Math Courses

Thanks for watching and please subscribe for more content. PART 1: Systems of Linear Equations and Matrices 00:00:00 Intro to linear equations 00:02:38 General form of systems of linear equations 00:04:22 Solutions to linear systems (2 unknowns) 00:05:26 Solutions to linear systems (3 unknowns) 00:07:38 Worked examples on solutions to linear systems 00:14:49 Augmented matrices 00:17:05 Row operations on augmented matrices 00:24:22 Row echelon forms 00:30:03 Worked examples on row echelon forms 00:34:34 Gauss-Jordan vs Gaussian elimination 00:42:59 Homogeneous linear systems 00:47:08 Gaussian elimination with back substitution 00:51:34 Matrix notation, vectors and size 00:54:17 Basic matrix operations (addition, subtraction, equality, scalar product, trace) 00:58:20 Matrix multiplication 01:03:50 Partitioned matrices 01:08:52 Matrix products and linear combinations 01:10:59 Matrix transpose 01:13:26 Intro to matrix inverse 01:19:13 Inverse of matrix products 01:21:24 Powers of matrices 01:24:48 Inverse of a 3x3 matrix by Gauss-Jordan elimination 01:30:09 Solving linear systems by matrix inversion 01:31:54 Inverse and powers of diagonal matrices 01:34:15 Triangular matrices, and their inverse and transpose 01:38:40 Symmetric matrices, inverse and transpose PART 2: Matrix Determinants and Inverse 01:40:24 Determinant of a matrix 01:49:09 Determinant by Gaussian elimination 01:53:25 Inverse using the adjoint matrix 01:57:23 Cramer's rule PART 3: Extending Vectors from 3-Space to n-Space 02:02:13 Vectors in 2D and 3D space 02:14:48 Vectors in n-space 02:25:02 Norm of a vector in n-space and standard unit vectors 02:32:39 Dot product in n-space 02:53:11 Orthogonality and projection using the dot product 03:04:00 Cross product and triple scalar product, area and volume PART 4: Real Vector Spaces, Fundamental Matrix Spaces, Matrix Transformations and Operators 03:25:09 Real vector spaces 03:44:21 Vector subspaces, span and linear combinations 04:09:13 Linearly independent vectors, linear independence, examples 04:24:20 Basis for a vector space, coordinate vectors 04:45:13 Dimension of a vector space 04:54:47 Change of basis, mapping and the transition matrix 05:21:32 Row space, column space and null space 05:52:22 Rank and nullity of a matrix 06:11:08 Matrix transformations, operators (projection, reflection, rotation and shear) 06:42:11 Compositions of matrix transformations, one-to-one, inverse of operator

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