroom discussion, use in exercises, etc. in order to demonstrate the value of mathematical thinking to students. Project leaders: Doug Baldwin, Bob Roos. Contact person: Doug Baldwin
- From the SIGCSE 2001 panel "How Mathematical Thinking Enhances Computer Science Problem Solving".
- From Allegheny College, collected by Bob Roos.
References to publications addressing the Relevance of Mathematical Thinking to "real world" computing. Contact person: Doug Baldwin.
On-Line Reviews of Print Materials related to mathematical reasoning in computer science. Project leader/contact person: Doug Baldwin

People

(If you're a member of the group and want to be listed here, send e-mail to baldwin@geneseo.edu giving the information you'd like listed -- e.g., how you want your name to appear, your affiliation, URL's to home pages, e-mail addresses, or anything else you'd like included. Only adding people when requested to do so hopefully increases people's privacy and control over distribution of personal information.)

Vicki L. Almstrum (e-mail: almstrum@cs.utexas.edu), Department of Computer Sciences, University of Texas at Austin
Hossein Arsham (e-mail harsham@ubalt.edu), Information and Quantitative Sciences Department, University of Baltimore
Doug Baldwin (e-mail baldwin@geneseo.edu), Dept. of Computer Science, SUNY Geneseo
Kim Bruce (e-mail kim@cs.pomona.edu), Dept. of Computer Science, Pomona College
Tom Cortina (e-mail: tcortina@cs.cmu.edu), Dept. of Computer Science, Carnegie Mellon University
Venu Dasigi (e-mail vdasigi@spsu.edu), Department of Computer Science, Southern Polytechnic State University
Scot Drysdale (e-mail scot@cs.dartmouth.edu), Department of Computer Science, Dartmouth College
Carol Anne Edmondson (e-mail cae@utas.edu.au), School of Computing and Information Systems, University of Tasmania
Abdol-Hossein Esfahanian, (e-mail esfahanian@cse.msu.edu), Department of Computer Science and Engineering, Michigan State University
Matthias Felleisen, Department of Computer Science, Northeastern University, Boston
Kathi Fisler (e-mail kfisler@cs.wpi.edu), Department of Computer Science, Worcester Polytechnic Institute
S. Jane Fritz (e-mail fritz@sjcny.edu), Dept. of Mathematics/Computer Science, St. Joseph's College, New York
Judith Gersting (e-mail gersting@hawaii.edu), University of Hawaii at Hilo
Don Goelman (e-mail don.goelman@villanova.edu), Department of Computing Sciences, Villanova University
David Gries, Associate Dean of Engineering, Cornell University
Valerie J. Harvey (e-mail harvey@rmu.edu), Department of Computer and Information Systems, Robert Morris University
David Hemmendinger (e-mail hemmendd@union.edu), Dept. of Computer Science, Union College
Pete Henderson (e-mail phenders@butler.edu), Dept. of Computer Science, Butler University
Lew Hitchner (e-mail hitchner@csc.calpoly.edu) Computer Science Dept., Cal Poly State Univ. (CSU San Luis Obispo)
Gregory Kapfhammer (e-mail gkapfham@allegheny.edu), Department of Computer Science, Allegheny College
Charles Kelemen (e-mail ckeleme1@swarthmore.edu), Computer Science Program, Swarthmore College
Kim Kihlstrom (e-mail kimkihls@westmont.edu), Dept. of Mathematics and Computer Science, Westmont College
Nancy Kinnersley (e-mail kinners@eecs.ku.edu), Dept. of Electrical Engineering and Computer Science, University of Kansas
Yana Kortsarts (e-mail yanako@cs.widener.edu), Computer Science Department, Widener University, Chester, PA
Bill Marion (e-mail: Bill.MarionJr@valpo.edu), Dept. of Mathematics and Computer Science, Valparaiso University
Hugh McGuire (e-mail: mcguire@cis.gvsu.edu), School of Computing & Information Systems, Grand Valley State University, MI
John O'Donnell (e-mail jtod@dcs.gla.ac.uk), Computing Science Department, University of Glasgow
S. Parthasarathy (e-mail drparth@gmail.com) Algologic Research and Solutions, Secunderabad, India
Hemant Pendharkar (e-mail hpendharkar@worcester.edu) Department of Computer Science Worcester State College
Chuck Riedesel (e-mail riedesel@cse.unl.edu), Computer Science & Engineering Department, University of Nebraska at Lincoln
Bob Roos (e-mail robert.roos@allegheny.edu), Department of Computer Science, Allegheny College
Christelle Scharff (e-mail cscharff@pace.edu) Computer Science Department, Pace University
Murali Sitaraman (e-mail: msitara@clemson.edu), School of Computing, Clemson University
Allen Tucker (e-mail allen@bowdoin.edu), Dept. of Computer Science, Bowdoin College
Peter Van Roy (e-mail: pvr@info.ucl.ac.be), Department of Computing Science and Engineering, Université Catholique de Louvain at Louvain-la-Neuve, Belgium

