Computations of classical Mahowald invariants at prime 2

We review the definition of Mahowald invariants and discuss the computational method of Mark Brehens introduced in [arXiv:math/0507182]. Then we examine the relationship between the algebraic Mahowald invariants and the $E$-filtered Mahowald invariants, and compute the Mahowald invariants for most elements up to the 26-stem.