I recently started refreshing my mathematics with Mathematical Foundations of Quantum Computing: A Scaffolding Approach, by Peter Y. Lee, James M. Yu, and Ran Cheng.
The book was published in 2025 and is specifically designed to build the mathematical background needed for quantum computing. It starts with the basics and gradually moves toward more advanced topics.
What I like about it is that it doesn’t assume that you remember everything from university. It begins with things such as complex numbers, trigonometry and summation, and then moves into vectors, matrices, linear algebra, tensor products, matrix decompositions, Dirac notation and probability.
That makes it a good fit for what I’m trying to do: refresh my math skills while learning mathematics that has a direct connection to quantum computing.
For example, I’m currently going back through things as simple as summation notation and infinite series. These may look basic, but rebuilding that intuition is useful before moving deeper into linear algebra and quantum mechanics.
The book follows what the authors call a “scaffolding approach”, introducing concepts progressively and revisiting them with increasing complexity. It is intended for learners ranging from introductory to more advanced levels.
So, for me, this isn’t really about becoming a mathematician. It’s about rebuilding the mathematical foundations I need to understand how quantum computing works, rather than simply learning how to use quantum programming libraries.
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