A Divides B
57 min 13 Examples
- Definition of Divisibility (Examples #1-3)
- Divisibility Theorems with proofs (Example #4)
- Prove the divisibility theorem (Examples #5-6)
- Division Algorithm and how to find quotient and remainder (Example #7)
- Identify quotient and remainder: (a div d) or (a mod d) (Examples #8-10)
- Identify quotient-remainder for negative integers: (a div d) or (a mod d) (Examples#11-13)
Modular Arithmetic
1 hr 19 min 17 Examples
- Practical overview of clock arithmetic
- Definition of congruence modulo and equivalence classes
- Congruence Modulo Properties
- Determine congruence (Examples #1-4)
- Prove modular congruence theorem (Example #5)
- Verify the addition and multiplication congruence identities (Examples #6-7)
- Evaluate using modular congruence properties (Examples #8-11)
- Arithmetic Modulo m notation (Examples #12-13)
- Evaluate using modular arithmetic (Examples #14-17)
Greatest Common Divisor
59 min 13 Examples
- Prime factorization and Prime Number Algorithm (Examples #1-3)
- Determine prime or composite and provide prime factorization (Examples #4-6)
- How to find the greatest common divisor (Examples #6-9)
- Definition of least common multiple — find the gcd and lcm (Example #10a-b)
- Overview of the Euclidean Algorithm for finding the gcd (Example #11)
- Find the gcd using the Euclidean Algorithm (Examples #12-13)
Boolean Algebra
1 hr 19 min 15 Examples
- Overview of Boolean Algebra operations, expressions, and functions (Example #1-2)
- Create a table to express the Boolean function (Examples #3-4)
- Show logical equivalence using a table (Examples #5-6)
- What is duality? Overview of Boolean Algebra properties
- Find the duals of the Boolean expression (Examples #7-10)
- Verify the Boolean identity using a table (Example #11)
- Prove using a direct proof (Examples #12-15)
Chapter Test
40 min 10 Practice Problems
- Find the value of c for the congruence modulo (Problems #1-2)
- List the congruence classes (Problem #3)
- Perform the modular arithmetic (Problem #4a-c)
- Use the Euclidean Algorithm to find the greatest common divisor (Problem #5)
- Find the quotient and remainder (Problem #6)
- Find the LCM and GCD (Problem #7)
- Simplify the Boolean expression (Problem #8a-b)
- Find the dual of the Boolean expression (Problem #8c)
- Create a Boolean membership table (Problem #9a-b)
- Prove the Boolean statement (Problem #10a-b)