How to Join

Electronic discussions are carried out on mailing list "math-thinking-l@geneseo.edu". All you have to do to join the group is subscribe to this list -- to do this, just point a Web browser at http://mail.geneseo.edu/mailman/listinfo/math-thinking-l/ and fill out the subscription form in the middle of the page.

(Group members can also maintain their subscription to the mailing list -- change delivery options, unsubscribe, etc. -- at the same URL, using the subscriber information "access panel" at the bottom of the page.)

Related Information

Upcoming events, on-line resources, and other miscellaneous items likely to be of interest to members of this group are listed below. Please send suggestions for further items to Doug Baldwin.

Events

FICS 2008, The First International Conference on Foundations of Informatics, Computing and Software, June 3 - 6, 2008, Shanghai, China.
PLDI 2008, the ACM SIGPLAN Conference on Programming Language Design and Implementation, including a Student Research Competition, June 7-13, 2008, Tucson, AZ, USA.
WADT 2008, 19th International Workshop on Algebraic Development Techniques, June 13-16, 2008, Pisa, Italy.
TASE 2008, 2nd IEEE Symposium on Theoretical Aspects of Software Engineering, June 17-19, 2008, Nanjing, China.
ITiCSE 2008, the 13th annual Conference on Innovation and Technology in Computer Science Education, June 30 - July 2, 2008, Madrid, Spain.
Summer School on Logic and Theorem Proving in Programming Languages, July 22 - 30, 2008, University of Oregon, Eugene, Oregon, USA.
ICER '08, the 4th International Computing Education Research Workshop, Sept. 6 - 7, 2008, University of Technology, Sydney, Australia.
ICFP 2008, 13th ACM SIGPLAN International Conference on Functional Programming, Sept. 22 - 24, 2008, Victoria, British Columbia, Canada.
LICS 2008, the 23rd Annual IEEE Symposium on Logic in Computer Science, Sept. 24 - 27, 2008, Carnegie Mellon University, Pittsburgh, PA, USA.
CCSC:MW 2008, the 2008 conference of the Consortium for Computing Sciences in Colleges (Midwestern region), Sept. 26 - 27, 2008, Hope College, Holland, MI, USA.
CCSC:NW, the 10th annual Consortium for Computing Sciences in Colleges Northwestern conference, Oct. 10 - 11, 2008, Southern Oregon University, Ashland, OR, USA.
CCSC:E, the 23rd annual Consortium for Computing Sciences in Colleges Eastern conference, Oct. 10 - 11, 2008, Hood College, Frederick, MD, USA.
CCSC:RM, the 17th annual Consortium for Computing Sciences in Colleges Rocky Mountain conference, Oct. 17 - 18, 2008, Colorado Technical University, Colorado Springs, CO, USA.
OOPSLA '08, the ACM SIGPLAN Object Oriented Programming Systems and Applications Conference, Oct. 19 - 23, 2008, Nashville, TN, USA.
CCSC:SE, the 22nd annual Consortium for Computing Sciences in Colleges Southeastern conference, Nov. 7 - 8, 2008, Augusta State University, Augusta, GA, USA.
FSE-16, the 16th International Symposium on Foundations of Software Engineering, Nov. 9 - 15, 2008, Atlanta, GA, USA.
POPL 2009, the Symposium on Principles of Programming Languages, Jan. 21 - 23, 2009, Savannah, Georgia, USA.
CSEE&T09, the 22nd IEEE-CS Conference on Software Engineering Education and Training, Feb. 17 - 19, 2009, Hyderabad, India.
SIGCSE 2009, the 40th ACM Technical Symposium on Computer Science Education, March 4 - 7, 2009, Chattanooga, TN USA.
CCSC:CP, the 15th annual Consortium for Computing Sciences in Colleges Central Plains conference, April 3 - 4, 2009, Southwest Baptist University, Bolivar, MO, USA.
CCSC:SC, the 20th annual Consortium for Computing Sciences in Colleges South Central conference, April 24 - 25, 2009, Southeastern Louisiana University, Hammond, LA, USA.
CCSC:NE, the 14th annual Consortium for Computing Sciences in Colleges Northeastern conference, April 24 - 25, 2009, SUNY Plattsburgh, Plattsburgh, NY, USA.
ITiCSE 2009, the 14th Annual Conference on Innovation and Technology in Computer Science Education, July 6 - 8, 2009, Université Pierre et Marie Curie, Paris, France.
CCSC:MW, the 16th annual Consortium for Computing Sciences in Colleges Midwestern conference, Sept. 25 - 26, 2009, St. Xavier University, Chicago, IL, USA.

