Math 374: Discrete Structures.

Section 001

Spring 2009

University of South Carolina

      Instructor  
      Matthew Boylan  
  Office     LeConte 400G  
  Phone     777-8874  
  E-mail     boylan@math.sc.edu  
  Office hours     Tues., 9 - 10  
  Weds., 3:30 - 4:30  
  Fri., 11 - 12  
  And by appointment  

  • University of South Carolina Mathematics Department .

    • Course information :

  • Prerequisite : Math 142 and CSCE 146.

  • Text : Mathematical Structures for Computer Sciences, by Gersting.
    6th ed., W. H. Freeman and Company New York. (2007).

  • Course objectives : Students will master concepts and solve problems on propositional and predicate logic; proof techniques; recursion and recurrence relations; sets, combinatorics, and probability; functions, relations, and matrices; algebraic structures.

  • Meeting schedule :

          Section 003  
      Lecture     MWF     2:30 - 3:20     LeConte 405  

  • Homework : Homework will be assigned each lecture but not collected.

  • Quizzes: Weekly quizzes will be given based on the homework. Missed quizzes will not be made up.

  • Exam schedule : (3 one-hour exams and a cumulative final exam)

      Exam 1:     Friday     February 13     2:30 - 3:20     LeConte 405  
      Exam 2:     Friday     March 20     2:30 - 3:20     LeConte 405  
      Exam 3:     Friday     April 17     2:30 - 3:20     LeConte 405  
      Final Exam:     Wednesday     April 29     2:00 - 5:00     LeConte 405  

    Missed exams will not be made up. Exceptions may be made for documented illness/family emergency.

  • Grading :

          Points/650     % of grade  
      Three hour exams:     100 pts. x 3     15% x 3  
      Final exam:     200 pts.     30%  
      Quizzes:     150 pts.     25%  
      Total:     650 pts.     100%  

    Letter grades will be assigned according to the following approximate scale unless otherwise noted:

      A     B     C     D     F  
      90 - 100     80 - 90     70 - 80     60 - 70     0 - 60  

    Note : The deadline to drop without a WF is Monday, February 23.

  • Calculators : Calculators (and computer software such as Maple) may be used on homework unless otherwise noted. They may not be used to do quizzes or exams.

  • Other help resources : Math Lab (free drop-in tutoring at various locations on campus, including LeConte 105), Private tutors , On-line materials for courses   (374 websites from past semesters), Math library .

  • Syllabus (which contains all of the above information): (pdf)   (ps)

    • Lectures and Homework :

