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MAT3707 Exam pack 2024(Questions and answers)
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MAT3707 EXAM PACK2024
QUESTIONS AND
ANSWERS
FOR ASSISTANCE CONTACT
EMAIL:gabrielmusyoka940@gmail.com
, lOMoARcPSD|31863004
Department of Mathematical Sciences
Discrete Mathematics
Only study guide for
MAT3707
University of South Africa
, lOMoARcPSD|31863004
iii MAT3707/1
Contents
The purpose of this study guide iv
Introduction to Discrete Mathematics v
I GRAPH THEORY 1
1 Introduction to graphs 3
2 Planar graphs 12
3 Euler cycles and Hamilton circuits 21
4 Graph Colouring 29
5 Trees 34
6 Minimal spanning trees 37
II ENUMERATIVE COMBINATORICS 40
7 Basic counting 42
8 Binomial identities 47
9 Generating functions 50
10 Exponential generating functions 55
11 Recurrence relations 57
12 The inclusion-exclusion formula 62
Downloaded by Gabriel Musyoka (gabrielmusyoka940@gmail.com)
, lOMoARcPSD|31863004
iv
The purpose of this study guide
This study guide shows you
• which parts of the textbook you need to study
• which definitions you should learn
• which theorems you should be able to prove
• which types of problems you should be able to solve
• common errors that are easy to avoid
Throughout this study guide we repeatedly refer to the prescribed book, which we abbreviate as Tuck
Tucker, Alan.2012.Applied Combinatorics.
6th edition.New York:John Wiley & Sons.
Note that only some terminology, definitions, theorems and corollaries of Tucker are, where deemed
sary,repeated in the study guide.
For each study unit you should read the indicated sections of Tucker,
using the “What to look out for” section in the study unit as
Once
guide.
you have mastered the material in
a study unit, you should immediately start doing the relevant problems in the assignments given in T
Letter 101.The amount of time that should be spent on each study unit differs from individual
to indi-
vidual.However, you should organize your studies around the closing dates for sending in the assignm
These dates are also indicated in Tutorial Letter 101.
Only after you have done the exercises in the assignments and you feel that you need to do more exe
should you look at the exercises found in Tucker.
Downloaded by Gabriel Musyoka (gabrielmusyoka940@gmail.com)
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