This document summarizes a course on mathematics for machine learning. The course covered topics like linear algebra, multivariate calculus, statistics, and optimization algorithms. The linear algebra modules covered vectors, operations on vectors, matrices, matrix multiplication, basis transformations, and eigenvectors/eigenvalues. The calculus modules generalized calculus tools to multivariate systems, covered the chain rule and its applications in neural networks, Taylor series, and optimization methods like gradient descent and Newton-Raphson. The document emphasizes that mathematics is crucial for machine learning as it provides the foundational toolkit and methods for tasks like data fitting, optimization, and modeling complex relationships in data.

1. Mathematics For
Machine Learning
By: Yash Khanna
11702261

2. What Is Machine Learning ?
• Machine learning (ML) is
the scientific
study of algorithms and statistical
models that computer systems use in
order to perform a specific task
effectively without using explicit
instructions, relying on patterns and
inference instead.
• It is all about creating an algorithm
that can learn from the data to make
a prediction.
• Machine learning is built on
mathematical prerequisites.

3. Parts In Mathematics
For Machine Learning:
• Linear algebra: This is a type of mathematics
that is important for projections, vector
spaces and norms in the future.
• Multivariate calculus: Integral calculus and
different calculus can all the parts of this
discipline of mathematics.
• Theory of statistics and probability: Statistics
is very different from ML but the
fundamental values of statistics and
probability machine learning.
• Complex optimizations and algorithms: This
is a type of mathematics that so important
for improving the efficiency of computations.

4. Mathematics For Machine Learning: Linear
Algebra
The course included 5 modules
Module 1:
In the first module we look how linear algebra is relevant to machine
learning then we wind up with module with an initial introduction to vectors.
Key Topic in module: a. Introduction of vectors b. Operation on vectors
Module 2:
In this module, we look at operations we can do with vectors- finding the
angle between the vectors, projections of one vector onto another.
Key Topic in module: a. Modulus and inner product b. Cosine and dot
product c. projection d. Changing basis e. Linear
independency

5. Module 3:
This module was all about matrices as tools to solve the linear algebra problems,
and we also look how to solve the system of linear equations using matrices then
we look towards how to solve the determinants and find the inverse of matrix.
Key topics in the module: a. transformation of matrix b. Derminents and
inverses of matrix
Module4:
In this module, we continue with matrices- how to code matrices and matrix
multiplication using the Einstein summation convention.
Then we look how matrix can transform a description of vector from one basis to
another
Key topics in the module: a. Matrices changing basis b. Orthogonal matrices
c. Gram-Schmidt process

6. Module 5:
This module was all about Eigen vectors that are unrotated by a
transformation matrix, and Eigen values are the amount by which Eigen
vectors are stretched.
These special ‘Eigen things’ are very useful in linear algebra and help us
in examine the Google’s famous PageRank algorithm for presenting
web search results.

7. Mathematics For Machine Learning:
Multivariate Calculus
This course was composed of 6 weeks
In week 1-4 we get familiar with a mathematics toolkit
In week 5-6 we learn how to apply this toolkit to optimization problem
Module 1:
This module was all about calculus as calculus plays very vital role in
understanding the machine learning. We start with very basics what the
function is and we also see when sketching a function on ea graph, the slope
describe the rate of change of output with respect to an input.
Key topic in module: a. Functions b. Rise over run c.Derivative
d. Product and chain rule

8. Module 2:
In this we generalize our calculus tools to handle multivariate systems. This means
we can take a function with multiple inputs and determine the influence separately.
Key topic in module: a. Differentiate with respect to anything b. The Jacobian
c. The sandpit d. The Hessian
Module 3:
In this module our focus was on chain rule and its applications. The multivariate
chain rule can be used to calculate the influence of each parameter of the networks
the real life example of this is neural networks
Key topic in module: a. Chain rule
Module4:
In this we discussed about taylor series. The taylor series is a method for re-
expressing functions as polynomial series. This approach is basically used to write
the complicated functions to simple linear approximations.
Finally we discuss the multivariate case and see how the jacobian and the Hessian
come in to play

9. Module 5:
In this we want to find the minimum and maximum points of a function
then we can use multivariate calculus to do this. First we will do this in
one dimension and use the gradient to give us estimates of where the
zero points of that function are, and then iterate in the Newton-
Raphson method.
Key topic in module: a. Newton-Raphson in one dimension
b. Lagrange multipliers
Module 6:
In order to optimize the fitting parameters , we need a way to define
how good our fit is. The goodness of fit is chi-squared, which we will
first apply to fitting into a straight line-linear regression.
Key topic in module: a. simple linear regression

10. Why Mathematics For
Machine Learning?
• Learning Machine learning brings in better career
opportunities.
• Machine learning jobs on the rise.
• Machine learning is directly linked to data science
• Most exciting domain

13. Thank You