Quantum computers have the potential to revolutionize how we think about computing. This two-quarter graduate course introduces recent advances in quantum algorithmic techniques for scientific computation. The two quarters are designed to form a sequence, but each may also be taken independently. The first quarter focuses on algorithms based on unitary evolution of pure states, including block encoding, linear combination of unitaries, qubitization, quantum signal processing, quantum singular value transformation, Hamiltonian simulation, quantum algorithms for solving linear systems, differential equations, and query lower bounds. The second quarter extends the discussion to general quantum channels and more statistical aspects of quantum computation, with topics including quantum Markov chains, Lindblad dynamics, mixing time, phase and eigenvalue estimation, and statistical lower bounds. The emphasis throughout is on general algorithmic principles rather than hardware-specific implementation. By the end of the sequence, students will have a solid foundation in modern quantum algorithms for scientific computation and be prepared to read current research and develop new algorithms in their own work. Part b not offered 2026-27.