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Jan 10 |
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Logic I. Introduction; propositions; truth tables. (1.1) |
pg 15: 8, 14, 15, 25, 26, 29, 30, 38, 42, 43, 46, 52, 53
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Jan 12 |
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Conditional statements. (1.2) |
pg 27: 1, 2, 11, 13, 16, 20 abc, 22 abc, 23 abc, 24, 25, 34, 35, 36, 49
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Jan 14 |
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Rules of inference. (1.3) |
pg 41: 2, 3, 13, 27, 28, 29, 39, 40, 42
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Jan 19 |
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Circuits; digital logic; binary and hexadecimal. (1.4, 1.5) |
pg 55: 2, 6, 10, 14, 23; pg 73: 2, 8, 14, 21, 47
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Jan 21 |
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Logic II. Quantification. (2.1) |
pg 86: 7, 11, 12, 16, 18, 28, 30, 31
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Jan 24 |
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Negation. (2.2) |
pg 95: 3, 4, 7, 12, 19, 26, 39, 45, 46
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Jan 26 |
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Multiple quantification. (2.3) |
pg 108: 4, 12, 18, 19, 28, 29, 39, 42, 43, 44, 57
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Jan 28 |
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Validity. (2.4) |
pg 122: 12, 13, 14, 15, 20, 26, 27, 34, 35, 36
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Jan 31 |
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Proving. Direct proof and counterexample. (3.1) |
pg 140: 29, 30, 33, 36, 37, 51, 52, 53, 58, 59
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Feb 2 |
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More proofs. (3.2-5) |
pg 146: 14, 15, 32; pg 154: 15, 16, 37
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Feb 4 |
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Contradiction and contrapositive. (3.6) |
pg 178: 10, 11, 12, 13, 14, 20a, 25b, 27
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Feb 7 |
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Review for test; algorithms. (3.8) |
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Feb 11 |
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Sequences and induction. Sequences. (4.1) |
pg 213: 1, 2, 14, 15, 18, 51, 56, 59, 69
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Feb 14 |
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Mathematical induction. (4.2) |
pg 226: 1, 2, 8, 9, 13, 14, 15, 31, 32, 33
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Feb 16 |
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More mathematical induction; correctness of algorithms. (4.3-4; 4.5) |
pg 233: 8, 9, 30, 33; pg 253: 3, 4, 5, 9
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Feb 18 |
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Set theory. Basic set theory and properties. (5.1; 5.2) |
pg 267: 9, 11, 12, 14, 21, 22, 27, 29; pg 280: 3, 4
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Feb 23 |
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More set properties. (5.2) |
pg 280: 3, 4, 7, 8, 9, 10, 28, 29, 30
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Feb 25 |
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Combinatorics and probability. Introduction to counting and probability. (6.1) |
pg 304: 6, 10, 12, 14, 19, 20, 21, 22
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Feb 28 |
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Combinations and permutations. (6.4) |
pg 318: 12, 15. pg 330: 2, 17. pg 347: 4, 5, 8, 9
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Mar 2 |
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Relations. Relations on sets. (10.1, 10.2) |
pg 582: 2, 4, 6, 10, 24. pg 592: 4, 5, 9, 17, 32
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Mar 4 |
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Equivalence relations. (10.3) |
pg 608: 3, 4, 12, 18, 19, 26, 28, 33, 34, 42
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Mar 14 |
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Partial orders. (10.5) |
pg 646: 4, 9, 10, 15, 16, 17, 23, 25, and extra problem (see above)
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Mar 16 |
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Test review and the halting problem (5.4) |
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Mar 21 |
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Functions. Introduction to functions. (7.1) |
pg 399: 2, 4, 7, 9, 10, 12, 13, 14, 23
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Mar 23 |
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More functions; introduction to ML (7.1) |
pg 401: 31, 32, 33, 41, 43, 44, 45
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Mar 28 |
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One-to-one and onto functions. (7.2) |
pg 417: 4, 5, 8, 13, 18, 19, 23, 32, 33, 40, 41, 45
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Mar 30 |
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One-to-one correspondences, inverse; the pigeon-hole principle. (7.2, 7.3) |
pg 430: 3, 4, 28, 30, 35 (due Apr 1 as usual); ML assignment (due Apr 6)
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Apr 1 |
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Composition of functions and cardinality. (7.4, 7.5) |
pg 441: 3, 4, 6, 15, 26, 30, 31
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Apr 4 |
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Recursion. Introduction to recursion. (8.1) |
pg 472: 1, 2, 4, 6, 22, 25, 28, 45, 46, 47
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Apr 6 |
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Recursive algorithms. (8.1) |
pg 473: 20, 21, 37, 52 (due Apr 8 as usual); ML assignment (due Apr 11)
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Apr 8 |
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Solving recursion by iteration. (8.2) |
pg 485: 6, 7, 11, 13, 20, 23, 25
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Apr 11 |
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Test review and countability. (7.5) |
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Apr 15 |
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Graph theory. Introduction to graphs. (11.1) |
pg 662: 2, 4, 6, 7, 17, 18, 24
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Apr 18 |
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Paths and cycles. (11.2) |
pg 663: 25, 26; pg 679: 2, 6, 9, 15, 18, 24, 32, 39
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Apr 20 |
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Isomorphisms and trees. (11.4, 11.5) |
pg 703: 9, 11, 24, 27, 28; pg 721: 16, 17, 33
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Apr 22 |
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Miscellany. Regular expressions and automata. (12.1, 12.2) |
pg 744: 26, 27; pg 760: 16, 37, 38
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Apr 25 |
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Efficiency of algorithms. (9) |
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Extra problem assigned March 14:
Fred needs to get dressed, to wear a belt, jacket, pants,
shirt, shoes, socks, tie, undershirt, undershorts, and watch.
Give a Hasse diagram showing the prerequisites and give a
topological sort.