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Due date if any
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Fuchsia means graded homework.
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30-3 April/May
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Section 8.2: 1, 2, 5, 6ac, 8.
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Section 8.1: 9, 11.
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For later problems, reading
Order of an Element may be helpful.
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23-27 April
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Section 8.1: 1, 2, 3.
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For the following problem, reading
Dirichlet Convolution (a slightly longer
version) may be helpful.
If r is multiplicative and invertible, then so is its Dirichlet inverse
r -1.
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Section 7.4: 15, 16.
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16-20 April
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Section 7.3: 1c, 4, 5, 7, 11c, 13.
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Section 7.2: 1, 3, 4ab, 5, 8, 10, 20.
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For the following problem, reading
Dirichlet Convolution (the short version)
may be helpful.
Generalize Theorem 6.4 of page 109 as follows.
If r and s are multiplicative, then so is their Dirichlet
convolution r * s.
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Section 6.2: 1, 3, 4abc.
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9-13 April
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Section 6.1: 1, 6, 7, 8, 9, 12, 14, 22.
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4-6 April
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Section 5.3: 1, 6, 9, 10.
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Section 5.2: 18.
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26 March
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19-23 March
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Section 5.2: 3, 4ad, 6a, 9.
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Section 5.2: 1, 2ab.
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5-9 March
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Section 4.4: 1abcd, 2ac, 3, 6, 10.
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Section 4.3: 19.
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Section 4.2: 9, 16.
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26-2 Feb/March
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Section 4.3: 6ab, 9, 23.
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Section 4.3: 2a, 4, 5a.
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Section 4.2: 13, 15.
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Section 4.2: 1, 3, 4, 8a.
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19-23 February
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Section 3.2: 2, 3, 13 (hard problem, but good).
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Find the prime factorizations of 123456789 and of 987654321.
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Section 3.1: 9a.
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Section 3.1: 3, 6.
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12-14 February
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Section 2.5: 8a.
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Section 2.5: 2, 5a, 6.
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5-9 February
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Section 2.5: 1.
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Section 2.4: 5a, 8.
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Section 2.4: 2cd, 4ab, 6.
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Section 2.3: 19a, 20abc, 21.
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29-2 Jan/February
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Section 2.3: 4b, 12, 14, 18.
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Section 2.3: 2, 6.
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Section 2.2: 2, 4.
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Section 2.1: 1, 2, 10.
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22-26 January
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Convert the decimal number 99 into binary.
Convert the binary number 10101 into decimal.
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When we expand (a+b)^13, what is the (binomial) coefficient in front of
a^9*b^4?
Write your final answer as a decimal number.
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Section 1.2: 1, 8.
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Think of a good more general formula than the one in Section 1.2.2.
Then try to prove this more general formula to be correct.
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Consider the sequence a_1, a_2, a_3, a_4, a_5, ... defined by
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a_n = 1/(1*2) + 1/(2*3) + 1/(3*4) + 1/(4*5) + ... + 1/(n*(n+1)).
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By trial and experiment find a `closed' simple expression for a_n.
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Prove by induction on n that this `closed' simple expression for a_n is always
correct.
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Section 1.2: 2, 3.
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17-19 January
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Section 1.1: 8.
Also, compute 12! (twelve factorial).
Also, consider the sequence a_1, a_2, a_3, a_4, a_5, ... defined by
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a_1 = 1, and for all n >= 2 we have a_n = a_1 + a_2 + a_3 + ... + a_(n-1).
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By trial and experiment find a `closed' simple expression for a_n.
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Prove by induction on n that this `closed' simple expression for a_n is always
correct.
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Section 1.1: 1ae, 2, 9.
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