Revision as of 08:35, 18 December 2015

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.

To edit: click on "user" and choose "log in" in the drop down menu. Enter Purdue ID and password. After logging in, click "actions" and select "edit". Then make the requisite changes in the editor you will see. Then click "save page" all the way down. Check that you wrote what you wanted.

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, {Hx₂} should be {H₂}.
• 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 a₁ 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•r¹ = A" should be "a_n^h = A•1ⁿ = A".
• 65. page 107, line -13, χ₂(n) should be ξ₂(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. gcd(a.b)=p^max(ap,bp) not min so as lcm(a,b)=p^min(ap,bp) not max.

Back to MA375