Calculus is the key to fully understanding how neural networks function. Go beyond a surface understanding of this mathematics discipline with these free course materials from MIT.

Mathematics is undoubtedly the language of machine learning. Statistics is the very foundation upon which machine learning is built. Linear algebra is also a core contributor. However, in order to fully understand neural networks and deep learning, one must have some knowledge of calculus.

Like all things in life, there are varying levels of comprehension of calculus which could be deemed sufficient for differing depths of neural networks understanding. You could, for instance, feel justified in possessing a basic intuition of derivatives and an understanding of how backpropagation works for updating neuron weights based on these operations, should you simply use popular libraries to implement tried and true strategies for non-novel use cases. Translation: you don’t a deep understanding of calculus in order to classify images using ResNet with Keras.

For an example of a simple but effective 30,000 foot explanation of what calculus is, here is the best single page introduction to calculus I have ever come across, a summary which would have saved me a lot of trouble a number of years ago:

Calculus Made Easy 2nd ed, 1914, Chapter 1 (edited by article author to remove non-inclusive language).

It is difficult, perhaps, to link this to neural networks, but the basic intuition of calculus is achieved. If you are looking for a more full treatment of this branch of mathematics, you will want to seek out some more robust learning tools. Here are 3 courses and a textbook to help out, all from MIT’s Open Courseware initiative, which will cover everything you need to know about calculus to understand deep learning — and far beyond.

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