mathematics [plural n., usually treated as singular]

the branch of science concerned with number, quantity, and space, either as abstract ideas [pure mathematics] or as applied to physics, engineering, and other subjects [applied mathematics].
- ORIGIN from Greek mathema ‘science’, from manthanein ‘learn’.

Oxford Dictionaries

Mathematics is one of the core learning areas in all primary and secondary schools along with language. While it can be studied as an individual subject, it is also found in most others through the use of its numbering and measurement systems. It is especially used in Science subjects.

There are multiple pages that can be accessed using either the page number boxes above or the links that follow.

This page looks at Mathematics - Algebra, Calculus, Fractions, Geometry, Problem Solving, Real Life Mathematics and other special areas.

The Second Page looks at Mathematicians, the History of Mathematics, different Mathematical Systems and general information.

Mathematics Dictionaries, Glossaries and Ask an Expert topics can now be found on these pages.

Other pages linked to this area include Mathematics Resources while information on several Tertiary Subject Pages may also be of value [Mathematics, Statistics].

Core Areas

Algebra

• Algebra Story and Word Problems
  Problems based on concepts, linked to varying levels of schooling. Interactive.
• Free Algebra Tutorials
  ‘If you have problems solving equations, simplifying expressions, working with fractions, radicals, polynomials, you have come to the right place ! We have lots of tutorials on all aspects of basic algebra - just click on the topic to display the tutorial. Free of charge’.
• KryssTal : Pascal’s Triangle
  Calculations and Algebra using a simple calculator. ‘By simple calculator I mean one that does the basics [+, -, x and ÷]. When you finish, you should be able to calculate quite difficult roots with this calculator’.
• MathDork
  Introduction to algebra. Uses interactive resources.
• The Art of Algebra
  History of algebra ‘from Al-Khwarizmi to Viète’.

Calculus

• Aid for Calculus Index
  ‘Typical Calculus topics, links to sample problems’.
• Karl’s Calculus Tutor
• Mathematics Animated
  An extensive collection of animations demonstrating various aspects. Requires Quicktime to view.
• Mathematics Online Tutorials
  Tutorials for Pre-Calculus, Single Variable Calculus, Multi-Variable Calculus.

Polynomials

A polynomial is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.

• About Polynomials
  ‘Introduces polynomial functions, shows you how to draw graphs of polynomials, as well as find zeros and turning points’.
• Factoring Polynomials
  Video on the topic from Google Video. Part of the Algebra in Simplest Terms series.
• Polynomial
  Forms, functions & equations, elementary properties, advanced examples, history, solving, polynomials & calculus, abstract algebra, classifications, extensions of the concept, links including to calculators for this area. From Wikipedia.
• Polynomials
  Multiple videos covering aspects of this topic.
• Polynomials : Definitions/Evaluation
  Text and formulae presentation.
• Polynomial [Wolfram Mathworld]
  Information, examples, links to further information. Geared to tertiary area.
• Polynomial Worksheets
  Collection covering polynomials and polynomial functions.

Textbooks

• Calculus
  Online text by Gilbert Strang. MIT Open Courseware. Has both an Instructor’s manual and a student Study Guide.
• Visit the Textbooks page for a listing of this and other area’s textbooks available for Free, online or in downloadable format.

• The Calculus Page
  Annotated links for students and instructors. Tutorials, problems, examination samples, animations, tools & software, history, more.
• Tutorials for the Calculus Phobe
  ‘The tutorials explain calculus audio-visually, and are the equivalent of a personal tutoring session. More than just boring lectures, the topics come alive with Flash animation. To view a lesson, simply click on its name’.

Decimals

Plus related fractions.

• Decimal Fast Facts
  Simple text/diagrammatic presentation for handling decimals.
• Decimals
  11 sets of lessons covering all areas from Naming Decimals to Dividing Decimals, Place Values to Equivalent Fractions & Decimals. Very simple, easy presentation.
• Decimals, Whole Numbers, Exponents
  Similar to the other sites but considerably more detail. From Decimal numbers to square roots.
• Kids Online Resources
  Annotated links. Fractions, decimals, percentages. Several of the sites are listed here.

Famous Curves

• Famous Curves Applet Index
  Choose from the applet listing to explore curves.
• Famous Curves Index
  ‘Click on the name of a curve for its history and some of its associated curves’.

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Fractions

• Fractions
  Basics, adding, comparing, converting, dividing, multiplying, reducing, divisibility rules, relationships, subtracting.
• Fractions [2]
  Information, primarily in text format. Quality information. 24 sections.
• Fractions [3]
  Visual. What is … , practice, equivalent fractions, reducing, improper and mixed numbers, multiply, divide, add, subtract.
• Fresh Baked Fractions
  Uses a game. multiple levels. Choose the Odd Man Out.
• Visual Fractions
  Identify, rename, compare, add, subtract, multiply, divide. Worksheets, Fraction Maker.
• Who Wants Pizza ?
  Information, practice activities. Several topic areas.

