
Explore basic algebra, including equations, the distributive property, variables, and linear equations, and learn to balance and solve for x, as well as interpret slope and intercepts on graphs.
Explore exponents and logs, including base, power, zero and negative exponents. Apply multiplication and division rules to add or subtract exponents, and use logarithms to identify exponents.
Explore polynomials, including identifying terms and exponents. Add polynomials by matching equal exponents, then multiply polynomials term-by-term and group like exponents to simplify.
Explore factoring by identifying factors of numbers and expressions, using the distributive property to rewrite 3x+9 as 3(x+3), and factor 2x^3-8x to 2x(x+2)(x-2).
Understand quadratic equations as polynomials ax^2 + bx + c and their parabolic graphs. Identify the line of symmetry, x-intercepts, and common forms like (x+e)^2 and (x-e)^2.
Define a function as an input-to-output relationship, with examples like x squared and age as a function of grade, including domain and continuity.
Explore the foundations of calculus, from continuous change and derivatives to partial derivatives and integration, and see how these ideas underpin machine learning and circle area derivations.
Examine the rate of change through delta y over delta x, relate it to speed and slope, and introduce limits as x approaches zero or infinity, leading to derivatives.
Learn how rate of change and limits yield the derivative, determine the slope at a point, and apply first-order derivatives to minimize errors in machine learning.
Explore derivative rules, including the power rule, and how derivatives indicate rate of change and slope for continuous functions, with vertical lines undefined and horizontal lines zero.
Use double derivatives and the second derivative test to identify local maxima and minima, with zero slope points and gradient descent intuition.
Use first and second derivatives to find and classify local and global extrema of a polynomial, solving for critical points and applying the second derivative test, with multi-variable notes.
Learn how partial derivatives handle multivariable functions, treating other variables as constants, and apply gradient descent to reach minima or maxima.
Explore how integration sums tiny rectangles to find the area under a curve between x1 and x2, using the limit delta x → zero for data science applications.
Explore vectors as arrows with direction and magnitude, including Cartesian and polar, unit vectors (hat), and basic vector operations. See their role in ML techniques like PCA, SVM, and SMOTE.
Learn to add and subtract vectors by combining their x and y components, and explore vector multiplication producing a perpendicular vector with magnitude |v1||v2| sin theta, equal to parallelogram area.
Explore how datasets and images become matrices and vectors, enabling feature transformations, with topics like rgb pixel matrices, smote, principal component analysis, and support vector machines.
Explore matrix arithmetic, including addition, subtraction, scalar multiplication, and dot-product multiplication, plus matrix inversion and division, with examples using a dataset and image pixel matrices relevant to machine learning.
Explore the identity matrix and its multiplicative property, compute the determinant for square matrices, and learn the inverse via the determinant-based formula, plus the transpose by swapping rows and columns.
Explore how a matrix transformation maps vectors via a two-by-two matrix, changing coordinates and enabling dimensionality reduction for graphics and gaming.
Explore change of basis and how a vector's coordinates change with different coordinate systems using a transformation matrix. Relate this to basis vectors and eigenvectors and eigenvalues.
Explore eigenvectors and eigenvalues in linear algebra, showing how certain vectors retain direction under a transformation while scaling by a corresponding eigenvalue, via the transformation matrix and coordinate changes.
Learn the basics of probability through coin tosses and dice, including experiments, outcomes, events, and the sample space. Understand how probabilities range from zero to one and guide classification decisions.
Learn how conditional probability updates the likelihood of events given another condition, illustrated with practical examples and a venn diagram approach for machine learning applications.
Explore random processes and random variables, distinguishing them from algebraic variables, and analyze how sums of two dice form a random variable with even values and their probabilities.
Congratulations if you are reading this. That simply means, you have understood the importance of mathematics to truly understand and learn Data Science and Machine Learning.
In this course, we will cover right from the foundations of Algebraic Equations, Linear Algebra, Calculus including Gradient using Single and Double order derivatives, Vectors, Matrices, Probability and much more.
Mathematics form the basis of almost all the Machine Learning algorithms. Without maths, there is no Machine Learning. Machine Learning uses mathematical implementation of the algorithms and without understanding the math behind it is like driving a car without knowing what kind of engine powers it.
You may have studied all these math topics during school or universities and may want to freshen it up. However, many of these topics, you may have studied in a different context without understanding why you were learning them. They may not have been taught intuitively or though you may know majority of the topics, you can not correlate them with Machine Learning.
This course of Math For Machine Learning, aims to bridge that gap. We will get you upto speed in the mathematics required for Machine Learning and Data Science. We will go through all the relevant concepts in great detail, derive various formulas and equations intuitively.
This course is divided into following sections,
Algebra Foundations
In this section, we will lay the very foundation of Algebraic Equations including Linear Equations and how to plot them. We will understand what are Exponents, Logs, Polynomial and quadratic equations. Almost all the Machine Learning algorithms use various functions for loss measurement or optimization. We will go through the basics of functions, how to represent them and what are continuous and non-continuous functions.
Calculus
It is said that without calculus and differential equations, Machine Learning would have never been possible. The Gradient Descent using derivatives is essence of minimizing errors for a Machine Learning algorithm. We will understand various terms of Rate of Change, Limits, What is Derivative, including Single, Double and Partial Derivatives. I will also explain with an example, how machine learning algorithms use calculus for optimization.
Linear Algebra
Linear Algebra is the mathematics of the 21st Century. Every record of data is bound by some form of algebraic equation. However, it's nearly impossible for humans to create such an equation from a dataset of thousands of records. That's where the ability of vectors and matrices to crunch those numerical equations and create meaningful insights in the form of linear equations help us. We will see, right from the foundations of Vectors, Vector Arithmetic, Matrices and various arithmetic operations on them. We will also see, how the vectors and matrices together can be used for various data transformations in Machine Learning and Data Science.
Probability
Probability plays an important role during classification type of machine learning problems. It is also the most important technique to understand the statistical distribution of the data. Conditional probability also helps in classification of the dependent variable or prediction of a class.
With all of that covered, you will start getting every mathematical term that is taught in any of the machine learning and data science class.
Mathematics has been my favorite subject since the childhood and you will see my passion in teaching maths as you go through the course.
I firmly believe in what Einstein said, "If you can not explain it simple enough, You have not understood it enough.". I hope I can live upto this statement.
I am super excited to see you inside the class. So hit the ENROLL button and I will see you inside the course.
You will truly enjoy Mathematics For Machine Learning....