Discrete Mathematics Course (Binary, Hex, Recursion, Big O Complexity) in 7 hours

Thanks for watching and please subscribe for more content.

PART 1: Number Bases and Binary Arithmetic
00:00:00 Number bases (decimal, binary, hexadecimal and octal)
00:04:19 Convert integer to binary
00:07:48 Convert integer to octal
00:09:40 Convert integer to hexadecimal
00:11:37 Convert non-integer to binary (repeating digits)
00:15:17 Convert non-integer to binary
00:16:36 Convert non-integer to hexadecimal
00:17:45 Convert hexadecimal to binary and octal
00:20:17 Adding binary numbers
00:22:03 Adding hexadecimal numbers
00:23:05 Subtracting binary numbers
00:25:07 Subtracting hexadecimal numbers
00:26:17 Multiplying binary numbers
00:28:27 Multiplying hexadecimal numbers
00:30:47 Dividing binary numbers
00:32:38 Dividing hexadecimal numbers
00:34:24 Ten's complement, subtraction
00:37:16 Two's complement, subtraction
00:40:20 Represent negative binary numbers using the two's complement
00:46:20 Normalised scientific notation
00:47:51 IEEE754 floating point standard for representing real numbers
00:51:55 Worked example on IEEE754 floating point representation
PART 2: Mathematical Computer Algorithms
00:54:39 Algorithms and Pseudocode
00:58:13 Horner's algorithm for evaluating polynomials
01:03:56 Collision detection algorithm in computer games
01:08:55 Encryption and decryption algorithm in cryptography
01:13:21 Lottery algorithm
PART 3: Iteration and Recursion
01:18:17 Sigma notation
01:21:58 Geometric series
01:24:10 Arithmetic series
01:28:31 Iteration, Fibonacci sequence
01:32:15 Recursion, Fibonacci sequence
01:34:14 Recurrence relation for the factorial sequence
PART 4: Recurrence Relations
01:13:50 Recurrence relations, standard form and properties
01:41:33 General solution to first order recurrence relations
01:44:02 General solution to second order recurrence relations
01:49:17 Worked example, Fibonacci recurrence relation
01:52:42 Worked example, recurrence relation with repeated root
01:55:41 Non-homogeneous second order recurrence relations
01:58:10 General solution to non-homogeneous second order recurrence relations, special cases
02:00:17 Worked example, 2nd order non-homogeneous recurrence relation
02:07:02 Worked example, 2nd order non-homogeneous recurrence relation
PART 5: Computational Complexity of Algorithms and Big O Notation
02:13:16 Intro to computational complexity
02:17:32 Informal definition of Big O
02:19:14 Comparing growth rates, logarithms
02:21:38 Typical growth rates
02:24:33 Big O, formal definition
02:26:51 Worked examples on formal definition of Big O
02:29:19 Worked example on Big O
02:31:59 Refining Big O calculations, triangle inequality
02:34:36 Obtaining better constants for Big O calculations
02:36:15 Refining Big O calculations using large N
02:38:44 Worked example on refining Big O calculations
02:41:17 Big O analysis of Bubble Sort algorithm
02:45:34 Big O analysis of Bubble Sort algorithm using the recurrence relation
02:51:18 Big O analysis of Merge Sort algorithm
03:06:53 Big O analysis of Binary Search algorithm
03:13:32 Big O analysis of Binary Search algorithm using the recurrence relation