**Math Online Assignment help from Eduexpertsonline**

Numbers (arithmetic and number theory), formulas and associated structures, shapes and the spaces they occupy (geometry), quantities and their transformations, and many other related disciplines all fall under the umbrella of mathematics (calculus and analysis). Most mathematical tasks involve employing one’s logical powers to ascertain or confirm the qualities of abstract things. These concepts might be reduced representations of natural occurrences or, in the context of modern mathematics, items endowed with properties expressed as axioms. Proof in mathematics is a set of deductions from known theorems, assumptions, and (in the case of abstraction from nature) essential properties that are taken to be the actual starting points of the system being explored. A mathematical proof, in other words, is constructed upon a foundation of previous mathematical proofs.

**Math Online Assignment help **

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**Area of Maths**

**Number Theory-**

Number theory began with studying how to manipulate numbers, also called natural numbers, and eventually grew to encompass integers and rational numbers. Historically, arithmetic is related to the study of numbers, but nowadays, “arithmetic” generally refers to numerical calculations.

Many seemingly straightforward arithmetic problems have complicated solutions that may be uncovered using methods from across the field. One famous example is Fermat’s last theorem. Pierre de Fermat first put out this conjecture in 1637, but it wasn’t verified until Andrew Wiles’s work in 1994. Many mathematical techniques, including category theory, homological algebra, and scheme theory from algebraic geometry, helped him do this.

**Geometry**

Geometry is one of mathematics’ oldest and most well-established specializations. Its roots may be traced back to empirical recipes addressing shapes like lines, angles, and circles that were mainly developed to meet the needs of surveying and architectural communities. Still, it has since expanded into several specialized areas.

There were no shifts in methodology or scope in Euclidean geometry during its growth before the 17th century, when René Descartes invented what is now called Cartesian coordinates. Because of this shift, real numbers are no longer defined as the lengths of line segments, and instead, points can be represented by their coordinates. Indeed, this was a significant turning point. This allows the use of algebra to solve geometric problems. As a result, two distinct branches of geometry emerged: synthetic geometry, which uses just geometrical methods, and analytic geometry, which systematically uses coordinates.

Analytical geometry permits the study of curves that are not connected to circles and straight lines. Through the perspective of a function graph, these curves become clear (whose investigation led to differential geometry).

**Algebra**

Algebra relies heavily on the ability to manipulate equations and formulas. Al-Khwarizmi and Diophantus were the two most influential people in the history of algebra. The first one did several equations using unidentified natural numbers, and he solved them by deducing new relations. Specifically, the second one provided systematic methods for modifying equations (such as moving a term from one side of an equation to the other). Algebra derives from the Arabic term al-jabr, which means “the reunion for fragmented parts.” The word “algebra” originated from the title of his first book when he described one of these methods.

Algebra as a distinct science didn’t emerge until Francois Viète (1540-1603) developed the use of letters to denote unknown or undetermined numbers. As a branch of mathematics, algebra is now an established discipline in its own right. For this reason, mathematical equations clearly allow mathematicians to define the required operations on the underlying integers.

**Calculus And Analysis**

Initially called infinitesimal calculus, Calculus was developed independently and simultaneously by two mathematicians working in the 17th century: Newton and Leibniz. Its core focus is on the investigation of interdependencies among various elements. The name “calculus” is currently most commonly used to refer to the rudimentary part of this theory. In contrast, the term “analysis” generally refers to the more advanced features.

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