Department of Applied Mathematics
Fall 2003

## Discrete Mathematics (Course number 1203024101 ) Fall 2003 - Academic Year 5264

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### Syllabus:

• An introduction to formal logic. Truth tables.
• Naive set theory: what is a set? Elements of a set. Venn diagrams. Inclusion (subsets), equality. Intersection, union. Difference, symmetric difference. Cartesian product.
• Binary relations: order, equivalence.
• Functions (mappings); domain, range. One-one functions, onto functions, one-to-one correspondence. Invertible mappings.
• Finite and infinite sets. Countable sets.
• Introduction to Combinatorics.
• An introduction to graphs and trees: non-oriented and oriented graphs, paths and cycles in a graph, binary trees, counting in a graph, matricial representation of a graph, etc.

The grade will be determined by final exam (85%) and weekly home work assignements (15%).

### Course Texts:

• Paul Halmos: Naive Set Theory, Springer Verlag.
• Kenneth Rosen: Discrete Mathematics and Applications, Mac Graw-Hill (1999).
• Avraham Shimron: Introduction to Set Theory (this book is in Hebrew: "Mavo LeTorat Hakvutzot VeTopologia Kevutzatit"), Akademon-Jerusalem (2002).

### Recommended Texts:

• L. Goldstein and al. : Finite Mathematics and Its Applications, Prentice Hall.

• On-line constructing of truth tables .
• Have a look at some graphical examples .
• The WIMS site at the University of Nice (France) provides many useful tools: 2D and 3D animated graphics, interactice exercises in many fields, including topics related to the present course.
• If you are interested in various mathematical topics (biographies of famous Mathematicians, famous curves, development of special topics, ...), have a look at the The MacTutor History of Mathematics archive .

Moreover, you can get from the lecturer a DOS executable program for building truth tables. Just ask him, and give him a new diskette for copying the program.

### Homework:

Every week, a homework sheet will be handed out, either at the end of the lecture, or in the evening after the lecture.

### Solution sheets:

Solutions for homework assignements will (hopefully) be available here, generally within one week. You're invited to use them. The files are either Postscript files or jpg files.

For Postscript files:
If you work with Unix/Linux and have Ghostview installed, the solution file will be opened automatically in a separate window;

If you need a previewer under Windows, you can download the executable file , run it and it will install GSview (think of it as Ghostview for Windows). If needed, you can get more information on GSview and more information on how to configure it as a viewer for Netscape Navigator.

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