Courtesy : Bachelor of Science Mathematics- PCM (Physics, Chemistry, Mathematics) Placement

Specific sciences

Mathematics has a special relationship with all sciences, broadly speaking. Data analysis (interpreting graphs, statistical data…) uses a variety of mathematical skills. More advanced mathematical tools appear in modeling.

All hard sciences, except for mathematics itself, deal with the real world. This understanding occurs by use of a model, which has a certain number of parameters considered as causes of a phenomenon. This model is a mathematical object. As such, it can be studied to better understand the studied phenomenon and eventually make a qualitative or quantitative phenomenon about its future evolution. # ISO certification in India

Modeling calls on skills that essentially come from analysis and probability, but algebraic or geometric methods are also used.

Physics

Diagram of a pendulum

Mathematics was born of the desire to comprehend ambient space: geometry from modeling idealized forms, and arithmetic from the need to manage quantities. Astronomy and geometry have long been confused with each other, even until Islamic civilization. Mathematics and physics, after having split from each other, have kept close links. The two subjects have influenced each other over their modern history. Modern physics abundantly uses mathematics and makes systematic models to understand the results of its experiments:

• Modeling can use already-developed mathematical tools. For example, metrics in differential geometry, developed by mathematician Minkowski and then by physicist Einstein, is an essential tool on which general relativity notably rests. It is also used in other post-Newtonian theories.
• Modeling encourages mathematicians to become more interested in mathematical structures for the needs of physics.
• However, modeling sometimes demands mathematical tools not yet developed and creates new mathematical perspectives. For example, Isaac Newton developed differential calculus to write the classical laws of movement. Interested in heat diffusion, Joseph Fourier discovered the series bearing his name, creating Fourier theory.  More recently, there are problems of quantifying geometry, Feynman integrals, Donaldson polynomials, and so on. # ISO certification in India

A specific field of research, mathematical physics, precisely tends to develop mathematical methods made for usage in physics.

The close link between mathematics and physics is reflected in higher education in mathematics. Physics education calls on courses of mathematics for physics. Also, it is not rare for university mathematics courses to include an optional initiation to physics.

However, Albert Einstein was one of the first to relativize the domain of mathematics in noting that physics uses it in many forms, according to its needs, and not just one. His theory of general relativity uses, for example, non-Euclidean geometry, formalized by Minkowski. He once said: “As it relates to reality, Euclidean geometry is not exact. As it is exact, it does not relate to reality.” Yvonne Choquet-Bruhat was the first to bring in 1952 mathematical proofs to the existence of solutions to the Einstein equation.# ISO certification in India

Computing

The rise of technology in the 20th century opened the way to a new science: computing. This field is closely related to mathematics in several ways. Research in theoretical computer science is essentially mathematical in nature, and other branches of computer science often use mathematics. New communication technologies have opened the way to applying branches of mathematics that may be very old (e.g., arithmetic), notably with respect to transmission security: cryptography and coding theory.

In return, computer science influences the modern evolution of mathematics.

Discrete mathematics is an area of mathematical research that develops techniques used in computer science. This includes complexity theory, information theory, graph theory, and so on. Among open problems, there is the famous P vs. NP in complexity theory, which is part of the seven Millennium Prize Problems. The one to decide whether P and NP are different or equal would receive a prize of US$1,000,000.

Computing has also become essential for obtaining new results (a group of techniques known as experimental mathematics). The most well-known example is the Four Color Theorem, which was proven in 1976 with the help of a computer. This revolutionized traditional mathematics, where the rule was that the mathematician should verify each part of the proof. In 1998, the Kepler conjecture seemed to also be partially proven by computer. An international team had since worked on writing a formal proof; it was finished (and verified) in 2015. # ISO certification in India

If a proof is written formally, it becomes possible to verify it using a program called a proof assistant. This is the best-known technique for being (almost) certain that a computer-assisted proof does not suffer from a bug. In the space of thirty years, the relationship between mathematicians and computer science had reversed. Although they were initially viewed as suspect instrument to avoid at all costs, computers have now become an indispensable tool.