MATH 2200. Introduction to Discrete Mathematics. Fall 2008

Course information

Math 2200 is a course on the fundamentals of discrete mathematics. Its purpose is two-fold. On the one hand, it is intended as an introduction to proofs and rigorous analytic thinking. You will learn how to understand and write short proofs, and you will improve your problem solving techniques. On the other hand, you will become acquainted with many basic and wonderful elements of mathematics such as: sets and relations, elementary number theory, combinatorics, discrete probability, graphs, algorithms. Therefore this course should also provide you with a good foundation for higher mathematics or computer science courses.

  • Prerequisites: Calculus III, Math 2210 or equivalent (may be taken concurrently).
  • Lecturer: Dan Ciubotaru; room LCB 106; e-mail: ciubo@math.utah.edu
  • Class meetings: Tue, Thu 12:25-1:45, ST 216.
  • Textbook: Rosen, Kenneth H., Discrete Mathematics and Its Applications, sixth edition. We may supplement the material by sets of notes which would be made available in electronic form throughout the semester.
  • Homework: Ten graded homework sets. Late homeworks are not allowed.
  • Exams: Two 60-minute and one 30-minute in class tests, and the two-hour final exam during the finals week. The final exam is cumulative. The exams will be closed book, closed notes, and no calculators are allowed (or needed). You will be allowed one lettersize sheet of paper with anything on it.
  • Grading: Final Exam 30%, Three in-class tests 40%, Homework 30%.
  • Final Exam: Wednesday, December 17, 10:30-12:30 pm (usual classroom)
  • Office Hours: Tuesday 11:15-12:15, Wednesday 11:45-12:45 in LCB106.

    Schedule

    Classes begin Monday 8/25 and end Friday 12/12. Fall break is during the week 10/13-10/17, and the other holidays are Labor Day 9/1, and Thanksgiving 11/27-11/28. There are 14 weeks of lectures.

    A scan of the first four sections 1.1-1.4 sections 1.1-1.4.

    Dates
    		  Textbook sections
    		  Topics
    		  Handouts
    		  Homework
    8/26 - 8/28
    		 1.1-1.4
    		 Fundamentals of logic
    		 lect082608 and lect082808
    		 Pset 1(due Sept 4)
    9/2 - 9/4
    		 1.5-1.6
    		 Introduction to proofs and proof methods
    		 lect090208
    		Pset 2(due Sept 11)
    9/9 - 9/11
    		 1.7, 2.1, 2.2
    		 More proofs, Set theory (sets, operations)
    		Pset 3(due Sept 18)
    9/16 - 9/18
    		 2.3, part of 2.4
    		 Functions; Cardinality
    		 lect091808
    		Pset 4(due Sept 25)
    9/23
    		Review for the first test
    		 lect092308

    9/25
    		First in-class test
    		 Midterm 1 and solutions

    9/30 - 10/2
    		 3.4, 3.5, part of 3.6
    		 Elementary number theory (integers, division, primes)
    		Pset 5(due Oct 9)
    10/7 - 10/9
    		 3.6, 3.7
    		 Number theory (modular arithmetic, chinese remainder)
    		 lect100708
    		 Pset 6(due Oct 23)
    10/21 - 10/23
    		 4.1,4.2
    		 Induction
    		Pset 7(due November 4, Tuesday!)
    10/28 - 10/30
    		 4.3, and review
    		 Recursion, Fibonacci numbers; Review: congruences, induction

    11/4 - 11/6
    		 5.1, 5.2, 7.5
    		 Basics of counting, pigeon-hole principle, inclusion-exclusion
    		Pset 8(due November 13)
    11/11 - 11/13
    		 5.3, 5.4
    		 Permutations and combinations
    		Pset 9(due November 25, Tuesday!)
    11/18
    		 Review for second test
    		 Induction, counting, permutations, combinations
    		 Practice Test II and solutions
    11/20
    		Second in-class test
    		 Midterm 2 and solutions

    11/25, 12/2-12/4
    		 6.1-6.3
    		 Discrete probability
    		 lect120408
    		Pset 10(due December 9, Tuesday!)
    12/9
    		Short test on probability
    		 Midterm 3 and solutions

    12/11
    		Review for the final
    		 Sample problems for the final and solutions
    		Practice final and solutions
    12/17
    		Final Exam: 10:30-12:30 pm
    		 Final and solutions Happy Holidays!