Finding Math Courses Online

The Internet has revolutionized almost every aspect of our lives and made education easily accessible online. There are different types of online courses available that vary from under-graduate to post-graduate but that is not all. Mathematics is one such subject that has moved from traditional classroom to online. Finding online maths courses is quite easy these days especially because of the many universities and private institutions offering the same.
One of the biggest advantages of choosing an online maths course is the convenience. Let's take a look at some of the institutions offering online maths courses:

Massachusetts Institute of Technology (mit.edu)

MIT, one of the most prestigious educational institutions of the world offers:

o Algebra I Course
o Introductory Geometry Course
o Probability and Statistics Course

Apart from the above courses, MIT also has almost 100 free online math courses made available to everyone and anyone through their innovative OpenCourseWare project. Under the OpenCourseWare project, you will get to study using slides, lectures, assignments, problem sets, and various other resources that will mainly assist self-study. Above all, you don't need to register for these courses.

University of Massachusetts, Boston (umb.edu)

Another great education institution, UMB offers three main online maths courses:

o Calculus I
o Calculus II

UMB offers 3 free online calculus courses that are bundled with comprehensive instructions. You can download them from their website and it will include suggested problems, multiple lessons, reading assignments and other resources. Above all, you don't need to register for these courses.

College of Eastern Utah (usu.edu)

You can get two standard online maths courses:

o Intermediate Algebra Course
o Quantitative Reasoning Course

The College of Eastern Utah's Mathematics Department has opened its doors to provide access to anyone who is interested in their two different math courses and these can be downloaded for free. You need to have RealPlayer for the Quantitative Reading Course and above all, you don't need to register for these courses.

Dixie State College of Utah (usu.edu)

This Utah College offers two online calculus courses, which are:

o Calculus I Course
o Calculus II Course

Dixie State College of Utah had recently started a pilot program, which provides free downloads of two excellent online math tutorials or courses. The course material includes exams, notes, and various important subject related resources. You don't need to register for any of these courses.

Carnegie Mellon University (cmu.edu)

One of the top universities in the US, Carnegie Melon offers a single online maths course called:

o Statistics Course

The free Statistics Course is available for download and study through Carnegie Mellon's Open Learning Initiative and can be compared to their full semester course that is currently being taught on their University campus. The course material will include virtual simulations, tests, text, interactive learning exercises, and other resources.

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Math Exams

When do you start preparing for school entrance exams? Structured preparation for one year before the exams is a good idea. Carefully paced preparation over a 12 month period should be sufficient, without running the risk of your child becoming bored or 'over prepared'.
Opinions vary on whether children should be intensively coached to maximise their performance in entrance exams. Some favour the view that the selection process should be based on 'natural ability', and others believe that every available resource should be applied to ensure an offer from a first choice school. The majority of parents' opinions fall somewhere between the two extremes, feeling that at least some degree of preparation is both appropriate and beneficial for their children, in the period leading up to entrance exams. At the end of the day, everyone should make an informed decision about what is right for their child, and their particular circumstances.
Children who are already in the independent school sector will more than likely receive suitable preparation at school.
Find out the format of the exams for the particular school you are applying to
Obtain specimen papers or past papers from the school, if they are available
Otherwise, obtain suitable practice papers and/or workbooks for your child to work through
Ensure your child is familiar with the vocabulary used in the specimen papers, past papers and practice papers
Make sure that your child practices with a wide variety of question types
Make sure your child understands the difference between short questions where only an answer is needed, and long questions where makes are awarded for method and workings, not just a final answer
Discuss timing with your child. If a paper is one hour in length and there is a maximum of 100 marks available, that means about 36 seconds per mark as a rough guide
Encourage your child to take extra care with spelling and punctuation
Word games, puzzles and logic problems can be a fun way to practice logical thinking and broaden vocabulary
Mental arithmetic skills are extremely useful. Children should know tables up to 12 reliably, and be able to add and subtract at least 3 digit numbers quickly and accurately.
Whatever style of preparation you opt for, the key to making the exams and the selection process less stressful is for both you and your child to know what to expect. Get as much information from the school as you can, in plenty of time. Many independent schools now require applicants to register and pay an administration fee at least one year before planned entry. The school will normally provide quite a detailed description of how an assessment day or exam day is structured. Claudine M Smith is a Maths tutor with over 12 years experience of tutoring children for common entrance and independent school entrance exams, as well as KS2 SAT, GCSE, IGCSE and A Levels. For more information and advice about preparing for entrance exams and Maths tuition you can visit http://witneymathstutors.co.uk

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Quadratic equations Exam

In mathematics, a quadratic equation is a polynomial equation of the second degree.

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The constants a, b, and c, are called respectively, the quadratic coefficient, the linear coefficient and the constant term or free term. The term "quadratic" comes from quadratus, which is the Latin word for "square". Quadratic equations can be solved by factoring, completing the square, graphing, Newton's method, and using the quadratic formula (given below).
One common use of quadratic equations is computing trajectories in projectile motion. Another common use is in electronic amplifier design for control of step response and stability.
Quadratic formula
A quadratic equation with real or complex coefficients has two solutions, called roots.

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Quadratic functions Exam

A quadratic function, in mathematics, is a polynomial function. The graph of a quadratic function is a parabola whose axis of symmetry is parallel to the y-axis.
The expression ax2 + bx + c in the definition of a quadratic function is a polynomial of degree 2 or second order, or a 2nd degree polynomial, because the highest exponent of x is 2.
If the quadratic function is set equal to zero, then the result is a quadratic equation. The solutions to the equation are called the roots of the equation.

