ECE 595 Homework Assignments

Summer 2016

  • Problem Set 1    Combinatorics, Graph Theory         (due Thursday 5/19/16)        
    • Graph Theory
      • HHM Section 1.1.2, numbers 1, 3, and 9 (pp. 9-10)
      • HHM Section 1.1.3, numbers 7, 9, and 10 (pp. 16-17)
      • HHM Section 1.6.1, numbers 1, 2, and 3 (p. 87)
      • HHM Section 1.6.4, number 1 (p. 101)
    • Combinatorics
      • HHM Section 2.1, numbers 1 (p. 134) and 7 (p. 136)
      • HHM Section 2.2, numbers 4 (p. 142) and 10 (p. 144)
      • HHM Section 2.3, number 11 (p. 150)
      • HHM Section 2.4, numbers 1 and 5 (pp. 154-155)
      • HHM Section 2.5, numbers 2 and 4 (pp. 161-162 )

  • Problem Set 2    Abstract Algebra, Probability         (due Wednesday 5/25/16)        
    • Combinatorics
      • Guichard Section 3.1, number 4, (p. 54)
    • Group Theory
      • HHM Section 2.7.1, numbers 4 and 9 (pp. 195-196)
      • Knapp Section 4.4, prove Corollary 4.27 (p. 153)
    • Probability
      • Schay Section 3.1, numbers 2, 6, and 7 (p. 41)
      • Schay Section 3.2, numbers 3, 5, and 11 (pp. 46-47)
      • Schay Section 3.3, numbers 3 and 6 (p. 53)
      • Schay Section 3.4, numbers 2 and 7 (pp. 58-59)
      • Schay Section 3.5, numbers 1, 2, 7, 8, and 11 (pp. 68-69)

  • Problem Set 3    Random Graphs         (due Tuesday 6/16/16)        
    • Bernoulli Random Graphs
      • Griffin Section 9.1, number 81, p. 128.
      • Griffin Section 9.1, page 128. Investigate the behavior of the bound in Theorem 9.7 for various values of n and k. Include the cases n = 11, 12, and k = 2, 5, 7, 10, 15, and 20, in addition to other behavior you find interesting.
    • Erdös-Rényi Random Graphs
      • Griffin Section 9.3, derive the result obtained in equation (9.9), providing a justification for each step.
      • Griffin Section 9.3, Theorem 9.30, p. 133. Investigate the value of the given result for a range of values of the variables m, n, and to see how it behaves. Include the cases n = 9, m = 10, 20, and 30, and s = 3.

  • Problem Set 4    Statistics and Logic         (due Thursday 6/16/16)        
    • Statistics
      • Schey Section 7.1, number 4 (p. 230 of the text; pp. 234 of pdf)
      • Schey Section 7.2, number 2 (p. 239 of the text; p. 243 of pdf)
      • Schey Section 7.3, number 5 (p. 244 of the text; pp. 248 of pdf)
      • Schey Section 7.4, numbers 1, and 2 (p. 252 of the text; p. 256 of pdf)
      • Schey Section 7.5, number 6 (p. 262 of the text; pp. 266 of pdf)
    • Logic
      • DG Section 1.1, number 6 (p. 13 of the text; p. 33 of the pdf)
      • DG Section 1.2, numbers 11 and 13 (p. 28 of the text; pp. 48 of the pdf)
      • DG Section 1.3, number 7 p. 43 of the text; pp. 63 of the pdf) Please justify all of your answers!
      • DG Section 1.4, numbers 3, 4, 6, and 7 (pp. 52-53 of the text; pp. 72-73 of the pdf)

  • Problem Set 5    Decision Theory         (due Wednesday 6/22/16)        
    • Decision Theory for Applications
      • LaValle Chapter 9, numbers 2, 3, 14, 15 (pp. 491-493)

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