 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 SL137
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: 9780817632489
(print), 9780817645298 (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: 9780387960982
(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, McGrawHill Ryerson 1989. ISBN: 9780075497332
 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: InclusionExclusion 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. 116129.
 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, TwoPlayer 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.
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Last modified December 13, 2018.

