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Between Mathematics and Mathematics Education: Examples from Two Courses for Prospective Mathematics Teachers
Matrix factorizations
Complex numbers and geometry
Block-matrix
Linear operaters on inner product spaces
Learning through exploration and storytelling
Spectrum of matrices
Laplace transform
Eigenvalues and eigenvectors
Linear algebra
Techniques in solving mathematical problems
Pascal's triangle
Determinants
Some strategies for solving mathematical problems
Functional equations in mathematics teaching
Geometric interpretation of complex functions
Totally positive matrices
The Hamilton-Cayley theorem for matrices of order 2
Tight frames
Finite Parseval frames
Some complex analysis and the fundamental theorem of algebra
Fundamental theorem of algebra
The Basel problem
Frames for finite-dimensional Hilbert spaces
Two tasks on the shortest path
Sequences and series of functions
Functional equations associated with certain mean value theorems
Some applications of linear algebra
Some generalizations of Lagrange's mean value theorem
Some generalizations of Rolle's theorem and Lagrange's mean value theorem
Mathematics 3
Some applications of Rolle's theorem and Lagrange's mean value theorem
The length of a path consisting of n line segments
Maps preserving rank-one matrices
Finite frames in Hilbert spaces
Hilbert C*-modules
Various proofs of the Cauchy-Schwarz-Bunjakovski inequality
Leslie matrix model of population growth
Linear functionals, bilinear and quadratic forms
Cauchy–Schwarz–Bunyakovsky inequality
Mathematics 4
Convex functions
p-norms on R^2, S_p circles and pi_p numbers
On continuous functions
Sequence spaces
Compact operators
ℓᵖ spaces
Continued fractions
Counterexamples in mathematical analysis
Banach and Hilbert spaces
Bounded linear operators on normed spaces
Representations and frames for Hilbert C*-modules
AF-algebras
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