Math is used colloquially in the English- speaking community of North America as a shortened form of the word "mathematics". However in UK, Australia and New Zealand, the word “maths” is used instead.
Mathematics is derived from Greek word “mathema” which means knowledge, study and learning. The discipline is dedicated to the study of quantity, structure, space and change. Mathematicians seek to observe patterns and formulate new assumptions. Mathematicians resolve the truth or falsity of these assumptions by mathematical proofs and through arguments which are sufficient to convince fellow mathematicians. However mathematical proofs are less formal and painstaking than proofs in mathematical logic, as these researches can take years or even centuries of sustained inquiry.
Through the use of abstraction and logical reasoning, mathematics evolved from counting, calculation, measurement and the systematic study of the shapes and motions of physical objects. Mathematics is used throughout the world as an essential and indispensable tool in many fields including natural science, engineering, medicine and social sciences. Applied mathematics, is concerned with application of mathematical knowledge in other fields which inspires and makes use of new mathematical discoveries and sometimes leads to the development of new mathematical disciplines, such as statistics and game theory.
Benjamin Peirce called mathematics “the science that draws necessary conclusions”. David Hilbert defined mathematics as follows: “We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules. Rather it’s a conceptual system possessing internal necessity that can only be so and by no means otherwise”. Albert Einstein stated that “as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality”.
The study of quantity starts with numbers, natural numbers and integers and arithmetical operations on them, which are characterized in arithmetic. The deeper properties of integers are studied in number theory, from which come popular results as Fermat’s Last Theorem. As the number system is further developed, the integers are recognized as a subset of the rational numbers. Pure math also includes quantity, structure, space, and change.
Applied mathematics is concerned with math methods that are typically used in science, engineering, business and industry, which brings us to a conclusion that applied mathematics, is a mathematical science with specialized knowledge. The term applied mathematics also describes the professional specialization with which mathematicians work on practical problems; as a profession focused on practical problems, applied mathematics focuses on the formulation and study of mathematical models.
|Courses/Topics we help on|
|Discrete Mathematics||Applied Calculus I||Applied Calculus II|
|Healthcare Statistics and Research||Advanced Engineering Mathematics I
||Advanced Engineering Mathematics II|
|Introduction to Algebra||Basic Algebra||Algebra for College Students|
|Algebra for College Students||Pre-Calculus||Statistics for Decision-Making|
|Polar Co-ordinates||Area in Polar Coordinates||Solving Systems of Equations|
|Systems of Inequalities||Quadratic Equations||Matrices and System of Equations|
|The Determinant of a Square Matrix||Cramer's Rule||Ellipse|
|Hyperbola||Rate of Change||Measurement of Speed|
|Finding Limits Graphically||Higher Order Derivatives||Rolle's Theorem and Mean Value Theorem|
|Concavity and Second Derivative Test||Limits at Infinity||Indefinite Integration|
|Definite Integration||Integration by Substitution||Area of a Region Between Two Curves|
|Volume by Shell Method and Disc Method||Integration by Parts||Trigonometric Integration|
|Differential Equations||Slope Fields||Growth and Decay|
|System of Differential Equations||Parametric Equations||Complex Numbers|
|The Inverse of a Square Matrix||Parabola||Functions and Their Graphs|
|Evaluating Limits Analytically||Increasing and Decreasing Functions||Newton's Method|
|Finding Area Using Integration||Numerical Integration||Moments|
|Partial Fractions||Separation of Variables||Second Order Differential Equations|