Computing and Software 701
Logic and Discrete Mathematics in Software Engineering
Fall 2005

Instructor: William M. Farmer

References

01 Introduction to Mathematics and Logic

  1. Chapter 3, K. H. Rosen, Discrete Mathematics and Its Applications, Fifth Edition, McGraw-Hill, 2003.
  2. D. M. Bressoud, Proofs and Confirmations: The Story of the Alternating-Sign Matrix Conjecture, Cambridge University Press, 1999.
  3. I. Lakatos, Proofs and Refutations, Cambridge University Press, 1976.
  4. Biographical Sketch of I. Lakatos.

02 Propositional Logic

  1. Chapter 1, K. H. Rosen, Discrete Mathematics and Its Applications, Fifth Edition, McGraw-Hill, 2003.
  2. E. Mendelson, Schaum's Outline of Boolean Algebra and Switching Circuits, McGraw-Hill, 1970.

03 Numbers, Sets, Functions, and Relations

  1. Chapters 1, 3, and 7, K. H. Rosen, Discrete Mathematics and Its Applications, Fifth Edition, McGraw-Hill, 2003.
  2. P. R. Halmos, Abstract Naive Set Theory, Springer-Verlag, 1987.
  3. MathWorld
  4. The Mathematics Section of the Wikipedia

04 First-Order Logic

  1. Chapter 1, K. H. Rosen, Discrete Mathematics and Its Applications, Fifth Edition, McGraw-Hill, 2003.
  2. C. C. Chang and H. J. Keisler, Model Theory, North Holland, 1990.
  3. H. B. Enderton, A Mathematical Introduction to Logic, Academic Press, 1972.
  4. R. M. Smullyan, First-Order Logic, Dover publications, 1995.

05 Recursion and Induction

  1. Chapter 3, K. H. Rosen, Discrete Mathematics and Its Applications, Fifth Edition, McGraw-Hill, 2003.
  2. 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

06 Simple Type Theory

  1. P. B. Andrews, An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof, Kluwer, 2002.
  2. A. Church, "A formulation of the simple theory of types", Journal of Symbolic Logic, 5:56-68, 1940.
  3. W. M. Farmer, "A basic extended simple type theory", SQRL Report No. 14, 12 pp., McMaster University, 2004. PDF
  4. W. M. Farmer, "The seven virtues of simple type theory", SQRL Report No. 18, 29 pp., McMaster University, 2005. PDF