Computing and Software 701
Logic and Discrete Mathematics in Software Engineering
Fall 2008
References
01 Introduction to Mathematics and Logic
- Chapter 3, K. H. Rosen, Discrete Mathematics and Its
Applications, Fifth Edition, McGraw-Hill, 2003.
- D. M. Bressoud, Proofs and Confirmations: The Story of the
Alternating-Sign Matrix Conjecture, Cambridge University Press,
1999.
- I. Lakatos, Proofs and Refutations,
Cambridge University Press, 1976.
-
Biographical Sketch of I. Lakatos.
02 Propositional Logic
- Chapter 1, K. H. Rosen, Discrete Mathematics and Its
Applications, Fifth Edition, McGraw-Hill, 2003.
- E. Mendelson, Schaum's Outline of Boolean Algebra and
Switching Circuits, McGraw-Hill, 1970.
03 Numbers, Sets, Functions, and Relations
- Chapters 1, 3, and 7, K. H. Rosen, Discrete Mathematics and Its
Applications, Fifth Edition, McGraw-Hill, 2003.
- P. R. Halmos, Abstract Naive Set Theory,
Springer-Verlag, 1987.
- MathWorld
- The Mathematics
Section of the Wikipedia
04 Orders and Lattices
05 First-Order Logic
- Chapter 1, K. H. Rosen, Discrete Mathematics and Its
Applications, Fifth Edition, McGraw-Hill, 2003.
- C. C. Chang and H. J. Keisler, Model Theory, North
Holland, 1990.
- H. B. Enderton, A Mathematical Introduction to Logic,
Academic Press, 1972.
- R. M. Smullyan, First-Order Logic, Dover publications,
1995.
06 Equational Logic and Algebraic Reasoning
- V. Sperschneider and G. Antoniou, Logic: A Foundation for
Computer Science, Addison Wesley, 1991.
- F. Baader and T. Nipkow, Term Rewriting and All That,
Springer, 1999.
07 Recursion and Induction
- Chapter 3, K. H. Rosen, Discrete Mathematics and Its
Applications, Fifth Edition, McGraw-Hill, 2003.
- W. M. Farmer, "A scheme for defining partial higher-order
functions by recursion", In: A. Butterfield, ed., 3rd Irish
Workshop on Formal Methods, 13 pp., electronic Workshops in
Computing, Springer-Verlag, 1999. PDF
08 Simple Type Theory
- P. B. Andrews, An Introduction to Mathematical Logic and Type
Theory: To Truth Through Proof, Kluwer, 2002.
- A. Church, "A formulation of the simple theory of types",
Journal of Symbolic Logic, 5:5668, 1940.
- W. M. Farmer, "A basic extended simple type theory", SQRL
Report No. 14, 12 pp., McMaster University, 2004. PDF
- W. M. Farmer, "The seven virtues of simple type theory",
Journal of Applied Logic, 6:267286, 2008.
09 Temporal Logic and Model Checking