Practise of Pure Awarenes

This monograph examines the private annotations that Ludwig Wittgenstein made to his copy of G.H. Hardy’s classic textbook, A Course of Pure Mathematics. Complete with actual images of the annotations, it gives readers a more complete picture of Wittgenstein’s remarks on irrational numbers, which have only been published in an excerpted form and, as a result, have often been unjustly criticized.

This book provides a comprehensive account of Kant’s development from the 1755/56 metaphysics to the cosmological antinomy of 1781. With the Theory of the Heavens (1755) and the Physical Monadology (1756), the young Kant had presented an ambitious approach to physical cosmology based on an atomistic theory of matter, which contributed to the foundations of an all-encompassing system of metaphysics.

This scientific biography of the mathematician Joseph Liouville is divided into two parts. The first part is a chronological account of Liouville's career including a description of the institutions he worked in, his relations with his teachers, colleagues and students, and the historical context of his works. It portrays the French scientific community in a period when Germany and England had surpassed France as the leading nations in mathematics and physics.

This book presents an enticing introduction to tropical circuits and their use as a rigorous mathematical model for dynamic programming (DP), which is one of the most fundamental algorithmic paradigms for solving combinatorial, discrete optimization problems.