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Foundations
FOUNDATION
12 units

Mathematical Methods for Quantum Research

A focused mathematical toolkit for quantum research: vector spaces, operators, spectra, complex methods, Fourier analysis, probability, distributions, and functional-analysis habits.

12 units18 hoursFOUNDATION
Open student course

Published syllabus

Course Units

Unit 1
90 min

Mathematical reasoning for quantum models

Admin-authored unit for Mathematical Methods for Quantum Research.

Course notes
3 objectives
Unit 2
90 min

Vectors, bases, and coordinate changes

Admin-authored unit for Mathematical Methods for Quantum Research.

Course notes
3 objectives
Unit 3
90 min

Linear maps, matrices, and adjoints

Admin-authored unit for Mathematical Methods for Quantum Research.

Course notes
3 objectives
Unit 4
90 min

Eigenvalues, spectra, and observables

Admin-authored unit for Mathematical Methods for Quantum Research.

Course notes
3 objectives
Unit 5
90 min

Hilbert spaces and orthonormal expansions

Admin-authored unit for Mathematical Methods for Quantum Research.

Course notes
3 objectives
Unit 6
90 min

Complex functions and analytic structure

Admin-authored unit for Mathematical Methods for Quantum Research.

Course notes
3 objectives
Unit 7
90 min

Contour integrals and residues

Admin-authored unit for Mathematical Methods for Quantum Research.

Course notes
3 objectives
Unit 8
90 min

Fourier series and transforms

Admin-authored unit for Mathematical Methods for Quantum Research.

Course notes
3 objectives
Unit 9
90 min

Green functions and differential operators

Admin-authored unit for Mathematical Methods for Quantum Research.

Course notes
3 objectives
Unit 10
90 min

Probability and stochastic processes

Admin-authored unit for Mathematical Methods for Quantum Research.

Course notes
3 objectives
Unit 11
90 min

Distributions and Dirac delta functions

Admin-authored unit for Mathematical Methods for Quantum Research.

Course notes
3 objectives
Unit 12
90 min

Functional analysis bridge to quantum theory

Admin-authored unit for Mathematical Methods for Quantum Research.

Course notes
3 objectives