ECE 539 Foundations of Advanced Engineering I

Fall, 2018

Formerly ECE595

Course Information

  • Instructor:  Prof. S. Koskie

  • Lectures:   MW 7:30–8:45 pm in SL-137

  • Detailed Course Information    (Updated December 13, 2018)

  • Recommended Texts by Topic    (Updated December 13, 2018)

    • Recommended Texts: Combinatorics and Graph Theory
    • Recommended Texts: Groups, Rings, and Fields
      • (Knapp) Basic Algebra by Anthony W. Knapp, Springer, 2008. ISBN: 978-0-8176-3248-9 (print), 978-0-8176-4529-8 (online) This text can be accessed through IUCAT once you have logged in.

      • (LaLonde) Notes on Abstract Algebra by Scott M. LaLonde, 2013.

    • Recommended Texts: Probability
    • Recommended Texts: Mathematical Reasoning
    • Recommended Texts: Decision Theory
      • (Berger) Statistical Decision Theory and Bayesian Analysis, 2nd ed. by James O. Berger, Springer, 1985. ISBN: 978-0-387-96098-2

      • (LaValle) Planning Algorithms by Steven M. LaValle, Cambridge University Press 2006. ISBN: 9780521862059

      • (RSH) Quantitative Analysis for Management, 12th ed. by Barry Render, Ralph M. Stair Jr., and Michael E. Hanna, Pearson 2015. ISBN: 9780133507331

      • (Tryfos) Business Statistics by Peter Tryfos, McGraw-Hill Ryerson 1989. ISBN: 978-0075497332

  • Assigned Readings (Updated December 13, 2018)
    • Combinatorics

      • Week 1
        • HHM Graph Theory: Introduction, Section 1.1, pp. 1–17.
        • HHM Combinatorics: Some Essential Problems, Section 2.1, pp. 129–137.
        • HHM Combinatorics: Binomial Coefficients, Section 2.2, pp. 137–144.
        • HHM Combinatorics: Multinomial Coefficients, Section 2.3, pp. 144–145 and 148–150 only.
        • HHM Combinatorics: Pigeonhole Principle, Section 2.4, pp. 150–152 and 150–152 .
        • HHM Combinatorics: Inclusion-Exclusion Principle, Section 2.5, pp. 156–164.
      • Week 2
        • HHM Generating Functions: Section 2.6, pp. 164–185.
        • Guichard, Chapter 3 Generating Functions, pp. 51–67.
      • Week 3
        • HHM Combinatorics: Permutation Groups, Section 2.7.1, pp. 191–196.
        • Schay, Chapter 2: Combinatorial Problems, pp. 15–36.
        • Knapp, Chapter 1: Preliminaries, pp. 1–32.
        • Knapp, Appendix A: Set Theory, pp. 131 –136.

    • Groups, Finite Fields, and Probability

      • Week 4
        • LaLonde, Chapter 1: Introduction, pp. 1–18.
        • LaLonde, Chapter 2: Group Theory, Sections 2.1–2.5, 2.7, and 2.9 pp. 19–58, 69–75, and 89–93.
        • Knapp, Section 4.1: Groups and Subgroups, pp. 116-129.
      • Week 5
        • LaLonde, Chapter 3: Ring Theory, pp. 111–130.
        • Knapp, Rings and Fields, Section 4.4, pp. 141–148.
        • Knapp, Fields and Galois Theory, Sections 9.1–9.3 pp. 452–464
      • Week 6
        • VLiP Foundations, Topics 1 through 8.
        • Schay, Chapter 1: The Algebra of Events, pp. 3–14.
        • VLiP Probability Spaces, Topics 1 through 5.
        • Schay, Chapter 3: Probabilities, pp. 37–70.
        • Schay, Chapter 4: Random Variables, Sections 4.1–4.5, pp. 71–126.
      • Week 7
        • Schay, Chapter 5: Expectation, Variance, Moments, Sections 5.1–5.3, pp. 127–148.
        • VLiP Chapter 4: Special Distributions: The Normal Distribution.
        • VLiP Chapter 4: Special Distributions: The Multivariate Normal Distribution.
        • VLiP Chapter 4: Special Distributions: Distributions associated with Bernoulli Trials: Bernoulli, Binomial, and Geometric
        • Schay, Chapter 6: Some Special Distributions, Sections 6.1–6.3, pp. 177– 200.

    • Statistics

      • Week 8
        • VLiP Chapter 5: Random Samples, Topics 1 through 4.
        • VLiP Chapter 6: Point Estimation, Topics 1 and 2.
        • VLiP Chapter 7: Set Estimation, Topics 1, 3, and 4.
        • Schay, Chapter 7: The Elements of Mathematical Statistics, Section 7.1 Estimation, pp. 221–231.
      • Week 9
        • VLiP Chapter 8: Hypothesis Testing, Topics 1, 2, and 5.
        • Schay, Chapter 7: Sections 7.2 and 7.3, pp. 231–244.
      • Week 10
        • Schay, Chapter 7: Sections 7.4 through 7.7 pp. 244–275.

    • Logic and Mathematical Reasoning

      • Week 11
        • Aspnes, Propositional Logic, Sections 2.1 and 2.2, pp. 9–24.
        • Schaefer, Chapters 6 through 9, pp. 14–25.
      • Week 12
        • Aspnes, Predicate Logic, Section 2.3, pp. 25–34.
      • Week 13
        • Kirby, Methods of Proof, pp. 69–82
        • Hildebrand, Sample Induction Proofs, pp. 1–7.

    • Decision Theory

      • Week 14
        • LaValle, Chapter 9: Basic Decision Theory and Games Against Nature, Sections 9.1 and 9.2, pp. 437–459
      • Week 15
        • LaValle, Two-Player Games, Section 9.3 and 9.4, pp. 437–476

  • Homework
  • Grading:  

    • 25% Homework, due at 7:30pm, on the date assigned.

    • 25% Midterm Exam 1, Friday, 10/26/18.

    • 25% Midterm Exam 2, Friday 11/30/18

    • 25% Final Exam held during scheduled exam period.

  • Exams: Please note that exams will be held on Friday evenings.

  • Some Useful Links:

Last modified December 13, 2018.