    Lectures Homework
      Dates     Sections     Topics     Problems     Quiz date  
      January  
      Week 1     12     M     1.1     Statements, Symbolic Representations, and Tautologies (1.1).     3, 5, 7, 10, 12, 17, 21 (1.1). Solutions.    1/23.  
      14     W     1.1, 1.2     Propositional Logic (1.2).     1, 8, 9, 16, 20, 21, 40, 44, 46 (1.2). Solutions.    1/23.  
      16     F     1.2             1/23.  
      Week 2     19     M         No Class.     Martin Luther King Jr. Day.      
      21     W     1.3     Quantifiers, predicates, and validity (1.3).     1, 2, 4, 8, 9, 15, 19, 21, 25 (1.3). Solutions.     1/30.  
      23     F     1.3     Quiz 1 on 1.1, 1.2.         1/30.  
      Week 3     26     M     1.4     Predicate logic (1.4).     7, 9, 11, 12, 17, 21, 33 (1.4). Solutions.    2/6.  
      28     W     1.4              
      30     F     1.5     Logic Programming (1.5); Quiz 2 on 1.3.     4, 5, 6, 9, 12, 14 (1.5). Solutions.    2/6.  
      February     Week 4     2     M     1.5             2/6.  
      4     W     1.6     Proof of correctness (1.6).     3, 4, 5, 7, 11, 12, 15 (1.6). Solutions.      
      6     F     1.6     Quiz 3 on 1.4, 1.5.          
      Week 5     9     M     2.1     Proof techniques (2.1).     3, 5, 9, 12, 13, 21, 23, 25, 28, 37, 38, 43, 47, 48, 62, 64 (2.1). Solutions.     2/20  
      11     W     2.1             2/20.  
      13     F     Exam 1 review guide.     Exam I. Solutions.     Covers: Sections 1.1 - 1.6;   Class Notes: 1/12 - 2/9; Quizzes: 1 - 3.     
      Week 6     16     M     2.2     Induction (2.2).     2, 4, 8, 12, 14, 29, 32, 44, 52, 70, 74 (2.2). Solutions.    2/20.  
      18     W     2.3     More on proof of correctness (2.3).     1, 3, 9, 12 (2.3). Solutions.    2/27.  
      20     F     2.3     Quiz 4 on 2.1.         2/27.  
      Week 7     23     M     2.4     Recursive definitions (2.4).     2, 3, 8, 9 ,14, 17, 19, 22, 37, 41, 45, 47, 53 (2.4). Solutions.    2/27.  
      25     W     2.4, 2.5     Recurrence relations (2.5).     2, 5, 8, 19, 21, 28, 32, 35, 40 (2.5). Solutions.     3/6.  
      27     F     2.5     Quiz 5 on 2.2, 2.3.        3/6.  
      March     Week 8     2     M     2.6     Analysis of algorithms (2.6).     3, 4, 10 (2.6). Solutions.     3/6.  
      4     W     2.6              
      6     F     3.1     Sets (3.1); Quiz 6 on 2.4, 2.5.     3, 9, 11, 13, 19, 20, 25, 38, 41, 50, 53, 60, 63, 65def, 82, 83 (3.1). Solutions.     
        8 - 15           No Class.     Spring Break.      
      Week 9     16     M     3.1, 3.2.     Counting (3.2).     3, 4, 10, 12, 19, 31, 36, 41, 42, 50, 59, 61, 64, 66. (3.2). Solutions.     3/27  
      18     W     3.2             3/27.  
      20     F     Exam 2 review guide.    Exam II. Solutions.     Covers: Sections 2.1 - 2.6.  Class Notes: 2/11 - 3/6; Quizzes: 4 - 6.     
      Week 10     23     M     3.3     Principle of inclusion and exclusion; pigeonhole principle (3.3).     1, 3, 8, 12, 14, 17, 20, 21, 25 (3.3). Solutions.     3/27.  
      25     W     3.3             4/3.  
      27     F     3.4     Permutations and combinations (3.4); Quiz 7 on 3.1, 3.2.    4, 6, 11, 13, 17, 19, 27, 31, 32, 35, 45, 52, 57, 64, 65, 68, 70, 79 (3.4). Solutions.     4/3.  
      Week 11     30     M     3.4             4/3.  
      April     1     W     3.6     Binomial theorem (3.6).     1fgh, 5, 10, 11, 13, 14, 15, 16, 20 (3.6). Solutions.     4/10.  
      3     F     3.6     Quiz 8.        4/10.  
      Week 12     6     M     4.1     Relations (4.1).     2, 3, 5, 7, 10, 11, 12 d - j, 13, 14, 37, 38 b, c, 39, 40, 43, 44 (4.1). Solutions.     4/10.  
      8     W     4.1              
      10     F     4.1     Quiz 9.         
      Week 13     13     M     4.1              
      15     W     4.4     Functions (4.4).     1, 2, 5, 6, 7, 10, 11, 18, 19, 21, 25, 29, 30, 32, 33, 34, 36 (4.4). Solutions.     
      17     F     Exam 3 review guide.     Exam III. Solutions.     Covers: Sections 3.1 - 3.4, 3.6.   Class Notes: 3/16 - 4/13; Quizzes: 7 - 9.      
      Week 14     20     M     4.4              
      22     W     4.4              
      24     F     4.4         66, 68, 71 (4.4).      
      Week 15     27     M     Review sheet for final.     Review.          
      May     Finals week     April 29     Weds.         Final Exam, 2 - 5 pm     Cumulative