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.
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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> |
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| 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> |
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| Tuesday, 9/3 |
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| 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> |
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| 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> |
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| Tuesday, 9/24 | 1.7 (finish) <slideshow><handouts> |
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| 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 |
<Homework Solutions-pdf><Homework Solutions-Word> |
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> |
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| Thursday, 10/10 | Review of Exam --- Curved +18 points | |
| Tuesday, 10/15 |
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| 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> |
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| 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> |
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| 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 |
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| Thursday, 11/7 |
<Sample Exam> <Homework Solutions-Word> 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> |
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| 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 |
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| 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 |
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| Tuesday, 12/3 | 4.3, "Choose Numbers" <slideshow><handouts> |
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| Thursday, 12/5 | 4.6, Binomial and Multinomial Coefficients <slideshow><handouts> |
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| 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. |
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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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