Mathematics in the Modern World

A set of vocabulary flashcards exploring the diverse applications of mathematics across sciences, social sciences, arts, and technology as detailed in the lecture modules.

Mathematics in Physical Sciences

The field where every rule and principle ultimately takes a mathematical form, giving a final shape to the rules of physics.

Quantum Mechanics (Mathematical Foundations)

An advanced topic in physical chemistry that relies heavily on group theory, linear algebra, and knowledge of topics such as Hilbert spaces and Hamiltonian operators.

Statistical Mechanics

A branch of physical chemistry that relies heavily on probability theory.

Biomathematics

A field involving mathematical neuron-physiology, software development for biological/medical problems, the theory of epidemics, and problems in biomechanics and bioengineering.

Mathematics in Engineering

Considered the foundation of the field, it is used for surveying, levelling, designing, estimating, and increasing the durability of constructions.

Mathematics in Agriculture

A science used for direct applications such as measurement of land area, average investment and expenditure, production per unit area, and seed rate.

Marshall's Economic Discovery

The direct application of mathematical reasoning to the discovery of economic truths which has rendered great services in the hands of master mathematicians.

Herbart's View on Psychology

The belief that it is not only possible but necessary that mathematics be applied to psychology, leading to the use of metrics like intelligence quotient, standard deviation, and correlation coefficient.

Actuary

A professional who uses mathematics and statistics to analyze projects, assess financial risks, model future financial outcomes, and advise organizations on decision-making.

Mathematics in Archaeology

The use of mathematical and statistical techniques to distinguish patterns in archaeological survey data to shed light on past human behavior.

D' Alembert's Definition of Geometry

The view that geometry is a "practical logic" because rules of reasoning are applied in the simplest and most sensible manner.

Leibnitz's Definition of Music

The description of music as a "hidden exercise in arithmetic of a mind unconscious of dealing with numbers."

SAPTSWAR

The musical notes whose rhythm is the result of innumerable permutations and combinations.

Mathematics in Arts

The conceptualization of the universe as being written in the language of mathematics, using characters such as triangles, circles, and other geometric figures.

Mathematics in Philosophy (Herbart's view)

The idea that the office of mathematics is to ward off the dangers of philosophy.

Mathematics in Social Networks

The application of techniques such as graph theory, text analysis, multidimensional scaling, and cluster analysis to analyze social data.

Mathematical Political Science

The use of mathematical models like Game Theory to analyze past election results, switching of votes among parties, and conflict resolution.

Mathematics in Linguistics

The study of structure and transformation, development of machine languages, and the use of information theory and mathematical biology.

Mathematics in Management

The use of mathematical models to discuss management problems regarding hospitals, public health, pollution, and educational planning.

Mathematics in Computers

The foundation of computer science, where most applications of mathematics to science and technology are executed via computer-based formal mathematical theories.