Origin of word

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The adjective quadratic comes from the Latin word quadratum for square. A term like x2 is called a square in algebra because it is the area of a square with side x.
In general, a prefix quadr(i)- indicates the number 4. Examples are quadrilateral and quadrant. Quadratum is the Latin word for square because a square has four sides.

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Sequences and series Exam

In mathematics, a sequence is an ordered list of objects (or events). Like a set, it contains members (also called elements or terms), and the number of terms (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. A sequence is a discrete function.

For example, (C, R, Y) is a sequence of letters that differs from (Y, C, R), as the ordering matters. Sequences can be finite, as in this example, or infinite, such as the sequence of all even positive integers (2, 4, 6,...). Finite sequences are sometimes known as strings or words and infinite sequences as streams. The empty sequence ( ) is included in most notions of sequence, but may be excluded depending on the context.

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A series is the sum of the terms of a sequence. Finite sequences and series have defined first and last terms, whereas infinite sequences and series continue indefinitely.

In mathematics, given an infinite sequence of numbers { an }, a series is informally the result of adding all those terms together: a1 + a2 + a3 + · · ·. These can be written more compactly using the summation symbol ∑. An example is the famous series from Zeno's dichotomy

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Logarithms Exam

The logarithm of a product of two numbers equals the sum of their logarithms:

This equation forms the basis for multiplying two numbers on a slide rule or using a logarithm table. Since adding is generally easier than multiplying, this led to the rapid adoption of logarithms for calculations after their invention by John Napier in the early 17th century. For such computational purposes, the logarithm to base b = 10 (common logarithm) was primarily used. The natural logarithm uses the constant e (approximately 2.718) as its base, and is especially widespread in calculus. The binary logarithm uses base b = 2 and primarily aids computing applications.

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Logarithmic scales reduce wide-ranging quantities to smaller scopes. For example, the Richter scale uses the common logarithm to measure the amplitude of seismic events. Logarithms are commonplace in scientific formulas, measure the complexity of algorithms and of fractals, and appear in formulas counting prime numbers. They describe musical intervals, inform some models in psychophysics and can aid in forensic accounting.
The complex logarithm is the inverse of the exponential function applied to complex numbers and generalizes the logarithm to complex numbers. The discrete logarithm is another variant; it has applications in public-key cryptography.

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Three-dimensional Exam

Three-dimensional space is a geometric model of the physical universe in which we live. The three dimensions are commonly called length, width, and depth (or height), although any three directions can be chosen, provided that they do not lie in the same plane.
In physics, our three-dimensional space is viewed as embedded in 4-dimensional space-time, called Minkowski space (see special relativity). The idea behind space-time is that time is hyperbolic-orthogonal to each of the three spatial dimensions.
In mathematics, analytic geometry (also called Cartesian geometry) describes every point in three-dimensional space by means of three coordinates. Three coordinate axes are given, usually each perpendicular to the other two at the origin, the point at which they cross. They are usually labeled x, y, and z. Relative to these axes, the position of any point in three-dimensional space is given by an ordered triple of real numbers, each number giving the distance of that point from the origin measured along the given axis, which is equal to the distance of that point from the plane determined by the other two axes.
Other popular methods of describing the location of a point in three-dimensional space include cylindrical coordinates and spherical coordinates, though there are an infinite number of possible methods.

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Another mathematical way of viewing three-dimensional space is found in linear algebra, where the idea of independence is crucial. Space has three dimensions because the length of a box is independent of its width or breadth. In the technical language of linear algebra, space is three dimensional because every point in space can be described by a linear combination of three independent vectors. In this view, space-time is four dimensional because the location of a point in time is independent of its location in space.
Three-dimensional space has a number of properties that distinguish it from spaces of other dimension numbers. For example, at least 3 dimensions are required to tie a knot in a piece of string. The understanding of three-dimensional space in humans is thought to be learned during infancy using unconscious inference, and is closely related to hand-eye coordination. The visual ability to perceive the world in three dimensions is called depth perception.
In mathematics, a relation is used to describe certain properties of things. That way, certain things may be connected in some way; this is called a relation. Formally, a relation is a set of n-tuples of equal degree. Thus a binary relation is a set of pairs, a ternary relation a set of 3-tuples, and so forth. A ternary relation however is always expressable as two binary relations. Specifically in the context of functions, this is known as currying.
Particularly concerning binary relations, the set of all the starting point is called the domain and the sets of the ending points is the range. The domain is the x's , and the range is the y's.
An example for such a relation might be a function. Functions associate keys with values. The set of all functions is a subset of the set of all relations - a function is a relation where the first value of every tuple is unique through the set.
Other well-known relations are the Equivalence relation and the Order relation. That way, sets of things can be ordered: Take the first element of a set, it is either equal to the element looked for, or there is an order relation that can be used to classify it. That way, the whole set can be classified (compared to some arbitrarily chosen element).
Relations can be transitive. One example of a transitive relation is "smaller-than". If X "is smaller than" Y, and Y is "smaller than" Z, then X "is smaller than" Z
Relations can be symmetric. One example of a symmetric relation is "is equal to".
Relations can be reflexive.
A reflexive relation is "smaller than or equal".

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Derivative Exam

In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's instantaneous velocity. Conversely, the integral of the object's velocity over time is how much the object's position changes from the time when the integral begins to the time when the integral ends.

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The derivative of a function at a chosen input value describes the best linear approximation of the function near that input value. For a real-valued function of a single real variable, the derivative at a point equals the slope of the tangent line to the graph of the function at that point. In higher dimensions, the derivative of a function at a point is a linear transformation called the linearization.The process of finding a derivative is called differentiation. The reverse process is called antidifferentiation. The fundamental theorem of calculus states that antidifferentiation is the same as integration. Differentiation and integration constitute the two fundamental operations in single-variable calculus.

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