This text is a basic introduction to those areas of discrete mathematics used by stu- dents of mathematics and computer science. Introductory courses on this material are now standard at many colleges and universities. Usually these courses are of one semester’s duration, and usually they are offered at the sophomore level. Very often this will be the first course where the students see several real proofs. The preparation of the students is very mixed, and one cannot assume a strong back- ground. In particular, the instructor should not assume that the students have seen a linear algebra course, or any introduction to number systems that goes beyond college algebra. In view of this, I have tried to avoid too much sophistication, while still re- taining rigor. I hope I have included enough problems so that the student can reinforce the concepts. Most of the problems are quite easy, with just a few dif- ficult exercises scattered through the text. If the class is weak, a small number of sections will be too hard, while the instructor who has a strong class will need to include some supplementary material. I think this is preferable to a book at a higher mathematical level, which will scare away weaker students.
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