On-Line Resources

Organizations

The ACM Special Interest Group on Algorithms and Computation Theory
The ACM Special Interest Group on Computer Graphics and Interactive Techniques
The ACM Special Interest Group on Computer Science Education
The ACM Special Interest Group on Programming Languages
The ACM Special Interest Group on Symbolic and Algebraic Manipulation
The Applied Geometry Lab at Caltech
The IEEE Computer Society's Educational Activities Board
The Mathematical Association of America
- CUPM (Committee on the Undergraduate Program in Mathematics)
The American Mathematical Society
The Society for Industrial and Applied Mathematics (SIAM)
The Consortium for Mathematics and its Applications (COMAP)
The Center for Discrete Mathematics and Computer Science (DIMACS)
The Clay Mathematics Institute, devoted to the dissemination and recognition of mathematical knowledge
The Consortium for Computing Sciences in Colleges.
The Computing Curricula 2001 task force.
ABET, the accrediting body for computing and engineering programs of study
The Software Engineering Institute's Educational Collaborations
The Software Engineering Body of Knowledge project.
The Verified Software: Theories, Tools, Experiments conference of 2005, A response to the Verified Software Grand Challenge.

Publishers/Conference Sponsors

Cambridge Journals Online, the online publishing arm of Cambridge University Press.
The Frontiers in Education Conferences' clearinghouse Web page.
Historia Mathematica, a journal on the history of mathematics.
The International Series in Formal Methods from Academic Press.
JERIC, the ACM Journal on Educational Resources in Computing.
The Journal of Logic and Computation, from Oxford University Press.
The Journal of On-Line Mathematics and its Applications, an on-line journal from the MAA.
Logical Methods in Computer Science, an open-access, referreed, free, on-line journal covering logical methods in all areas of computer science.
National Educational Computing Association, sponsors of the National Educational Computing Conference.
Teaching Mathematics and its Applications, a journal from Oxford University Press.

Funding Sources

NSF, the U.S. National Science Foundation.
FIPSE, the U. S. Department of Education Fund for the Improvement of Postsecondary Education.

Directories/Collections

Bibliographies for computer science, including sub-collections in areas such as Theory of Computation and Computational Mathematics
Computing Curricula references and links, maintained by Martin Dickey, University of Washington.
CSTC, the Computer Science Teaching Center.
Directory of DIMACS Educational Programs (undergraduate and K-12).
Formal Methods Education Resources, maintained by Kathi Fisler, Worcester Polytechnic Institute.
Alexander Sakharov's Foundations of Mathematics, a collection of links to articles dealing with the foundations of mathematics, organized to form a coherent "book."
Interactive Mathematics Miscellany and Puzzles, by Alexander Bogomolny
MacTutor History of Mathematics Archive at the University of St. Andrews.
The Math Archives at the University of Tennessee at Knoxville, a collection of general mathematics resources.
The Mathematical Atlas, a collection of introductory articles on areas of modern mathematics.
The Math Forum, reference and educational resources for all levels -- K-12, college, and beyond
"More Math than Science," a collection of tutorials and tools for miscellaneous topics in pre-calculus mathematics
The National Science Digital Library (NSDL)
SIGCSE Education Links, links to computer science teaching resources
Teaching Maths the Right Way, a collection of links and commentaries on many aspects of mathematics, maintained by Dr. S. Parthasarathy
Theoretical Computer Science on the Web, maintained by Suresh Venkat, Stanford University.
The World Library for Formal Methods, maintained by Jonathan Bowen, at South Bank University
The World of Mathematics reference pages at Wolfram Research -- a quick reference source for a great deal of mathematics.

