CSCI2427 --- Discrete Mathematical Structures
Robert Hochberg, Instructor

The Syllabus can be found here.

Points assigned to each problem are shown in brackets following the problems (after they are handed in).  Note that not all problems will necessarily be graded.

We have a new Discussion Board.  Please submit your questions and comments there so that everyone can benefit from the question and response.  (Click on <Communication> and then <Discussion Board>.)

You can see your Grades also.  (Click on <Student Tools> then <Check Grade>.)
 

Date
Sections to be covered
Homework
Note:  Homework is now displayed on the day that it is due
Thursday, 8/22 Sections 1.1 and 1.2, Logic and Propositional Equivalences 
<slideshow><handouts>
 
Tuesday, 8/27 Section 1.2, Logical Equivalence
<slideshow><handouts>
 1.1 #2, 6, 12, 14, 20, 22, 26, 28, 40[XC]
Thursday, 8/29 More on Logical Equivalence
<slideshow><handouts>
 
Tuesday, 9/3
No Class --- Follows Monday schedule
 
Thursday, 9/5 Sections 1.3 and 1.4(start), Predicates, quantifiers and sets
<slideshow><handouts>
1.2 #4[1], 8[2], 10[2], 20[1], 26[4]
Tuesday, 9/10 Sections 1.4 (finish) and 1.5, Sets and set operations
<slideshow><handouts>
 
Thursday, 9/12 Section 1.6, Functions
<slideshow><handouts>
1.3 #2, 6[2], 8, 20[2], 40[XC+3]
1.4 #2, 4[2], 6[2], 12[2], 14
(see red note at top)
Tuesday, 9/17 Sections 1.6 (finish) and 1.7, Sequences and Summation
<slideshow><handouts>
1.5 #2[2], 4, 10[2], 14, 18, 22, 28[2], 34[XC+2]
1.6 #2[2], 4, 8[2]
(see red note at top)
Thursday, 9/19 1.7, Countable and Uncountable
<slideshow><handouts>
 
Tuesday, 9/24 1.7 (finish) 
<slideshow><handouts>
 
Thursday, 9/26 2.1 Introduction to Algorithms
<slideshow><handouts>
1.6 #10[2], 12[1], 14, 16[2], 28
1.7 #2[2], 4, 6(a, b, c, e), 
10(a, b, f), 16[2], 18[1], 34, 32[XC +1 for each part]
(out of order on purpose)
Tuesday, 10/1 7.7 and 7.8, Introduction to Graphs and Graph Coloring  
Thursday, 10/3
 Exam 1 --- Exam 1 --- Exam 1
<Homework Solutions-pdf><Homework Solutions-Word>
Study guide:  All homework problems, problems 1-8 on p. 383 of student solutions manual, read pp 407-408, p. 415 except for composition and big-O notation.
Homework:
Read sections 2.1 and 2.2. 
There is nothing to turn in.
Tuesday, 10/8 2.1 (finish) and 2.2, Complexity of Algorithms
<slideshow><handouts>
 
Thursday, 10/10 Review of Exam --- Curved +18 points   
Tuesday, 10/15
No Class --- Fall Break
 
Thursday, 10/17 2.2 (finish)
<slideshow><handouts>
2.1 #2, 10[2], 12, 14[3], 18[2+2XC], 24[3+2XC]
2.2 #4[3], 7, 8, 10[2], 12
Tuesday, 10/22 2.3, Integers, divisors and the phi-function
<slideshow><handouts>
 
Thursday, 10/24 2.3, Modular Arithmetic
<slideshow><handouts>
2.2 #16[3]
2.3 #4[3], 8, 10[3], 14[3], 20,
        22[3], 24, 28[XC+3]
Tuesday, 10/29 2.4, The Euclidean Algorithm
<slideshow><handouts>
 
Thursday, 10/31 2.5, Fermat's Little Theorem and RSA Encryption
<slideshow><handouts>
2.3 #16, 30, 50
2.4 #2, 6, 8, 32
Tuesday, 11/5 Review for exam
 
Thursday, 11/7
 Exam 2 --- Exam 2 --- Exam 2
<Sample Exam>
<Homework Solutions-Word>
Study guide:  All homework problems from sections 1.7 to 2.5
More to come...
2.5 #4, 6, 10, 24, 38
Find gcd(84, 106) using the
Euclidean Algorithm, showing all
steps.  Same for gcd(455, 715).
Tuesday, 11/12 3.1, Introduction to Proof Techniques
<slideshow><handouts>
 
Thursday, 11/14 3.1, Some examples of proofs
<slideshow><handouts>
Hand in the stuff due on 11/7, and
3.1 #16, 26 (XC #18 and #22, +3 each)
Tuesday, 11/19 Review of Exam 2
 
Thursday, 11/21 3.2, Proofs by induction
<slideshow><handouts>
No homework due.  Please review exam 2
in preparation for the final
Tuesday, 11/26 3.2, Induction and 4.1, Intro to Counting
<slideshow><handouts>
 Homework due Tuesday
3.2 #8, 60[5], 62
a. can be [1]
b. can be [1]
c. cannot be even for n = 1 [2]
d. can be [1]
b. and d. are easy to see, because the
boards are multiples of board a.
Thursday, 11/28
No Class --- Thanksgiving
 
Tuesday, 12/3 4.3, "Choose Numbers"
<slideshow><handouts>
 
Thursday, 12/5 4.6, Binomial and Multinomial Coefficients
<slideshow><handouts>
 
Tuesday, 12/10 Finite Difference Tables (not in book) This homework is worth 20 points
4.1 #2[2], 4, 8, 10, 12, 14, 22, 30, 32
4.3 #2, 6, 8, 10[2], 12[2], 16, 26, 38[2], 44
4.6 #18[3], 26, 28[3], 32[3], 34a, 36, 51[3]
Find the next term in each of these sequences:

a.  1, 3, 6, 10, 15, ___
formula: (n+1)(n+2)/2

b.  0, 2, 6, 12, 20,  30, ___
formula: n(n+1)

c.  0, 0, 6, 24, 60, 120, ___
formula: n^3 - n

d.  0, 0, 4, 18, 48, 100, ___

formula: n^3 - n^2

[XC+3 each]

Find a formula for the nth term in each of those sequences, assuming that each sequences begins with the 0th term.
Final Exam
Thursday, December 12, 8-10am, in the usual room

Sections from book that will be covered:
The sections below contain all the material on the exam, but the converse is not true.  Please correlate the sections given below with the material actually covered in class (see the slideshows and handouts in the table above) so that you know what can be safely skipped.  
1.1-1.7
2.1-2.5
3.1-3.2
4.1, 4.3, 4.6

How to study for the final exam::
Start NOW!
Make sure that you can do all the homework problems
Make sure that you can do the previous two exams, as well as the <Sample Exam> for test 2
Use the Discussion Board. to discuss questions and answers with other students and me
Bring questions to the last day of class, and I will be glad to answer them then.
If there are questions which you can answer, but you are not sure that you really have the idea, please try similar problems in the book, or invent a similar problem and post it and your solution on the discussion board (anonymously if you wish) so that I can tell you if you're on the right track.

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