
Define matrices as rectangular arrangements of numbers with rows and columns, explain entries and that the order equals rows by columns, using two by three as an example.
Identify matrix types used in data science, including square, rectangular, identity, zero, and one-by-n matrices. Differentiate upper and lower triangular forms and recognize identity and zero matrices.
Explore the matrix transpose, define symmetric matrices (A^T = A), skew-symmetric ones (A^T = -A), and the conjugate followed by transpose leading to Hermitian and skew-Hermitian cases.
Learn to add and subtract matrices, and multiply matrices of matching sizes. Understand determinants and core factors, and expand by minors in 3 by 3 matrices.
Learn to solve linear systems with cramer's rule by computing determinants, replacing columns to find x and y, and deriving a matrix inverse.
Solve a system of three equations using cramer's rule, compute determinants, replace columns with constants, and obtain x=24, y=-21, z=-7.
Learn how to identify the pivot and ensure all entries below the leading entries are zero to obtain echelon form of a matrix.
Explore echelon and reduced echelon forms of matrices, identifying leading ones and zeroes above and below. Learn to convert augmented systems using row operations with examples.
Learn to solve linear systems using Gauss's elimination by converting an augmented matrix to row form, applying row operations to create leading ones and zeros, and determine x, y, z.
Learn how to apply the Gauss elimination method to convert augmented matrices to row echelon and reduced row echelon forms, determine matrix rank, and solve for x, y, z.
Define vector spaces as sets with addition and scalar multiplication over a field, obeying closure, identity, and inverses. Learn about subspaces and spans via linear combinations and spanning sets.
Explore linear independence and dependence in vector spaces, including bases and spans, and introduce linear transformations and inner product concepts. Delve into eigenvalues and eigenvectors with practical examples.
Learn how Gram-Schmidt constructs an orthonormal basis from a given basis in an inner product space by orthogonalizing vectors and normalizing them through projections.
Explore sets as well-defined collections, including empty and singleton sets, and master unions, intersections, differences, complements, and the universal set.
Master how Venn diagrams visualize unions and intersections, identify universal and empty sets, and apply complements and subset relationships to analyze elements in A and B.
Explore the sample space as all possible outcomes, build spaces with coins and dice, and distinguish finite and discrete from continuous spaces, plus events, independent vs dependent, and complements.
Explore probability basics, including experimental and theoretical probability, complements, sample space, and practical examples such as coin tosses, marbles, cards, and random variables.
Explores the difference between combinations and permutations, defines their formulas nCk and nPk, and shows multiple examples, including word repetitions and selecting items.
Explore permutations and combinations through practical examples, using factorial calculations for distinguishable arrangements with repetition, such as letters in a word and medals among eight contestants.
Explore how pie charts and bar graphs depict data as parts of a whole, convert fractions to percentages, and compare representations through practical examples.
Explore line graphs to interpret trends in music sales and downloads across years 2011-2018, and learn histogram construction, frequency distributions, density, and cumulative frequencies through real data examples.
Learn how to compute mean, median, mode, and range from raw and grouped data, and apply variance and standard deviation to measure dispersion in data sets.
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In this course, we will learn math for data science and machine learning. We will also discuss the importance of Math for data science and machine learning in practical words. Moreover, Math for data science and machine learning course is a bundle of two courses in linear algebra and probability and statistics. So, students will learn the complete contents of probability and statistics and linear algebra. It is not like you will not complete all the contents in this 7 hours video course. This is a beautiful course and I have designed this course according to the need of the students.
WHERE THIS COURSE IS APPLICABLE?
Linear algebra and probability and statistics are usually offered for students of data science, machine learning, python, and IT students. So, that's why I have prepared this dual course for different sciences.
METHODOLOGY
I have taught this course multiple times in my university classes. It is offered usually in two different modes like it is offered as linear algebra for 100 marks paper and probability and statistics as another 100 marks paper for two different or in the same semesters. I usually focus on the method and examples while teaching this course. Examples clear the concepts of the students in a variety of ways, they can understand the main idea that the instructor wants to deliver if they feel typical the method of the subject or topics. So, focusing on examples makes the course easy and understandable for the students.
2 IN 1 STUFF
Many instructors (not kidding anyone but it is reality) put the 30 + hours just on one topic like linear algebra, which I think is useless. Students don't have the time to see the huge videos. So, that's why I am giving the two kinds of stuff in one stuff (2 in 1), linear algebra and probability and statistics. The complete course is very highly recognized and all the videos are high-definition videos.
LINEAR ALGEBRA SECTIONS INCLUDE
In linear algebra, the students will master the concepts of matrix and determinant, solution of nonlinear equations by different methods, vector spaces, linearly dependent and independent sets of vectors, linear transformation, and Gram's Schmidt normalization process.
PROBABILITY AND STATISTICS SECTIONS INCLUDE
While in Probability and Statistics, the students will learn sample spaces, distributions, mean, median, mode, and range. They will also learn the other contents of probability and statistics in a detailed way.
THE COMPLETE DETAIL OF THE CONTENTS
To see the complete contents, please visits the contents sections of this course. The videos are relatively long videos that start from 10 minutes and end in 50 minutes. And the course has been designed on PowerPoint slides. All the concepts have been illustrated with the mouse cursor on the slides. Just follow the voice-over and the mouse cursor to understand the concepts.