Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline.
Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature or—in modern mathematics—entities that are stipulated to have certain properties, called axioms. A proof consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, and—in case of abstraction from nature—some basic properties that are considered true starting points of the theory under consideration.Mathematics is essential in the natural sciences, engineering, medicine, finance, computer science and the social sciences. Although mathematics is extensively used for modeling phenomena, the fundamental truths of mathematics are independent from any scientific experimentation. Some areas of mathematics, such as statistics and game theory, are developed in close correlation with their applications and are often grouped under applied mathematics. Other areas are developed independently from any application (and are therefore called pure mathematics), but often later find practical applications. The problem of integer factorization, for example, which goes back to Euclid in 300 BC, had no practical application before its use in the RSA cryptosystem, now widely used for the security of computer networks.
Historically, the concept of a proof and its associated mathematical rigour first appeared in Greek mathematics, most notably in Euclid's Elements. Since its beginning, mathematics was essentially divided into geometry and arithmetic (the manipulation of natural numbers and fractions), until the 16th and 17th centuries, when algebra and infinitesimal calculus were introduced as new areas. Since then, the interaction between mathematical innovations and scientific discoveries has led to a rapid lockstep increase in the development of both. At the end of the 19th century, the foundational crisis of mathematics led to the systematization of the axiomatic method, which heralded a dramatic increase in the number of mathematical areas and their fields of application. The contemporary Mathematics Subject Classification lists more than 60 first-level areas of mathematics.
Hi all.
I'm looking for some insight from parents/teachers/uni lecturers about predictors that might indicate a student is talented enough to do a Maths degree and excel at it. My little girl is now in year 10 and about to do her GCSEs next year and is trying to figure out what she wants to do...
I am Sorry it's a silly question but its been bothering me, So I needed to ask...
In the process of division, when there is a condition like- 4/5
when the divisor is greater then the dividend.
why is the Remainder 4 ? as when the divisor is greater then the dividend then the division goes in...
Hi all!
I'm a Maths and Physics student at the Open Uni currently (doing a B.Sc.); It's online because of health problems, which prevents me from travelling a lot.
I'd like to study theoretical physics in the future.
My main goal is finishing my B.Sc. (of course) and trying to find a Maths and...
Do not discourage me after reading this but please listen. I always loved maths and physics but i hated Organic chemistry so in order to avoid chemistry i ended up choosing commerce with maths.
Now, I am in 2nd yr of my college doing BBA. My class 11th and 12th was in lockdown so i did not...
I'm a recent bachelor student into physics and I am really struggling with these type of maths. Especially infinite series and its tests, the Integral Test and etc. If it was easy for you, what type of books did you use or methods?
Hello. Thanks for having me. I'm Paul, from the UK. I'm interested in physics, and maths, and science generally, but mainly physics, and within that mainly cosmology. I'm maybe around GCSE level regards maths and physics, roughly high school diploma level in the US, according to Google, although...