CF

Mathematical Foundations of Machine Learning

16h 25m 26s
English
Paid

Mathematics forms the core of data science and machine learning. To excel as a data scientist, it's crucial to have a deep understanding of the most relevant mathematical concepts. While high-level libraries like Scikit-learn and Keras make it easy to start, comprehending the mathematics behind these algorithms can unlock endless possibilities.

Understanding the underlying math can help you identify modeling issues and create innovative and more powerful solutions, significantly enhancing your career impact. This course, led by deep learning expert Dr. Jon Krohn, provides a comprehensive understanding of the essential mathematics—including linear algebra and calculus—that supports machine learning algorithms and data science models.

Course Sections

  1. Linear Algebra Data Structures: Explore the fundamental structures that form the basis of linear algebra in data science.

  2. Tensor Operations: Delve into operations on tensors, which are generalizations of vectors and matrices.

  3. Matrix Properties: Understand the essential properties of matrices and how they apply to data models.

  4. Eigenvectors and Eigenvalues: Learn how these concepts are vital for dimensionality reduction and stability investigations.

  5. Matrix Operations for Machine Learning: Discover how to apply matrix operations specifically in the context of machine learning.

  6. Limits: Grasp the concept of limits, fundamental to understanding calculus.

  7. Derivatives and Differentiation: Master the art of differentiation and learn how derivatives play a pivotal role in optimization algorithms.

  8. Automatic Differentiation: Familiarize yourself with tools and techniques that streamline the differentiation process.

  9. Partial-Derivative Calculus: Explore the nuances of partial derivatives, especially in functions of multiple variables.

  10. Integral Calculus: Learn integral calculus and its applications in calculating areas, volumes, and solving differential equations.

Each section features hands-on assignments, Python code demos, and practical exercises designed to enhance your mathematical skills and apply them effectively in data science and machine learning projects.

About the Author: Udemy

Udemy thumbnail

Udemy is the largest open marketplace for online courses on the internet. Founded in 2010 by Eren Bali, Oktay Caglar, and Gagan Biyani and headquartered in San Francisco, the company went public on the Nasdaq in 2021 under the ticker UDMY. The platform hosts well over two hundred thousand courses across software development, IT and cloud, data science, design, business, marketing, and creative skills, taught by tens of thousands of independent instructors. Roughly seventy million learners use it worldwide, and the corporate arm — Udemy Business — supplies a curated subset of that catalog to enterprise customers.

Because Udemy is a marketplace rather than a single editorial publisher, the catalog is uneven by design. The strongest material lives in the long-form, project-based courses authored by working engineers — full-stack JavaScript, React, Node.js, Python data science, AWS, Docker and Kubernetes, mobile development with Flutter and React Native, and cloud certification preparation. The CourseFlix listing under this source is the slice of that catalog that has been mirrored here for offline-friendly viewing, organized by topic and updated as new releases land. Pricing on Udemy itself swings dramatically with the site's near-permanent sales, which is why the platform is best treated as a deep reference catalog: pick instructors with strong reviews and a track record of updating their material rather than buying on the headline price alone.

Watch Online 112 lessons

This is a demo lesson (10:00 remaining)

You can watch up to 10 minutes for free. Subscribe to unlock all 112 lessons in this course and access 10,000+ hours of premium content across all courses.

