Copyright
© Diane Donovan, at The Department of Mathematics, the University of Queensland ,
Brisbane , Australia
You may print and reproduce this material for your
personal use.
Course Organisation
|
Copyright © Diane Donovan, at The Department of Mathematics, the You may print and reproduce this material for your personal use. |
The
learning material for this course consists of nine components. These are:
1. A Course Profile
2. A Textbook: Discrete
Mathematics with Applications, by Susanna Epp.
3. A Study Guide (at front of
Workbook)
4. A Workbook
5. A Reader (at back of
Workbook)
6. Assignment Questions
7. Practice Midsemester
and Practice End of Semester Exams
8. Solutions to Assignments and
Practice Midsemester and End of Semester Exams
(available on webpage)
9. Course Web Page: http://www.maths.uq.edu.au/~dmd/teaching/MATH1061/MATH1061-5-2004.htm
Students
purchase the textbook. The Workbook can be purchased (see Course Profile for
details) or down-loaded from the Course Web Page.
The
Course Profile lists all the
administrative information relevant to this course, you must read it.
The
Textbook is the basic resource
material on which the course is based. All students require a copy of this
book.
The
Study Guide gives a detailed
description of the material to be covered in this course. It is important to
read this documents as it tells you what to study and when to study it.
The Workbook is for students to record important definitions and theorems. It also provides extra examples which students may work. Note that the numbering of sections in the workbook follows the numbering of the corresponding sections in the textbook, but not in the same order as the textbook. Solutions to all exercises presented in the Workbook are available on the Course Web Page.
The
Reader contains extra material not
presented in the textbook. The Study Guide directs students to the Reader when
necessary
Assignments are usually set on a weekly
basis, three of these will could towards assessment.
For information relating to assessment of assignments refer to the Course
Profile.
Practice Midsemester and Practice End of Semester
Exams are provided as they give an indication of the standards of
assessment for this course.
Solutions to Assignments and practice
exams can be obtained from the web page.
The Course Web Page should be checked
regularly; all important announcements are posted on this web page. It also
contains links to files for the Workbook, Solutions to the Workbook, the Reader
and Solutions to Assignments.
MATH1061
STUDY GUIDE
Students should use this guide to plan their study. Each section of the Study Guide directs students to:
1. Read background material (includes detailed information of relevant pages in the textbook or reader).
2. Write a summary of reading material in the workbook and to work extra examples to reinforce the ideas covered in the reading.
3. Work extra problems the check to material has been
fully understood. You should make sure you do these problems.
The sequencing of material follows the order in which the material will be presented in lectures. The numbering of chapters and sections roughly follows the numbering used in the textbook. For instance we will study Chapter 11, of the textbook, immediately after Chapter 5. We will not study Chapter 9 of the textbook and we include a final chapter on groups and fields which is not covered in the textbook. To try and reduce confusion, the numbering of chapters and sections in the study guide (and the workbook and reader) follows the numbers of the chapters and sections in the textbook. Hence the order we follow is:
Chapter 1: Sections 1.1, 1.2, 1.3 and 1.4
Chapter 2: Sections 2.1, 2.2 and 2.3
Chapter 3: Sections 3.0, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9 and 3.10
Chapter 4: Sections 4.1, 4.2, 4.3 and 4.4
Chapter 5: Sections 5.1, 5.2 and 5.3
Chapter 11: Sections 11.1, 11.2, 11.3 and 11.5
Chapter 10: Sections 10.1, 10.2, 10.3 and 10.5
Chapter 7: Sections 7.1, 12.2, 7.2, 7.3, 7.4 and 7.5
The Last Chapter: Sections G1, G2 and G3
Chapter 6: Sections 6.1, 6.2, 6.3, 6.4, 6.5, 6.6 and 6.7
Chapter 8: Sections 8.1, 8.3 and 8.4
Chapter 1: Logic
Read (Unless otherwise stated the reading is from the textbook, Discrete Mathematics with Applications (3rd Edition) by Susanna Epp) |
Write (Complete the definitions and work the example from the Workbook) |
Problems (Complete the following problems from of the textbook, Discrete Mathematics with Applications (3rd Edition) by Susanna Epp, Check your answers using the solutions at the back of the textbook.) |
Section 1.1, pages 1—15
|
Exercises 1.1.1 and 1.1.2
|
pages 15—17, Questions 5a, 6, 8a,
10ac, 14, 16, 18, 19, 21, 23, 25, 29, 31, 35, 37, 41, 42, 45, 47, 52a.
|
Section 1.2, pages
17—27
|
Exercises 1.2.1 and 1.2.2
|
pages 27—29, Questions 1, 3, 5, 7, 9, 19, 20adf, 38, 40.
