Discrete Structures for Mathematics Teachers
Autumn 1999-2000
Instructor: Dr. Jeanne LaDuke
Byrne Hall 556
Telephone: 773-325-1342
E-mail: jladuke@condor.depaul.edu
Meeting Times:
September 18: 9:00-5:00
September 19: 11:00-5:00
October 16: 9:00-5:00
October 17: 11:00-5:00
November 14: 9:00-5:00
Textbook: Epp, Susanna S. Discrete Mathematics with Applications, Second Edition, PWS or Brooks/ColePublishing, 1995
Rationale: This course is intended to clarify the logical basis for much of high school mathematics and to provide a solid foundation for the study of abstract mathematics and theoretical computer science. The first part of this course focuses on the basic principles of logical reasoning and how to apply these principles to formulate and explore the truth and falsity of mathematical statements. Proof, disproof, and conjecture all figure prominently. The main vehicle for exploration is number theory, including the representation of real numbers on a number line, divisibility properties of integers, properties of rational numbers, the irrationality of the square root of 2, and the infinitude of the prime numbers.. The second part of the course focuses on sets, functions, cardinality, and recursion, and on combinatorial reasoning and its applications in a variety of different areas.
This course will probably place greater emphasis on communication, both written and oral, than other mathematics courses you may have taken previously. Justifying a belief in the truth or falsity of a mathematical assertion requires a rational argument. A main theme of this course is learning to express such arguments with clarity and precision.
Course Content:
| Sections | Content |
| 1.1 - 1.3 | Logic of Compound Statements |
| 2.1 - 2.3 | Logic of Quantified Statements |
| 3.1 - 3.4, 3.6, 3.7 | Elementary Number Theory and Methods of Proof |
| 4.1 - 4.4 | Sequences and Mathematical Induction |
| 8.1 - 8.2 | Recursion |
| 5.1 – 5.3 | Set Theory |
| 7.1, 7.3, 7.5, 7.6 | Functions and Cardinality |
| 6.1 - 6.4 | Combinatorial Reasoning |
| 6.6 - 6.7 | Pascal's Triangle and the Binomial Theorem |
Evaluation: Exams will test knowledge of definitions and basic facts and techniques, primarily through problems similar to those assigned as homework. There will be a midterm exam on October 16 and a final exam on November 14. Homework will be collected on October 17. The midterm examination will count 40% of your grade, the final examination will count 50%, and homework and class participation will count 10%.
Academic Integrity: Cheating and plagiarism
are examples of academic misconduct that can result in course failure and
possible additional disciplinary action.
MAT 660: Discrete Structures for Mathematics Teachers
Assignment 1: Autumn 1999 (Due October 17)
The following problems form the basis for the midterm
examination on October 16.
| Problems to practice on . . . | Problems to hand in . . . |
| 1.1 #1, 3, 5, 8, 10ac, 12,14, 27, 29, 33 | 1.1 #18, 28, 32, 36 |
| 1.2 # 1, 3, 5, 9, 12, 15, 16adf, 18adf, 19adf, 20, 22, 25, 34, 36, 38 | 1.2 # 14, 16b, 18b, 19b, 24, 27, 40 |
| 1.3 # 1, 3, 6, 8, 11, 12a, 21, 23, 24, 26, 36, 37ad | 1.3 # 5, 10, 11, 25, 34, 37bc |
| 2.1 #1, 4, 6, 8, 9, 11ac, 12a, 13, 15ac, 16a, 19, 20ac, 21a, 22ac, 24, 26, 28ac, 29, 31, 33, 35 | 2.1 # 10, 14, 18, 25, 27, 28be, 32 |
| 2.2 # 1, 3, 5, 7, 9, 10, 13,118, 20a, 24, 31, 33, 35, 37, 39, 41, 42a | 2.2 # 2, 15, 20bc |
| 2.3 # 1-3, 5, 7-10, 21, 23, 27,29 | 2.3 # 4, 6, 20, 28, 30 |
| 3.1 # 1, 3, 8, 10, 11, 13, 15, 17, 19, 21, 22, 25 | 3.1 # 4, 12, 14, 24, 26 |
| 3.2 # 1, 3, 6, 9, 11, 12, 13, 30, 31 | 3.2 #2, 7, 8, 14-17, 29, 32 |
| 3.3 # 1, 3, 5-7, 9, 11, 13, 14, 18, 27, 30a, 31a, 34 | 3.3 # 15, 21, 23, 24, 29, 30b, 36 |
| 3.4 # 1, 3, 5, 13, 21 | 3.4 # 14, 20, 22, 36 |
| 3.6 # 1, 2, 5-7, 9, 16, 17 | 3.6 # 10, 18, 21 |
| 3.7 # 2, 5 | 3.7 # 1, 4, 13, 18 |
| 4.1 #1, 3, 10-12, 18a-d, 19, 26, 29, 32, 33, 48, 51, 52, 54, 55 | 4.1 # 36, 53 |
| 4.2 # 1, 3, 5, 6, 9, 12, 19, 21, 22, 24 | 4.2 # 8, 11, 13, 23 |
MAT 660: Discrete Structures for Mathematics Teachers
Assignment 2: Autumn 1999 (Due November 14)
| Problems to practice on . . . | Problems to hand in . . . |
| 3.1 #43 | 4.2 #14, 20 |
| 4.3 # 1, 3, 6, 8, 16, 21 | 4.3 #7, 9 |
| 4.4 #1 | 4.4 #5 |
| 8.1 #1, 3, 5, 18ac, 21ac, 23a, 24a, 25, 27b, 29 | 8.1 #18b, 21ac, 22, 23bc, 27ac |
| 8.2 #1ab, 2ac, 3, 5, 7, 26 | 8.2 #1c, 2bd, 4, 23, 28, 37 |
| 5.1 #1, 6abfi, 11a, 12ab, 13ab | 5.1 #2, 6cdeghj, 12cd |
| 5.2 #1ab, 2, 3, 5, 8 | 5.2 #1c, 4, 10 |
| 5.3 #6a | 5.3 #6bc |
| 7.1 #1, 3ab, 4a, 6, 8, 11a, 14ac, 15ac, 16, 18, 28 | 7.1 #3cd, 4bc, 10, 14bde, 15bdefg |
| 7.3 #1, 2, 3a, 5a, 8, 10a, 12, 13, 23a, 24, 31, 33, 34, 42 | 7.3 #5bc, 9b, 11, 25, 36 |
| 7.5 #1, 3, 8, 11a, 14a, 15, 20 | 7.5 #10, 14bc, 16, 17, 18, 23 |
| 7.6 #1, 3, 7 | |
| 6.1 #2, 5-9 |
| Problems to practice on . . . |
| 2.2 #41 |
| 7.6 #2, 11, 12, 19 |
| 6.2 #8, 9 ,14 |
| 6.3 #6 |
| 6.4 #6, 8, 19 |
| 6.6 #1, 3, 9 |
| 6.7 #1, 2, 6, 11, 13, 14 |