View Pricing
0:00
/
#1: What Linear Algebra Is
All Course Lessons (112)
#Lesson TitleDurationAccess
1
What Linear Algebra Is Demo
23:30
2
Plotting a System of Linear Equations
09:19
3
Linear Algebra Exercise
05:07
4
Tensors
02:34
5
Scalars
13:05
6
Vectors and Vector Transposition
12:20
7
Norms and Unit Vectors
14:38
8
Basis, Orthogonal, and Orthonormal Vectors
04:31
9
Matrix Tensors
08:24
10
Generic Tensor Notation
06:44
11
Exercises on Algebra Data Structures
02:08
12
Segment Intro
01:20
13
Tensor Transposition
03:53
14
Basic Tensor Arithmetic, incl. the Hadamard Product
06:13
15
Tensor Reduction
03:32
16
The Dot Product
05:14
17
Exercises on Tensor Operations
02:39
18
Solving Linear Systems with Substitution
09:48
19
Solving Linear Systems with Elimination
11:48
20
Visualizing Linear Systems
11:00
21
Segment Intro
02:06
22
The Frobenius Norm
05:02
23
Matrix Multiplication
24:29
24
Symmetric and Identity Matrices
04:42
25
Matrix Multiplication Exercises
07:22
26
Matrix Inversion
17:07
27
Diagonal Matrices
03:26
28
Orthogonal Matrices
05:17
29
Orthogonal Matrix Exercises
15:00
30
Segment Intro
17:53
31
Applying Matrices
07:32
32
Affine Transformations
18:21
33
Eigenvectors and Eigenvalues
26:14
34
Matrix Determinants
08:05
35
Determinants of Larger Matrices
08:42
36
Determinant Exercises
04:42
37
Determinants and Eigenvalues
15:44
38
Eigendecomposition
12:16
39
Eigenvector and Eigenvalue Applications
12:30
40
Segment Intro
03:22
41
Singular Value Decomposition
10:50
42
Data Compression with SVD
11:00
43
The Moore-Penrose Pseudoinverse
12:24
44
Regression with the Pseudoinverse
18:25
45
The Trace Operator
04:37
46
Principal Component Analysis (PCA)
08:28
47
Resources for Further Study of Linear Algebra
05:38
48
Segment Intro
03:40
49
Intro to Differential Calculus
13:26
50
Intro to Integral Calculus
02:25
51
The Method of Exhaustion
06:46
52
Calculus of the Infinitesimals
09:34
53
Calculus Applications
08:36
54
Calculating Limits
17:50
55
Exercises on Limits
06:07
56
Segment Intro
01:17
57
The Delta Method
15:47
58
How Derivatives Arise from Limits
13:53
59
Derivative Notation
04:20
60
The Derivative of a Constant
01:30
61
The Power Rule
01:17
62
The Constant Multiple Rule
03:11
63
The Sum Rule
02:27
64
Exercises on Derivative Rules
11:09
65
The Product Rule
03:51
66
The Quotient Rule
04:05
67
The Chain Rule
06:46
68
Advanced Exercises on Derivative Rules
11:49
69
The Power Rule on a Function Chain
04:38
70
Segment Intro
01:50
71
What Automatic Differentiation Is
04:43
72
Autodiff with PyTorch
06:18
73
Autodiff with TensorFlow
03:53
74
The Line Equation as a Tensor Graph
19:42
75
Machine Learning with Autodiff
40:12
76
Segment Intro
22:39
77
What Partial Derivatives Are
29:23
78
Partial Derivative Exercises
06:16
79
Calculating Partial Derivatives with Autodiff
05:19
80
Advanced Partial Derivatives
14:40
81
Advanced Partial-Derivative Exercises
06:12
82
Partial Derivative Notation
02:28
83
The Chain Rule for Partial Derivatives
09:18
84
Exercises on the Multivariate Chain Rule
05:19
85
Point-by-Point Regression
15:25
86
The Gradient of Quadratic Cost
15:17
87
Descending the Gradient of Cost
12:53
88
The Gradient of Mean Squared Error
24:22
89
Backpropagation
06:00
90
Higher-Order Partial Derivatives
11:54
91
Exercise on Higher-Order Partial Derivatives
02:56
92
Segment Intro
02:45
93
Binary Classification
09:14
94
The Confusion Matrix
02:30
95
The Receiver-Operating Characteristic (ROC) Curve
09:43
96
What Integral Calculus Is
06:15
97
The Integral Calculus Rules
05:38
98
Indefinite Integral Exercises
02:59
99
Definite Integrals
06:48
100
Numeric Integration with Python
04:52
101
Definite Integral Exercise
04:25
102
Finding the Area Under the ROC Curve
03:36
103
Resources for the Further Study of Calculus
04:02
104
Congratulations!
01:56
105
Probability & Information Theory
07:40
106
A Brief History of Probability Theory
03:37
107
What Probability Theory Is
05:16
108
Events and Sample Spaces
08:36
109
Multiple Independent Observations
08:03
110
Combinatorics
06:48
111
Exercises on Event Probabilities
09:57
112
More Lectures are on their Way!
00:22
Unlock unlimited learning

Get instant access to all 111 lessons in this course, plus thousands of other premium courses. One subscription, unlimited knowledge.

Learn more about subscription

Related courses

Frequently asked questions

What prerequisites are needed for this course?
A basic understanding of high school level algebra and calculus will be helpful for taking this course. Familiarity with vectors, matrices, and basic calculus concepts will allow you to engage more deeply with the material, especially since the course covers linear algebra and calculus in depth.
What projects or exercises will I work on in the course?
The course includes various exercises such as plotting a system of linear equations, solving linear systems with substitution and elimination, and working on matrix multiplication exercises. You'll also engage in exercises on algebra data structures, tensor operations, and limits, which are designed to reinforce the mathematical concepts taught.
Who is the target audience for this course?
This course is ideal for data science professionals or students who want to deepen their understanding of the mathematical foundations of machine learning. It is also suitable for software engineers and researchers who work with machine learning algorithms and wish to comprehend the underlying mathematical principles.
How does this course compare in scope to other machine learning courses?
Unlike many machine learning courses that focus primarily on programming and algorithm implementation, this course provides a comprehensive understanding of the mathematical concepts behind machine learning. It covers essential topics such as linear algebra, tensor operations, and calculus, which are crucial for developing more robust and innovative machine learning models.
What specific mathematical tools or platforms will I learn to use?
The course focuses on mathematical concepts rather than specific software tools. You will learn to work with linear algebra structures like matrices and tensors and perform operations such as matrix inversion, eigendecomposition, and singular value decomposition. These concepts are applicable across various machine learning frameworks.
What is not covered in this course?
The course does not cover programming languages or specific machine learning libraries like Scikit-learn or Keras in detail. It focuses on the mathematical foundations rather than coding implementations or software development practices.
How much time should I expect to commit to this course?
The course consists of 112 lessons, and while the exact runtime is not specified, students should anticipate spending several hours each week to fully grasp the material, complete exercises, and review concepts. The time commitment will vary depending on your prior knowledge and study habits.