|
Section 1.3, pages
29—31 (stopping before Modus Ponens and Modus
Tollens)
|
Exercises 1.3.1 and 1.3.2
|
pages 41--43, Questions 6, 8, 22, (for the remaining problems, just determine
validity) 24, 25, 36, 37.
|
Section 1.4, pages 43—53 (stopping before Example 1.4.6) |
Exercises 1.4.1 and 1.4.2 |
pages 55—57, Questions 1, 3, 5, 7, 9, 11, 13, 16, 18, 22, 24.
|
Chapter 2: Quantified Statements
Read (Unless otherwise stated the reading is from the textbook, Discrete Mathematics with Applications (3rd Edition) by Susanna Epp) |
Write (Complete the definitions and work the example from the Workbook) |
Problems (Complete the following problems from of the textbook, Discrete Mathematics with Applications (3rd Edition) by Susanna Epp, Check your answers using the solutions at the back of the textbook.) |
Section 2.1, pages
75—85 (stopping before Tarski’s World)
|
|
Pages 86—88, Questions
1ab, 9, 11, 13, 16a, 17a.
|
Section 2.2, pages
88—91 (stopping halfway through page 91 at ``THE RELATION AMONG
",
$,
Ů,
AND Ú”.)
|
Exercises 2.1.1 and 2.1.2
|
Pages 95---97, Questions
11, 13, 20, 22.
|
Section 2.3, pages
97—103, (omit Examples 2.3.1 and 2.3.2, stop just before Example 2.3.8 on
page 103)
|
Exercises 2.2.1 and 2.2.2
|
Pages 108—111, Questions 14, 16, 28, 36, 38.
|
Chapter 3: Number Theory
Read (Unless otherwise stated the reading is from the textbook, Discrete Mathematics with Applications (3rd Edition) by Susanna Epp) |
Write (Complete the definitions and work the example from the Workbook) |
Problems (Complete the following problems from of the textbook, Discrete Mathematics with Applications (3rd Edition) by Susanna Epp, Check your answers using the solutions at the back of the textbook.) |
|
Section 3.0, pages 4--7 of the
Reader. |
Exercises 3.0.1 and 3.0.2
|
|
Section 3.1, pages
125--139
|
Exercises 3.1.1 and 3.1.2
|
Pages 139--141, Questions 2, 4, 7, 11, 17, 20, 22,
29, 34, 35, 36, 39, 43.
|
Section 3.2, pages
141--146
|
Exercises 3.2.1 and 3.2.2
|
Pages 146--147, Questions 1, 3, 4, 11, 30, 34.
|
Section 3.3, pages
148--154
|
Exercises 3.3.1 and 3.3.2
|
Pages 154--156 Questions 1, 4, 12, 15, 29.
|
Section 3.4, pages 156--163 |
Exercises 3.4.1 and 3.4.2 |
Pages 163--164, Questions 1, 3, 5, 7, 13, 28, 39.
|
Section 3.5, pages 164--170 |
Exercises 3.5.1 and 3.5.2 |
Pages 170--171, Questions 1, 3, 18, 19.
|
Section 3.6, pages 171--178 |
Exercises 3.6.1 and 3.6.2 |
Pages 178--179, Questions 5, 8b, 17, 21, 24.
|
Section 3.7, pages 179--184 |
Exercises 3.7.1 and 3.7.2 |
Pages 184--185, Questions 3, 19, 31a.
|
|
Section 3.8, page 8 of the Reader. Section
3.8 of the textbook contains more detailed information on algorithms than is
necessary for this course. You may read Section 3.8 of the textbook if you
like but only pages 192--194 are directly relevant to this course. |
Exercises 3.8.1 and 3.8.2 |
Pages 196--198, Questions 9, 10, 13, 25a.
|
Section 3.9, pages 9--12 of the Reader. |
Exercises 3.9.1 and 3.9.2 |
Questions For each of the following Linear
Diophantine equations, determine whether or not a solution exists. If a
solution does exist, find one such solution. 1. 21x+15y=9 2. 158m+57n=20000 3. 354a+258b=45 Solutions will be provided on the Web. |
Section 3.10, pages 13--15 of the Reader. |
Exercises 3.10.1 and 3.10.2 |
Questions For each equation, use the solution you found in the previous section to find the general solution. Then list all solutions which involve only positive integers.1. 21x+15y=9 2. 158m+57n=20000Solutions will be provided on the Web. |
Chapter 4: Sequences & Mathematical Induction
Read (Unless otherwise stated the reading is from the textbook, Discrete Mathematics with Applications (3rd Edition) by Susanna Epp) |
Write (Complete the definitions and work the example from the Workbook) |
Problems (Complete the following problems from of the textbook, Discrete Mathematics with Applications (3rd Edition) by Susanna Epp, Check your answers using the solutions at the back of the textbook.) |
Section 4.1, pages 199--211 (stopping just before
Example 4.1.17)
|
Exercises 4.1.1 and 4.1.2
|
Pages 213--215, Questions 19, 20, 27, 38, 40, 42, 48, 49, 51ac.
