CIS/CSE 607 home page

CIS/CSE 607
 Mathematical Basis of Computing 

Tuesday 18.30 -- 21.30 111 Bowne Hall

Prof. Howard A. BLAIR

Rainbow Line

Office: 3-185 Center for Science and Technology
Office Hours :
By Appointment
& Tuesday 12.20 - 15.20
Syracuse University
Syracuse, New York 13244-4100 USA
Phone: 315.443.3565
Fax: 315.443.2583
Email: blair at ecs.syr.edu

UPDATES and NOTICES:

  • The course will concentrate on "discrete" mathematics for computer science and engineering. The term "discrete" signifies areas of mathematics normally thought of as not involving calculus. Such a veiwpoint is fundamentally misguided, but servicable for the purposes of the course. The topics are generally more advanced than calculus. The goal of the course >is not to learn about topics in discrete math. The goal is to see clearly in a cognitive sense. One learns how to see clearly by fine-tuning a rationally skeptical attitude relentlessly devoted to it, that is, to seeing clearly.

Workbook


Course Objective and Purpose

  • The Objective of this course is to equip participants with a way of seeing based upon mathematical logic and the fundamental building blocks of mathematics: sets, relations, and functions.

  • The Purpose of this way of seeing is to empower one to engineer anything in the design space that is the mathematical universe, the only limits being those imposed by logical consistency.

Course Rationale

  • The mathematical universe displays extreme consilience; in particular, the structure and function of any part of it impacts the structure and function of every other part.

  • Artifacts of technology as well as the the virtual worlds of computing are realizations of structures in the mathematical universe.

  • Therefore, the greater one's powers to roam at will through the design space that is the mathematical universe, the greater will be one's powers to create and to wield artefacts of technology and the virtual worlds of computing.

Course Outcomes

To realize the course's purpose, upon completion of the course participants will be able to:

  • Begin to read mathematical research papers in computer science and engineering.

  • Recognize rigorous logical reasoning.

  • To use mathematics and rigorous logical rasoning to facilitate deep learning of new technical concepts on one's own.

  • To formalize rigorous reasoning and appreciate the issues involved in formally modeling natural reasoning.

  • To apply mathematical logic to showing that hardware and software conform to desired specifications.

Week by Week Calendar of Topics with Tentative Exam Dates


Bibliography - None of the books in this bibliography are required. However, the book on "discrete" mathmatics by Rosen is strongly recommended. It contains a huge number of problems having to do with topics of central importance in computer science and engineering.

The WorkBook is the main text for this course.

  • (Recommended - Older Edition 2 or 3): George S. Boolos, (John P. Burgess) and Richard C. Jeffrey: Computability and Logic (2nd or 3rd edition, Paperback) Cambridge University Press. These editions are out of print, but if you can find edition 3, buy it! Avoid edition 4.

  • (Strongly Recommended): Richard L. Epstein and Walter A. Carnielli: Computability (2nd edition) Wadsworth Pub Co. 1999. ISBN 0534546447.

  • (A freeware text on mathematical logic. There is much more here than needed for the present course and it is easy to get bogged down in this material. Still, it's a useful companion): S. Bilaniuk, A Problem Course in Mathematical Logic

  • (Helpful review of undergraduate discrete mathematics for computer science. An edition is currently used in CIS 275. Consult the SU Bookstore. Earlier editions are OK.): Rosen, Kenneth H.: Discrete Mathematics and Its Applications with MathZone, McGraw-Hill Science/Engineering/Math; 6 edition (July 27, 2006) Eariler editions are OK. ISBN 0073312711. 910 pages!!



Grading: max(AVG(Exam1,Exam2,Labs,Final), Final). All parts of all questions on exams are graded on a scale of 0.0 to 4.0 i.e. F through A. Exam scores are then obtained by weighted averaging.