Mathematical Foundations of Machine Learning

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 Solve for unknowns with both simple techniques (e.g., elimination) and advanced techniques (e.g., pseudoinversion) Develop an understanding of what's going on beneath the hood of machine learning algorithms, including those used for deep 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. 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.