|
Section 4.2, pages
215--225
|
Exercises 4.2.1 and 4.2.2
|
Pages 226--227, Questions 6, 10, 13, 15.
|
Section 4.3, pages
227--233
|
Exercises 4.3.1 and 4.3.2
|
Pages 233—235, Questions 3, 6, 8, 13, 19, 24.
|
Section 4.4, pages 235--242 |
Exercises 4.4.1 and 4.4.2 |
Pages 242—244, Questions 1, 22.
|
Chapter 5: Set Theory
Read (Unless otherwise stated the reading is from the textbook, Discrete Mathematics with Applications (3rd Edition) by Susanna Epp) |
Write (Complete the definitions and work the example from the Workbook) |
Problems (Complete the following problems from of the textbook, Discrete Mathematics with Applications (3rd Edition) by Susanna Epp, Check your answers using the solutions at the back of the textbook.) |
Section 5.1, pages
255--265 (stopping just before the heading AN ALGORITHM TO CHECK
WHETHER)
|
Exercises 5.1.1 and 5.1.2
|
Pages 267--269, Questions 1, 4a, 8abfi, 10, 17ab,
20a, 22ad, 23, 26abc, 27a, 28b, 29a, 30a.
|
Section 5.2, pages
269--280 The textbook uses element
arguments in the proofs of set properties. In the workbook examples you use
truth tables, and the logical connectives from Chapters 1 and 2, to prove set
properties.
|
Exercises 5.2.1 and 5.2.2
|
Pages 280--282, Questions 3, 25, 28.
|
Section 5.3, pages
282--290
|
Exercises 5.3.1 and 5.3.2
|
Pages 290—293, Questions 1, 5, 18a, 40.
|
Chapter 11: Graph Theory
Read (Unless otherwise stated the reading is from the textbook, Discrete Mathematics with Applications (3rd Edition) by Susanna Epp) |
Write (Complete the definitions and work the example from the Workbook) |
Problems (Complete the following problems from of the textbook, Discrete Mathematics with Applications (3rd Edition) by Susanna Epp, Check your answers using the solutions at the back of the textbook.) |
Section 11.1, pages
649---662
|
Exercises 11.1.1 and 11.1.2
|
Pages 662--665, Questions 1, 5, 8, 12, 15, 16, 19,
22, 24a, 25a, 28.
|
Section 12.2, pages
665--679
|
Exercises 11.2.1 and 11.2.2
|
Pages 679--683, Questions 1, 4, 6a, 9a, 12, 14, 19.
|
Section 11.3, pages
683—687 (stopping after Example 11.3.4 halfway through page 687)
|
Exercises 11.3.1 and 11.3.2
|
Pages 695—697, Questions 4a, 4c, 5a.
|
Section 11.5, pages 705—714 (stopping after Example 11.5.8 on page 714) |
Exercises 11.5.1 and 11.5.2 |
Page 721, Questions 22, 25, 27.
|
Chapter 10: Relations
Read (Unless otherwise stated the reading is from the textbook, Discrete Mathematics with Applications (3rd Edition) by Susanna Epp) |
Write (Complete the definitions and work the example from the Workbook) |
Problems (Complete the following problems from of the textbook, Discrete Mathematics with Applications (3rd Edition) by Susanna Epp, Check your answers using the solutions at the back of the textbook.) |
Section 10.1, pages
571—580, (stopping on page 580 at
“N-ARY RELATIONS & RELATIONAL DATABASES")
|
Exercises 10.1.1 and 10.1.2
|
Pages 582--583, Questions 1, 3a, 5ab, 8ab, 9a, 10a,
12, 13, 16, 17, 23, 25.
|
Section 10.2, pages
584—592
|
Exercises 10.2.1 and 10.2.2
|
Pages 592--594, Questions 1, 3, 6, 12, 14, 15, 23,
26, 30, 31, 34, 37ac.
|
Section 10.3, pages
594—608
|
Exercises 10.3.1 and 10.3.2
|
Pages 608—610, Questions 2a, 3, 5, 7, 13a, 14a, 15a,
16a, 18, 23, 25.
|
Section 10.5, pages 632—636, (stopping half-way through page 636 at LEXICOGRAPHIC ORDER) You should also read the bottom half of page 639. |
Exercises 10.5.1 and 10.5.2 |
Pages 646--648, Questions 1a, 1b, 2, 8, 21a.
|
Chapter 7: Functions
Read (Unless otherwise stated the reading is from the textbook, Discrete Mathematics with Applications (3rd Edition) by Susanna Epp) |
Write (Complete the definitions and work the example from the Workbook) |
Problems (Complete the following problems from of the textbook, Discrete Mathematics with Applications (3rd Edition) by Susanna Epp, Check your answers using the solutions at the back of the textbook.) |
Section 7.1, pages
389—398
|
Exercises 7.1.1 and 7.1.2
|
Pages 399--402, Questions 1, 3ab, 5a, 7, 23a, 26a,
28a, 31, 35abc.