Position Statements, Articles, Et Cetera

"Do Software Engineers Need Mathematics?", by Keith Devlin, at MAA Online.
"Mathematics in Computer Science Curricula", by Jeannette M. Wing -- slides presented at the Sixth International Conference on Mathematics of Program Construction, July 2002, Dagstuhl, Germany.
"What Math is Relevant for a CS or SE Student? An Employer's Perspective" by Dennis J. Frailey, Principal Fellow, Raytheon Company, originally published in SIGSOFT Software Engineering Notes, May 2006.
"What Should Computer Students Learn from Mathematics" by Y. C. Tay, National University of Singapore. (Also available in SIGACT News, June 2005.)

Post-Secondary Teaching Resources

The BESEME Project -- "Better Software Engineering through Mathematics Education"
Susanna Epp's Collection of Discrete Math Applets
The Computational Discrete Mathematics course at Carnegie-Mellon University
Supplemental materials for Peter Van Roy and Seif Haridi's text "Concepts, Techniques, and Models of Computer Programming"
The Great Theoretical Ideas in Computer Science course at Carnegie-Mellon University.
David Gries's Introduction to Teaching Logic as a Tool
LINK -- Software for manipulating and visualizing discrete math
An on-line course on Logic and Proofs at Carnegie-Mellon University, part of CMU's Open Learning Initiative
The Mathematical Experiments in Computer Science course at Stonehill College
A Java package for Polynomials over Rings.
ProofBuilder, a Java program that helps students learn to do proofs for a first course on discrete mathematics, including induction, sets, summations, O(), mod, and combinatorics.
The Reusable Software Research Group at Ohio State University and Clemson University, studying formally-specified component-based software; includes software tools to help students reason mathematically about software specifications and tests.
Notes and sources for "Teaching with Original Historical Sources in Mathematics" at New Mexico State University, with a sub-project on "Teaching Discrete Mathematics via Primary Historical Sources."

K-12 Teaching Resources

CyberChase, a public television series, with associated on-line and print activities, devoted to showing 8-to-12-year-old children the importance and fun of mathematics.
The Discrete Math Workshop at Tufts University for K-8 teachers.
HeyMath, electronic learning resources to support teachers and students in grades 5 through 12
The Making Math Engaging: Discrete Mathematics for K-8 Teachers Web site
MATHmaniaCS, devoted to "passing on the excitement of mathematics and computer science to kids of all ages."
Math for America, an organization of investment bankers, educators, and mathematicians dedicated to improving mathematics education in US public schools.
The METIP Project, helping kids appreciate the math behind digital images.
Computer Science Unplugged, introducing computer science topics to kids without the need for computers.
MegaMath, bringing important mathematical ideas to elementary schools.
Magic of Math, "a forum to communicate and share the delight of mathematics with children"
Views on High School Mathematics Education, mathematicians' and educators' responses to a set of questions about secondary mathematics education in the United States
The WebLabs project, aimed at "creating new ways of representing and expressing mathematical and scientific knowledge in European communities of young learners (10-14 years)"

Studies

Lew Hitchner's rough survey of the Status of Discrete Structures/Discrete Math Courses in computer science and similar programs.
Pete Henderson's Survey of Alumni Satisfaction concerning a mathematically-oriented introduction to computer science.
Timothy Lethbridge's Software Engineering Education Relevance Survey.
A casual survey of the audience for Kelemen et al.'s ITiCSE 2000 paper "Has Our Curriculum Become Math-Phobic (An American Perspective)", on the Changing Importance of Math in CS Curricula.

Contests

Mathematical Modelling contests, sponsored by COMAP.

This page maintained by Doug Baldwin, baldwin@geneseo.edu, with help from Peter Henderson.

Last updated August 14, 2008.