At the following link, you can download and read Nicolas Laos’s Lectures on Pure
and Applied Mathematics and Epistemology. This series of Nicolas Laos’s Lectures
covers the following topics: Mathematical Philosophy; Mathematical Logic; the
Structure of Number Sets and the Theory of Real Numbers, Arithmetic and Axiomatic
Number Theory, and Algebra (including the study of Sequences and Series); Matrices
and Applications in Input-Output Analysis and Linear Programming; Probability and
Statistics; Classical Euclidean Geometry, Analytic Geometry, and Trigonometry;
Vectors, Vector Spaces, Normed Vector Spaces, and Metric Spaces; basic principles
of non-Euclidean Geometries and Metric Geometry; Infinitesimal Calculus and basic
Topology (Functions, Limits, Continuity, Topological Structures, Homeomorphisms,
Differentiation, and Integration, including Multivariable Calculus and Vector
Calculus); Complex Numbers and Complex Analysis; basic principles of Ordinary
Differential Equations; as well as mathematical methods and mathematical modeling
in the natural sciences (including physics, engineering, biology, and neuroscience)
and in the social sciences (including economics, management, strategic studies, and
warfare problems).
Every civilized person must have some familiarity with structured, logical, and
mathematical thinking, as well as with epistemology in general. This is necessary to
develop reality awareness and efficient ways of action, which are necessary
underpinnings of the dignity of humanity. The study of interdisciplinary mathematics
and epistemology develops our capacity for logical and rational thinking, and it
enables us to approach problems objectively, to thoroughly evaluate evidence, and to
make rigorous judgments, fostering a methodical and creative approach to decision-
making. This is a rigorous way of defending the dignity of humanity in the era of
advanced modernity.