# Rhea Section for MA375 Professor Walther, Fall 2015

This page refers to the "Lecture Notes in Discrete Mathematics" of MA 375 in Fall of 2015, by Uli Walther.

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Do not delete or edit previously listed typos.

Please list any typo found in the course notes below. Mimic the first two entries: indicate page, line from above (positive numbers) or from the bottom (negative numbers), old text and new text. Add a new line for each typo.

- 1. page 3, line -5, "Week 5" should be omitted.
- 2. page 4, line 8, "Week 7" should be omitted.
- 3. page 9, line -2, {Hx
_{2}} should be {H_{2}}. - 4. page 14, line 6, R| should be |R|.
- 5. page 15, line 23, |A and B and C| should be |A or B or C|.
- 6. page 11, line 13, n! should be n.
- 7. page 11: Exercise 1.8 Question Number 10: The question does not say what set the equation is under. I assume that the set is under all natural numbers greater than or equal to 1 since excluding the numbers and just looking at 2n-1=n^2 if 0 is inserted it makes the equation -1=0 which is not true.
- 8. page 28, line -1, x = 79*l should be x = 7+9*l.
- 9. page 29, line -13, x = r*i*b - s*j*a should be x = r*i*b + s*j*a.
- 10. page 31, line 12, p*(a-1) should be a*(p-1).
- 11. page 45,line 12, the question says find the total of amount of..., The first "of" should be omitted
- 12. page 38, question 3.21, The question seems misworded in that it can be thought to mean if the intersection of E1 and E2 are independent of F rather than finding out if each one is independent of F. I would recommend breaking this question into subparts.
- 13. page 41, line 19, "Iphone" either has the wrong capitalization or has an extra "I". It should read either "phone" or "iPhone".
- 14. page 45, line 12, "amount of inversions" should read "number of inversions".
- 15. page 37, line 8, u'(y) dy) should be u'(y) dy (parenthesis typo).
- 16. page 39, line 7, p(e) should be p(E).
- 17. page 39, line -7, if an only if should be if and only if.
- 18. page 40, line 6, ambiguous expression: sqrt(3)/2*r should be r*sqrt(3)/2, like in the next line.
- 19. page 40, line 7, sqrt(2)/3 should be sqrt(3)/2.
- 20. page 40, line -18, should on should be should not.
- 21. page 40, line -16, unformly should be uniformly.
- 22. page 49, line 3, It says "The setup it", but it should say "The setup is"
- 23. page 40, line 20, f(g(y) should be f(g(y))
- 24. page 61, line -14, this paragraph should be indented.
- 25. page 61, line -16, this paragraph should be indented.
- 26. page 61, line -8, "(2,2) These" should be "(2,2). These"
- 27. page 49, exercise 4.4 (4) "......exactly the same number of acquaintances in the audience?" should be "....exactly the same number of acquaintances in the attendance?"
- 28. page 56, line -19, {(1,2,3)} should be {1,2,3}.
- 29. page 56, line 11, change actual should be actual change.
- 30. page 57, line 14, imaging should be imagine.
- 31. page 70, line 6, a
_{n+1}should be a_{n-1}. - 32. page 70, line 15, an initial condition for a
_{1}is needed to solve. - 33. page 72, line -2, Suppse should be Suppose.
- 34. page 74, line 11, "is greater (resp. smaller)" should be "is smaller (resp. greater)".
- 35. page 82, Exercise 6.15 seems to be in a smaller font which makes one think that it might be part of the recall notation.
- 36. page 78, line 9, "To each graph", should be "For each graph."
- 37. page 38, last line, "a(t least one)", should be "(at least one)"
- 38. page 61, line 3, "4(2a_n-2 +1)", should be "4(2a_n-3 +1)"
- 39. page 78, line -14, "(i,i)" should be "(i,j)"