Geometry

Includes 2D and 3D shapes and properties, general information, portal sites.

• 3Dimensional Geometry
  GFor higher levels. Annotated links to information, activities, explanations, more.
• Circumference and Area of Circles
  Free lessons, with additional lessons able to be purchased from Maths Goodies, on circumference and area.
• Geometry
  Simple home page leads to directories including Basic Terms, Space Figures, Basic Solids. Angles, figures, polygons, area, perimeter, coordinates, basic solids. Presentation is plain but clear.
• Geometry [LearningMath]
  ‘Geometry introduces geometric reasoning as a method for problem solving. Throughout the first nine sessions, you will explore the properties of geometric figures, make constructions using pencil and paper and dynamic software, practice using mathematical language to express ideas and justify your reasoning and begin to explore the basis of formal mathematical proofs and solid geometry’. Includes videos.
• Geometry [MathsisFun]
  ‘The idea behind the site is to offer mathematics as well as some fun bits and to combine the two wherever possible’. Covers all areas of Geometry.
• Geometry Calculators
  Access Plane Geometry and Solid Geometry Calculators. Select Geometry, either of the two options, then specific calculators from either group.
• Geometry Calculators [iFigure]
  Includes not only calculators, but also concepts, a text, glossary and general Geometry material.
• Geometry Calculators and Solvers
  ‘Easy to use online geometry calculators and solvers for topics in geometry such as calculate area, volume, distance, points of intersection’. Links to tutorials, help in geometry and other areas of mathematics.
• Geometry Centre
  ‘Patterns, Shapes, Symmetry ! You will find these themes everywhere in the Geometry Centre. Browse through an exhibit, or jump right in and start experimenting !’ Interactive material.
• Geometry Online
  ‘Find activities for middle or high school geometry’. Directories from History to Impossible Triangles, a Glossary.
• Geometric Shapes and Figures
  Annotated links to all aspects of geometrical figures including information, activities.
• Geometric Solids and Their Properties
  Online, activity based series of lessons, with a sound mathematical basis.
• Geometry Topics
  5 Major areas - Geometry Facts & Calculations, Area, Perimeter & Circumference, Surface Area, Volume. Split into specific topics, e.g., classifying triangles by angles, area of a parallelogram, circumference of a circle, surface area of a cube, volume of a cone.
• Geometry Topics [AAAMaths]
  Covers ‘Facts & Calculations, Area, Perimeter & Circumference, Surface Area and Volume’. Multiple topics for each major area.
• K-12 Internet Geometry Resources
  Directories of annotated links. Classroom materials, software, internet projects, interactive resources, discussion forums, more.
• Perimeter
  ‘Activities and lesson plans for measuring perimeter. Interactive exercises, quizzes, games, worksheets. eThemes resources on area of polygons and circumference’.
• Perimeter & Area of Polygons
  Free lessons, with additional lessons able to be purchased from Maths Goodies, on perimeter and area.

Mathematics Help

• Eric Weisstein’s World of Mathematics
  Encyclopaedia of terms, derivations, equations.
• Interactive Mathematics Online
  Explanations for mathematical ideas.
• Free Mathematics How-to Library
  Provided for 12 areas of Mathematics from Algebra to Trigonometry. Each has specific topics which are covered, e.g. Algebra → Evaluating Expressions.
• Great MathsWebsites to Explore
  Australian collection. Links are well annotated. Many sites use an interactive process.
• Math.com
  Help site. Formulae are explained, even an indicator on resources [US based].
• Mathematics Dictionary and Glossary for Students
  ‘With over 2 000 terms defined, this dictionary is ideal for supporting students who are studying mathematics or related subjects. All terms in our dictionary are cross-referenced and linked for ease of use, making finding information quick and easy. The definitions of terms and concepts included within our dictionary include the majority of words that students will come across when studying mathematics at secondary school’.
• Mathematics Internet Library
  Part of the Student Internet Library [see Homework Helpers]. Links for mathematical assistance.
• Mathematics [2004] Support Materials
  Queensland Studies Authority. Extensive resources to download in either Word or PDF formats.
• Maths Links and Online Tools
  University of Vienna. ‘Selected links which are relevant for learning and teaching of mathematics’. Links cover all levels but with an emphasis on the tertiary. Grouped under Tools, Links [by topic], Collections.
• Math-Mate
  ‘Math-Hundreds of free math tutorial lessons filled with explanations, worked solutions, handy hints. School students can use the free math lessons to help understand their school homework and prepare for exams and assignments. Parents can work through the easy to understand tutorials with their child’.
• Math Motivation
  Includes links to games, Calculus projects, real world applications, Trigonometry and Algebra Notes, more. Some are suited to tertiary education. A second page provides an even wider link to Resources For Teaching Mathematics including videos, reasoning skills, more.
• Maths.com : References
  Formulae, the history of mathematics, a number of mathematical tools.
• Maths for Morons Like Us
  Thinkquest. Helps you understand concepts better. Quizzes, sample problems, tutorials. Graphical or Text options.
• Maths Nerds
  Answers to questions to the end of secondary. Database of FAQs.
• Number for Primary
  Centre of Learning Innovation, NSW. Links to resources and assistance with Online Tools, Early Stage 1, Stage 1, Stage 2 and 3, teachers, parents.
• Online Mathematics
  Australian. Develops mathematical skills to Y12 level. A cost in AU$, but it is reasonable. Access notes, past papers, glossary, summaries, self-marking tests, a study guide, links.
• QuickMath Automatic Math Solutions
  ‘Automated service for answering over the internet. Think of it as an online calculator. It solves equations and does all sorts of algebra and calculus problems - instantly and automatically ! Best of all, QuickMath is 100% Free !’
• Skillswise - Numbers
  From the BBC. Work with Whole Numbers; Measures, shapes & space; Fractions, Decimals & Percentages; Handling data. Multiple activities in each section.
• This is MEGA Mathematics
  Secondary students, but fun anyway. Created by experts from Los Alamos.
• Visual Math Learning
  ‘Free educational site featuring an interactive on-line tutorial for teaching elementary mathematics and basic arithmetic for grades K-12 at the pre-algebra level’.

