MATH 126 - Basic Discrete Mathematics
Announcements
None at this time.
Homework Problems
A list of recommended practice problems is available here. The exercises themselves are available here in a password-protected PDF file (11MB). The password will be provided in class.
Assignment | Sections of Textbook | Due Date | |
Assignment 1 | Solutions | 1.1, 1.2, 1.3, 1.4 | TBA |
Assignment 2 | Solutions | 1.5, 1.6, 1.7, 1.8, 2.1, 2.2, 8.5 | TBA |
Assignment 3 | Solutions | 2.3, 2.4, 2.5, 3.2, 4.1 | TBA |
Assignment 4 | Solutions | 4.2, 4.3, 5.1 | TBA |
Assignment 5 | Solutions | 5.2, 5.3, 6.1, 6.2, 6.3 | TBA |
Assignment 6 | Solutions | 6.4, 6.5, 7.1, 8.1, 8.3 | TBA |
Assignment 7 | Solutions | 10.1, 10.2, 10.4, 10.5 | TBA |
Term Tests
Test | Sections of Textbook | Test Date | Sample Tests |
Test 1 Solutions |
1.1 Propositional Logic 1.2 Applications of Propositional Logic 1.3 Propositional Equivalences 1.4 Predicates and Quantifiers 1.5 Nested Quantifiers 1.6 Rules of Inference 1.7 Introduction to Proofs 1.8 Proof Methods and Strategy 2.1 Sets 2.2 Set Operations 8.5 Inclusion-Exclusion |
TBA | Sample Test 1X Solutions Sample Test 1Y Solutions Sample Test 1Z Solutions |
Test 2 Solutions |
2.3 Functions 2.4 Sequences and Summations 2.5 Cardinality of Sets 3.2 The Growth of Functions 4.1 Divisibility and Modular Arithmetic 4.2 Integer Representations and Algorithms 4.3 Primes and Greatest Common Divisors 5.1 Mathematical Induction |
TBA | Sample Test 2X Solutions Sample Test 2Y Solutions Sample Test 2Z Solutions |
Test 3 Solutions |
5.2 Strong Induction and Well-Ordering 5.3 Recursive Definitions and Structural Induction 6.1 The Basics of Counting 6.2 The Pigeonhole Principle 6.3 Permutations and Combinations 6.4 Binomial Coefficients and Identities 6.5 Generalized Permutations and Combinations 7.1 An Introduction to Discrete Probability 8.1 Applications of Recurrence Relations 8.3 Divide-and-Conquer Algorithms and Recurrence Relations |
TBA | Sample Test 3X Solutions Sample Test 3Y Solutions Sample Test 3Z Solutions |
Note: The
final exam will also cover the following sections: 10.1 Graphs and Graph Models 10.2 Graph Terminology and Special Types of Graphs 10.4 Connectivity 10.5 Euler and Hamilton Paths |
Final Exam
The MATH 126 final exam will be a comprehensive, three hour exam and it will take place sometime during the final exam period. You must write the final exam at the scheduled time as per Camosun College's policy on final examinations.
Documents
- MATH 126 Course Outline
- Sharp EL-531X Calculator Operation Manual
- Conditional Statements (Sec 1.1)
- Logical Equivalences (Sec 1.3)
- Logical Equivalences Involving Conditional and Biconditional Statements (Sec 1.3)
- Example of a Proof Using Logical Equivalences (Sec 1.3)
- Exercise using Nested Quantifiers (Sec 1.5)
- Arguments (Sec 1.6)
- Proof of Validity of Argument Example 5 (Sec 1.6)
- Rules of Inference (Sec 1.6)
- Methods of Proof (Sec 1.7)
- Proof Exercises (Sec 1.7-1.8)
- Exhaustive Proof (Sec 1.8)
- A Guide to Proof-Writing (from the textbook publisher)
- Set Operations (Sec 2.2)
- Set Identities (Sec 2.2)
- Images of Set Unions and Intersections (Sec 2.3)
- One-to-One and Onto (Sec 2.3)
- Floor and Ceiling Functions (Sec 2.3)
- Cardinality of Sets (Sec 2.5)
- Asymptotic Notation (Sec 3.2)
- Comparing the Growth of Functions (Sec 3.2)
- Big-O Example (Sec 3.2)
- Congruence (Sec 4.1)
- Days of the Week (Sec 4.1)
- Common Number Representations (Sec 4.2)
- Odd Integers Prime Joke (Sec 4.3)
- Sieve of Eratosthenes (Sec 4.3)
- Classic Open Problems in Number Theory (Sec 4.3)
- Fermat's Last Theorem (Sec 4.3)
- Mathematical Induction (Sec 5.1)
- Horse of a Different Colour (Sec 5.1)
- Strong Induction (Sec 5.2)
- Fibonacci Numbers (Sec 5.3)
- Fibonacci Numbers from Pascal's Triangle (Sec 5.3)
- Fibonachos Foxtrot Comic (Sec 5.3)
- Product and Sum Rules of Counting (Sec 6.1)
- Counting Functions and Relations (Sec 6.1)
- Pigeonhole Principle (Sec 6.2)
- Permutations and Combinations (Sec 6.3)
- Counting Poker Hands (click here for B&W version) [3.6MB] (Sec 6.3)
- Binomial Theorem (Sec 6.4)
- Pascal's Triangle (Sec 6.4)
- 3-Letter Arrangements of the Letters ABCD (Sec 6.5)
- Divide-and-Conquer Theorems (Sec 8.3)
- Basic Graph Terminology (Sec 10.1)
- Seven Bridges of Königsberg (Sec 10.5)
- Euler and Hamilton Paths and Circuits (Sec 10.5)
- Hamilton Circuit in a Dodecahedron (Sec 10.5)
Links
- Domino PCs - YouTube Video
- Smarties Commercial - YouTube Video
- Towers of Hanoi Animation
- The Oracle of Bacon
- Collaboration Distance - Erdös Number