- 40. page 82, line 18, "Let us denote denote" should be "let us denote"
- 41. page 82, line 10, this paragraph should be indented.
- 42. page 80, line 2, of exercise 6.8.2, The word sum should be changed to sums.
- 43. page 82, line -3, Exercise 6.15 is here.
- 44. page 55, line -21, "solver" should be "silver".
- 45. page 78, line -17, "vertex appears as endpoint" should be "vertex appears as an endpoint".
- 46. page 79, line -2, "with even sum" should be "with an even sum"
- 47. page 80, line -20, there should be a comma after the V_2.
- 48. page 80, line -7, "in turn be "American". And so on. should be "in turn be "American", and so on."
- 49. page 90, line 14, "each edge has degree" should be "each vertice has degree"
- 50. page 84, line 27, " that such bijection" should be "that such a bijection"
- 51. page 79, line 18, K
_{2,3}should be K_{3,3}. - 52. page 82, line 17, "more then one" should be "more than one".
- 53. page 85, line 14, "P/NPbelow" should be "P/NP below".
- 54. page 91, line 21, "a point the we already" should be "a point that we already".
- 55. page 92, line -1, "is is" should be "it is".
- 56. page 93, line 19, "homeomorphis" should be "homeomorphic".
- 57. Page 97, line 11, "(5) d=3,D=4: this is the icosahedron, a 20-sided solid" should be "d=5, D=3".
- 58. page 97, line 18, "are in approximate the same" should say "are in approximately the same"
- 59. page 102, line -7, "X
_{G'2}(n)" should be "X_{G2}(n)" - 60. page 101, line -13, "the hard past" should be "the hard part".
- 61. page 103, line 2, "n(n-1)
^{2}" should be "n(n-1)(n-2)^{2}". - 62. page 103, line -10, "graph will by the disjoint union" should be "graph will be the disjoint union"
- 63. page 107, line 6, "a a rooted tree" should be "a rooted tree".
- 64. page 107, line 16, "a
_{n}^{h}= A•r^{1}= A" should be "a_{n}^{h}= A•1^{n}= A". - 65. page 107, line -13, χ
_{2}(n) should be ξ_{2}(n). - 66. page 108, line 3, "that can you draw" should be "that you can draw">
- 67. page 109, line 9, "the root has degree n" should be "the root has degree m"
- 68. page 111, line 12, "Given is" should be "Given that"
- 69. page 113, line 4, The vertices aren't labeled on parts 1 and 2 for exercise 6.108. They need to be labeled with letters in order to find the shortest path from a to z.
- 70. page 113, line 2, The answer to example 6.107 is incorrect. There is a shorter path then the one given as the answer. The shortest path should be A to F to E to Z. This yields a distance of 8. The error occurs in your table for row e; instead of 8 from f, it should be 6.This changes how the rest of the problem is completed.
- 71. page 100, REMARK 6.58 sphere -> surface?
- 72. page 110. REMARK 6.100, t(G) = t(Ge)+t(Gehat), should not be e
- 73. page 90, line 17, "their degrees is at least |G|/2" should say "|G|"
- 74. page 90, line -13, "and one arc for each vertex" should say "and one arc for each edge"
- 75. page 84, line 3 under '2. Graph Isomorphisms', the word isomorphy should be isomorphism"
- 76. page 83, exercise 6.18 line 2, A^(4)_v,v' should read A^(4)_v,v
- 77. page 113, The table has another mistake with the error of e to d being 8 rather than 7, but this does not change the answer as mentioned above with e to f being 6.etc.
- 78. page 17, line line -12. Definition 2.1 (3) should read as: "the law of distribution applies: r*(s+t)=r*s+r*t", rather than r*(s+t)=r*t+s*t.
- 79. page 55. chapter is about permutation with repetition but line 25. Exercise 4.20 number 2 is permutation without repetitions
- 80. page 22. It should be gcd(a.b)=p^max(ap,bp) not min, so as lcm(a,b)=p^min(ap,bp) not max.