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Numerals & Numbers

Number systems - how they looked, when they were used, how they changed, more.

• Arabic
• Babylonian
• Egyptian
• Greek
• Indian
• Math & Numbers in Early History
• Roman
• Roman Numerals, History and Use

Other Specific Mathematical Areas

• [3.14ever - - ]
  Everything about the value of PI ? History, religious connections, interactive information, more.
• Cuisenaire Learning Place
  For students at primary level.
• The Fractory
  Thinkquest. Creating and exploring fractals.
• Measurement Links
  Part of the Dictionary of Units of Measurement site. Annotated links to sites, converter, history of measurement, more.
• TotallyTessellated
  Thinkquest. Introduction to Tessellations. History, the basic maths behind them. Works with Escher tessellations.
• Uniform Polyhedra
  Information about polyhedra with an animated presentation of each.
• What’s Special About This Number ?
  Find distinctive facts about numbers from 1 to 9 999. Links to information about the specific fact and include examples of how to discover the information as well as what it is.
  For example 9 999 is a Kaprekar number, that is, a non-negative integer, the representation of whose square in that base can be split into two parts that add up to the original number again. [Explanation from Wikipedia]

Probability

• Powerhouse Museum : Gambling
  ‘Learn about mathematics and probability, as applied to lotto, instant scratchies, roulette, poker machines’. Teacher section. Australian.
• Probability Central
  Thinkquest. Looks at probability, clarifies your understanding. Play poker while you learn.

Problem Solving

• Elementary Problem of the Week
  Designed to have primary level students look at non-routine problems and discuss how they solved them.
• Kid’s Place Brain Teasers
  Problems in primary and secondary groupings. Look at them in different ways.
• Mathematical Problems
  Wrap your brain around these.
• Maths Challenge
  Suitable for the family. Cartoon characters pose various problems for you to solve.
• Maths Problem Solving
  Maths Association of Victoria. Problems for different levels of schooling and all aspects of problem solving.
• Math Word Problems for Children
  Definitely a site to visit. 2 000+ to choose from. Sorted by difficulty level.
• Word Problems For Kids
  ‘Word problems for students and teachers. Problems classified into grade levels from 5 to 12 - a set of carefully selected problems which help you improve problem solving skills. Get helpful hints by following the Hints Link’.

Real Life Mathematics

• Introducing MegaMaths
  Real-life mathematics using fun activities based on everyday things.
• Maths in Daily Life
  Practical usage of maths for skills and understanding as you ‘look at the language of numbers through common situations, such as playing games or cooking. Put your decision-making skills to the test by deciding whether buying or leasing a new car is right for you, predict how much you can save for your retirement by using an interest calculator’.
• Moneystuff
  Designed to help young people learn how to develop independent living skills and handle personal finances.
• PUMAS - Practical Uses of Math and Science

Trigonometry

• SOS Mathematics - Trigonometry
  Tutorials covering aspects of trigonometry.
• Trigonometry
  Learn about trigonometry.
• Trigonometry Tutorial
  Tutorial in PDF format.
• Trigonometry Tutorials & Problems
  ‘Free tutorials and problems on solving trigonometric equations, trigonometric identities and formulas can also be found. Java applets used to explore, interactively, important topics in trigonometry such as graphs of the 6 trigonometric functions, inverse trigonometric functions, unit circle, angle, sine law’.

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