|
Section 12.2, pages
744—752, (stopping at (“DESIGNING A FINITE—STATE AUTOMATON”)
|
Exercises 7.2.1 and 7.2.2
|
Pages 760--763, Questions 2, 5, 7, 8, 10c, 12.
|
Section 7.2, pages
402--417
|
Exercises 7.3.1 and 7.3.2
|
Pages 417--419, Questions 1, 6, 7a, 9a, 12, 14a, 16,
17, 21, 24a, 36, 38, 39, 40, 43.
|
Section 7.3, pages 420--429 |
Exercises 7.4.1 and 7.4.2 |
Pages 430--431, Questions 3, 5, 9, 10, 12, 14, 17,
25, 26, 29.
|
Section 7.4, pages 431--441 |
Exercises 7.5.1 and 7.5.2 |
Pages 441--443, Questions 1, 3, 9, 16.
|
Section 7.5, pages 443—447 (stopping at “THE SEARCH FOR LARGER INFINITES”) |
Exercises 7.6.1 and 7.6.2 |
Pages 454--456, Questions 1.
|
Chapter 6: Counting
Read (Unless otherwise stated the reading is from the textbook, Discrete Mathematics with Applications (3rd Edition) by Susanna Epp) |
Write (Complete the definitions and work the example from the Workbook) |
Problems (Complete the following problems from of the textbook, Discrete Mathematics with Applications (3rd Edition) by Susanna Epp, Check your answers using the solutions at the back of the textbook.) |
Section 6.1, pages
297--304
|
Exercises 6.1.1 and 6.1.2
|
Pages 304--306, Questions 13a, 21, 23cd, 26, 28.
|
Section 6.2, pages 306--317
|
Exercises 6.2.1 and 6.2.2
|
Pages 318--320, Questions 6, 8, 9, 11ab, 12ab, 14abd,
16a, 17, 19d, 21, 29ab, 32, 34a, 35a, 36a, 38.
|
Section 6.3, pages
321—330
|
Exercises 6.3.1 and 6.3.2
|
Pages 330—333, Questions 1a, 3, 4, 6, 9, 11, 14, 21a, 26ab, 28.
|
Section 6.4, pages 334--346 |
Exercises 6.4.1 and 6.4.2 |
Pages 347--349, Questions 1, 5ab, 6, 9b, 15, 17a, 19,
24.
|
Section 6.5, pages 13—14 of the Reader |
Exercises 6.5.1 and 6.5.2 |
Pages 355--356, Questions 3, 5 (refer to Example
6.5.3, page 352), 10, 11.
|
Section 6.6, pages 356--361 |
Exercises 6.6.1 and 6.6.2 |
Pages 361--362, Questions 1, 5, 14, 17a.
|
Section 6.7, pages 362--369 |
Exercises 6.7.1 and 6.7.2 |
Page 369, Questions 1, 3, 11, 13.
|
Chapter 8: Recursion
Read (Unless otherwise stated the reading is from the textbook, Discrete Mathematics with Applications (3rd Edition) by Susanna Epp) |
Write (Complete the definitions and work the example from the Workbook) |
Problems (Complete the following problems from of the textbook, Discrete Mathematics with Applications (3rd Edition) by Susanna Epp. Check your answers using the solutions at the back of the textbook.) |
Section 8.1, pages
457--472
|
Exercises 8.1.1 and 8.1.2
|
Pages 472--475, Questions 1, 3, 5, 7, 9, 11, 13, 15,
36.
|
Section 8.3, pages 487—495 (stopping before ‘THE
SINGLE--ROOT CASE’)
|
Exercises 8.3.1 and 8.3.2
|
Pages 498—499, Questions 1, 3a, 5, 8, 13, 25.
|
Section 8.4, pages 499—504 |
Exercises 8.4.1 and 8.4.2 |
Pages 507--509, Questions 15, 23
|
The Last Chapter: Groups and Fields
Read (These pages refer to the Reader) |
Write (Complete the definitions and work the example from the Workbook) |
Problems (Complete the following problems from the Reader. Check your answers using the solutions at the back of the Reader.) |
Section G.1, pages
19--26 of the
Reader.
|
Exercises G.1.1 and G.1.2
|
Pages 26—28 of the Reader, Questions
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15
|
Section G.2, pages
29--32 of the
Reader.
|
Exercises G.2.1 and G.2.2
|
Page 32 of the Reader, Questions 1,2,3,4,5
|
Section G.3, page 33
of the
Reader.
|
Exercises G.3.1 and G.3.2
|
|