The following course in Mathematics is provided in its entirety by Atlantic International University's "Open Access Initiative " which strives to make knowledge and education readily available to those seeking advancement regardless of their socio-economic situation, location or other previously limiting factors. The University's Open Courses are free and do not require any purchase or registration, they are open to the public.
The course in Mathematics contains the following:
The Administrative Staff may be part of a degree program paying up to three college credits. The lessons of the course can be taken on line Through distance learning. The content and access are open to the public according to the "Open Access" and " Open Access " Atlantic International University initiative. Participants who wish to receive credit and / or term certificate , must register as students.
Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects.
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A number is a mathematical object used to count, label, and measure. In mathematics, the definition of number has been extended over the years to include such numbers as 0, negative numbers, rational numbers, irrational numbers, real numbers, and complex numbers.
Mathematical operations are certain procedures that take one or more numbers as input and produce a number as output. Unary operations take a single input number and produce a single output number. For example, the successor operation adds 1 to an integer, and thus the successor of 4 is 5.
Lesson 3: Exponents
Exponentiation is a mathematical operation, written as bn, involving two numbers, the base b and the exponent (or power) n. When n is a positive integer, exponentiation corresponds to repeated multiplication; in other words, a product of n factors, each of which is equal to b (the product itself can also be called power)
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Lesson 4: Logarithms
In mathematics, the logarithm of a number is the exponent to which another fixed value, the base, must be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 10 to the power 3 is 1000: 1000 = 10 × 10 × 10 = 103. More generally, for any two real numbers b and x where b is positive and b ≠ 1,
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Lesson 5: Algebra in Administration
Algebra (from Arabic al-jebr meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form algebra is the study of symbols and the rules for manipulating symbols and is a unifying thread of all of mathematics.As such, it includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields.
Lecture MaterialsLesson 6: Mathematical Functions
In mathematics, a function[1] is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x2. The output of a function f corresponding to an input x is denoted by f(x) (read "f of x"). In this example, if the input is −3, then the output is 9, and we may write f(−3) = 9. The input variable(s) are sometimes referred to as the argument(s) of the function.
Lecture MaterialsLesson 7: MATRICES
Matrices of the same size can be added or subtracted element by element. The rule for matrix multiplication, however, is that two matrices can be multiplied only when the number of columns in the first equals the number of rows in the second. A major application of matrices is to represent linear transformations, that is, generalizations of linear functions such as f(x) = 4x. For example, the rotation of vectors in three dimensional space is a linear transformation which can be represented by a rotation matrix R. If v is a column vector (a matrix with only one column) describing the position of a point in space, the product Rv is a column vector describing the position of that point after a rotation.
Lesson 8: Derivatives
The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function or dependent variable) which is determined by another quantity (the independent variable). It is a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time is advanced. The derivative measures the instantaneous rate of change of the function, as distinct from its average rate of change, and is defined as the limit of the average rate of change in the function as the length of the interval on which the average is computed tends to zero.
Lecture MaterialsLesson 9: Maximum
In mathematics, the maximum and minimum (plural: maxima and minima) of a function, known collectively as extrema (singular: extremum), are the largest and smallest value that the function takes at a point either within a given neighborhood (local or relative extremum) or on the function domain in its entirety (global or absolute extremum). Pierre de Fermat was one of the first mathematicians to propose a general technique (called adequality) for finding maxima and minima.
Lecture MaterialsLesson 10: Indefinite integral
Integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus. The principles of integration were formulated independently by Isaac Newton and Gottfried Leibniz in the late 17th century.
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