Mathematical Foundations of Machine Learning

Essential Linear Algebra and Calculus Hands-On in NumPy, TensorFlow, and PyTorch

Mathematics forms the core of data science and machine learning. Thus, to be the best data scientist you can be, you must have a working understanding of the most relevant math.

What you’ll learn

  • Understand the fundamentals of linear algebra and calculus, critical mathematical subjects underlying all of machine learning and data science.
  • Manipulate tensors using all three of the most important Python tensor libraries: NumPy, TensorFlow, and PyTorch.
  • How to apply all of the essential vector and matrix operations for machine learning and data science.
  • Reduce the dimensionality of complex data to the most informative elements with eigenvectors, SVD, and PCA.
  • Solve for unknowns with both simple techniques (e.g., elimination) and advanced techniques (e.g., pseudoinversion).
  • Appreciate how calculus works, from first principles, via interactive code demos in Python.
  • Intimately understand advanced differentiation rules like the chain rule.
  • Compute the partial derivatives of machine-learning cost functions by hand as well as with TensorFlow and PyTorch.
  • Grasp exactly what gradients are and appreciate why they are essential for enabling ML via gradient descent.
  • Use integral calculus to determine the area under any given curve.
  • Be able to more intimately grasp the details of cutting-edge machine learning papers.
  • Develop an understanding of what’s going on beneath the hood of machine learning algorithms, including those used for deep learning.

Course Content

  • Data Structures for Linear Algebra –> 12 lectures • 1hr 44min.
  • Tensor Operations –> 9 lectures • 55min.
  • Matrix Properties –> 9 lectures • 1hr 24min.
  • Eigenvectors and Eigenvalues –> 10 lectures • 2hr 12min.
  • Matrix Operations for Machine Learning –> 8 lectures • 1hr 15min.
  • Limits –> 8 lectures • 1hr 8min.
  • Derivatives and Differentiation –> 14 lectures • 1hr 26min.
  • Automatic Differentiation –> 6 lectures • 1hr 17min.
  • Partial Derivative Calculus –> 16 lectures • 3hr 10min.
  • Integral Calculus –> 13 lectures • 1hr 3min.

Mathematical Foundations of Machine Learning


  • All code demos will be in Python so experience with it or another object-oriented programming language would be helpful for following along with the hands-on examples..
  • Familiarity with secondary school-level mathematics will make the class easier to follow along with. If you are comfortable dealing with quantitative information — such as understanding charts and rearranging simple equations — then you should be well-prepared to follow along with all of the mathematics..

Mathematics forms the core of data science and machine learning. Thus, to be the best data scientist you can be, you must have a working understanding of the most relevant math.

Getting started in data science is easy thanks to high-level libraries like Scikit-learn and Keras. But understanding the math behind the algorithms in these libraries opens an infinite number of possibilities up to you. From identifying modeling issues to inventing new and more powerful solutions, understanding the math behind it all can dramatically increasing the impact you can make over the course of your career.

Led by deep learning guru Dr. Jon Krohn, this course provides a firm grasp of the mathematics — namely the linear algebra and calculus — that underlies machine learning algorithms and data science models.


Course Sections

  1. Linear Algebra Data Structures
  2. Tensor Operations
  3. Matrix Properties
  4. Eigenvectors and Eigenvalues
  5. Matrix Operations for Machine Learning
  6. Limits
  7. Derivatives and Differentiation
  8. Automatic Differentiation
  9. Partial-Derivative Calculus
  10. Integral Calculus

Throughout each of the sections, you’ll find plenty of hands-on assignments, Python code demos, and practical exercises to get your math game in top form!

This Mathematical Foundations of Machine Learning course is complete, but in the future we intend on adding bonus content from related subjects beyond math, namely: probability, statistics, data structures, algorithms, and optimization. Enrollment now includes free, unlimited access to all of this future course content — over 25 hours in total.


Are you ready to become an outstanding data scientist? See you in the classroom.