COSC 311 — Discrete Structures 
Fall 2011

For a student of mathematics to hear someone talk about mathematics does hardly any more good than for a student of swimming to hear someone talk about swimming. You can’t learn swimming techniques by having someone tell you where to put your arms and legs; and you can’t learn to solve problems by having someone tell you to complete the square or to substitute sin u for y. — Paul Halmos (1975)

Directory

Contact Information

Instructor:
Bruce MacLennan, PhD
Phone: 974-5067
Office: Claxton Complex 217
Hours: MF 3:35–4:30 or make an appointment
Email: maclennan@eecs.utk.edu

Teaching Assistant:
Zahra Mahoor
Office: Claxton Complex 110C
Hours: TR 10:00–12:00 or make an appointment
Email:  zmahoor at utk.edu

Classes: MWF 2:30–3:20, Claxton 205

This page: http://web.eecs.utk.edu/~mclennan/Classes/311

Catalog Description

Sets, functions, relations, equivalence relations, partial orderings and proof techniques, especially mathematical induction. Application of proof techniques to prove correctness of algorithms. Introduction to basic counting and combinatorics.

Note: As of Fall 2011, the old course sequence Mat 300 – COSC 311 has been replaced by a new course sequence COSC 311 – COSC 312. Therefore the new COSC 311 covers some of the material in Mat 300 (in particular, proof techniques). As a consequence, if you have already had Mat 300, then you will find some overlap with the new COSC 311.

Prerequisites

COSC 140, MAT 142.

Texts

Schedule

Since this is the first time this version of COSC 311 has been taught, the schedule is of necessity tentative.
  1. Fundamentals of Logic [Grimaldi, ch. 2]
  2. Mathematical Proof and Problem Solving [Solow, chs. 2, 4–11, 13]
  3. Fundamental Principles of Counting [G(rimaldi) 1.1–1.4]
  4. Set Theory [G 3.1–3.4, 3.8]
  5. Properties of the Integers and Induction [G 4.1–4.2; Solow 12; perhaps G 4.3–4.5]
  6. Relations and Functions [G 5.1–5.5; perhaps 5.6–5.8, 7.1–7.4]
  7. Supplementary Topics:

Topics

SUBJECT TO CHANGE!

 Basic Logic

Topics

Learning Outcomes

  1. Apply formal methods of symbolic propositional and predicate logic.
  2. Describe how formal tools of symbolic logic are used to model real-life situations, including those arising in computing contexts such as program correctness, database queries, and algorithms.
  3. Use formal logic proofs and/or informal but rigorous logical reasoning to, for example, predict the behavior of software or to solve problems such as puzzles.
  4. Describe the importance and limitations of predicate logic.

 Proof Techniques

Topics

Learning Outcomes

  1. Outline the basic structure of and give examples of each proof technique described in this unit.
  2. Discuss which type of proof is best for a given problem.
  3. Relate the ideas of mathematical induction to recursion and recursively defined structures.
  4. Use proof techniques to prove properties about data structures and algorithms presented in CS140.
  5. Use proof techniques to prove various properties about boolean algebra.

Functions, Relations, and Sets

Topics

Learning Outcomes

  1. Explain with examples the basic terminology of functions, relations, and sets.
  2. Perform the operations associated with sets, functions, and relations.
  3. Relate practical examples, such as relational databases, to the appropriate set, function, or relation model, and interpret the associated operations and terminology in context.

Basics of Counting

Topics (Time permitting, to be covered more extensively in COSC 312). Some of the topics, denoted in italic, are optional and may be covered at the instructor’s discretion:

Learning Outcomes

  1. Compute permutations and combinations of a set, and interpret the meaning in the context of the particular application.
  2. Solve a variety of basic recurrence equations.
  3. Analyze a problem to create relevant recurrence equations or to identify important counting questions.

Homework and Tests

SUBJECT TO CHANGE! We will assign (approximately) weekly homework, which will count a total of 15% of your Homework + Test average.

In addition, there will be three Tests, each of which will count 25% of your Homework + Test average.

Finally, there will be a quiz over the last chapter we cover, counting 10% of your Homework + Test average.

Homework Assignments:

Tentative Test Schedule:

Final Exam and Grading

SUBJECT TO CHANGE! It is anticipated that your grade will be 50% Homework + Tests and 50% Final Exam. However, if you are satisfied with your Homework + Test average, you will not have to take the Final Exam. Furthermore, if your Final Exam grade is better than your Homework + Tests average, then it will count for 95% of your grade.

The Final Exam is Mon. Dec. 5, 2:45–4:45.  The cumulative Final Exam will be two hours worth of questions similar in difficulty to those on the Tests.

For Students with Disabilities

The Office of Disability Services and the Campus Disability Monitors have asked us to pass this statement along in our syllabi:
Students who have a disability that require accommodation(s) should make an appointment with the Office of Disability Services (974-6087) to discuss their specific needs as well as schedule an appointment with me during my office hours.

Handouts

Some charts to help you with mathematical proofs:

There is a supplemental handout [pdf] with problems for practice in writing inductive proofs.

Return to MacLennan's home page

Send mail to Bruce MacLennan / MacLennan@eecs.utk.edu

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Last updated: 2011-11-30.