Big missing undergraduate theorems

Linear algebra

• Classification of finite type modules over principal ideal domains, including the case of finite abelian groups
• Frobenius normal form (using the above point), Jordan normal form

Bilinear algebra

• diagonalization of normal endomorphisms This is coming, self-adjoint maps are done in #9995

Group theory

• orthogonality of irreducible characters

Real analysis

• Various forms of Taylor's theorem
• Cauchy-Lipschitz Theorem this is coming in #9791

Complex analysis

• Cauchy formula Yury is working on it
• Analyticity of holomorphic functions
• residue theorem
• zeros and poles of a meromorphic function are isolated

Integration and Fourier theory

• change of variables formula in higher dimensions
• Dirichlet theorem and Fejer theorem for Fourier series
• Fourier inversion theorem, Plancherel’s theorem

Probability theory

• Weak and strong law of large numbers
• Central limit theorem