|
 |
 |
 |
 |
mathematics [plural noun 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]. DERIVATIVES mathematical, adjective; mathematically, adverb; mathematician, noun.
- ORIGIN from Greek mathema
‘science’, from manthanein ‘learn’.
This page provides links to information and resources for units and topics covered in this subject at a range of Australian universities. It does not attempt to include all these. Be aware some units/topics have different titles in different universities, even though content may be the same or similar. Australian information is supplied wherever possible.
They are at undergraduate level and listed in alphabetical groupings for ease of access. Some information may be useful at a higher level.
In addition, there are journals, search engines, annual reviews, reference material and other general information where these are seen to be relevant.
Additional unit material will be included as time permits.
If you are aware of any worthwhile information which is not included, suggestions or additions are welcome and will be given every consideration.
A - F
Algebra
Covers aspects from the basics to Linear Algebra.
- For other links to Algebra, especially the basics, check the Mathematics curriculum page.
- Elementary Linear Algebra
Lecture Notes, link to a matrix calculator program, solutions. Not new but has been modified more recently. - Linear Algebra
Information, explanations, useful theorems, references, external links, more. From Wikipedia. - Linear Algebra [Text]
‘Free for downloading. It covers an undergraduate first course, with a prerequisite of Calculus I. You can use it either as a main text, or as a supplement to another text, or for independent study. A separate file with all answers, fully worked, is also freely downloadable’. - Linear Algebra Toolkit
‘Each module is designed to help a linear algebra student learn and practice a basic linear algebra procedure, such as Gauss-Jordan reduction, calculating the determinant, or checking for linear independence’. - MIT Open Courseware, Linear Algebra
Video lectures. You need RealOne™ Realplayer software to watch them. The course Home is found here, as are resources, study materials, etc.. - Paul’s Online Math Notes
‘Online notes for my Linear Algebra course that I teach. You can navigate through this E-Book using the menu. For E-Books that have a Chapter/Section organization each option in the menu to the left indicates a chapter and will open a menu showing the sections in that chapter’. Also download in PDF format.
Books, Documents, Journals, …
- Free Mathematics Books
‘Here is an alphabetical list of online mathematics books, textbooks, monographs, lecture notes, and other mathematics related documents Freely available on the web’. - Free Mathematics eBooks
Select from topic areas from Algebra to Trigonometry. - Online Mathematics Textbooks
Nearly 70 links to Online Texts, Free to use. Covers all areas of mathematics from Calculus to Introduction to Vectors. - Plus
Articles showing links between mathematical applications and the sciences, engineering and economics, interviews with present day mathematicians, new developments in mathematics. - PrePrint Archive
‘Access the contents of the Chemistry, Mathematics and Computer Science Preprint Archives’. Registration is required but Free.
Excellent resource. - The Electronic Library of Mathematics
‘Online journals, article collections, monographs, other electronic resources in the field of mathematics. All material is in electronic form and access is generally Free, except for some periodicals with a moving wall, i.e. a delay period, after which resources become freely available’. - Check the Textbooks page for a listing of textbooks available for Free, online or in downloadable format.
- Wiley InterScience : Mathematics & Statistics
Select by category, then product type. Books, journals, databases, more.
Calculus
- Calculus and Analysis
Several hundred links in 25 directories. Calculus to Dynamical, Systems, Integral Transforms, to Special Functions. Each further subdivided. Explanations, references, etc., provided. - Calculus on the Web
‘Internet utility for learning and practicing calculus. The principal purpose of COW is to provide you, the student or interested user, with the opportunity to learn and practice problems in calculus in a friendly environment via the internet. The most important feature is that you get to know whether your answer is correct almost immediately. It is as if you had a tutor looking over your shoulder and helping you along’. -
First Year Calculus
Downloadable chapters in PDF format for use in the first year of tertiary studies. Used in at least one Australian university. You can now also access a range of lecture notes in Mathematics from the same page.
G - L
General Sites
- Academic Info : Mathematics
Directory of information on tertiary mathematics. - Clark University : Mathematics Links
Specialist links to Euclid’s Elements, short trigonometry course, Mandelbrot and fractals, what is claimed to be the most important speech ever given by a mathematician to other mathematicians - Hilbert’s address of 1900 in Paris. - Cramster Maths Help
‘Global online study community centred on providing understanding to math questions whether it’s related to homework, exam preparation or general learning’. Based on specific textbooks used, leading to related solutions. Other resources. - Common Errors in Undergraduate Maths
‘Errors that I have seen most frequently in undergraduate mathematics, the likely causes of those errors, and their remedies. I am tired of seeing these same old errors over and over again. I would rather see new, original errors !’
Check this ! - Eric Weisstein’s World of Mathematics
From algebra to applied mathematics, calculus, analysis to topology. Designed for tertiary.
Exceptional ! - HyperMath
‘A growing collection of examples of applied mathematics with links to their applications to problems in physics and astronomy’. - Intute Mathematics
Multiple sections cover all areas of mathematics. - Langara
Canadian site linked to tertiary mathematics. - Links to Other Sites
‘These are some other pages which you may find useful concerning topics related to mathematics’. MacTutor, St Andrews University. -
Mathematics Resources
Find resources by Course, Topic, Resource Type or search for a particular resource. A second site for Mathematics Resources [Yale University Library] can be found here. - Free Online Course Materials - MIT OpenCourseWare
An extensive range of courses from Algebra to Random Matrix Theory and Its Applications and beyond. Many have video lectures in addition to documentation. - The Math Forum Home Page
Resources in levels, Key Issues in Maths, Math Forum Internet Mathematics Library, research, quick reference. - Understanding Mathematics
American university study guide. Check instructions at top before starting. - White Group Mathematics
As one part of this site, there are two sections - The Question Locker [Parts 1 and 2] and Beyond H2 Maths, that have Free question/answer resources in mathematics at the beginning tertiary level.
History, Mathematical
- History of Mechanical Calculators - Part I
Links to Parts 2 and 3. Mechanical calculators from the abacus to Napier’s Bones. - Mathematics and Mathematicians
For further historical information including biographies of mathematicians, visit this site page. - The History of Mathematics
Trinity College, Dublin. Several collections, extensive links.
M - R
Mathematical Archives
- Maths Archives
British site. Portals to topics such as those below, software, teaching materials, other features, links.
- Mathematics Archives - Links
Links in directories including Bibliography, For Undergraduates, Electronic Journals, Published Journals, Professional Societies, Other Sites, Mathsearch, more. - Mathematics Archives - Topics in Mathematics
40 topics covered, Abstract Algebra to Trigonometry. For secondary and tertiary studies.
Mathematical Databases
- MathSciNet
60 year database of mathematical writing. 1 700+ Mathematical journals. American Mathematical Society. - Mathematics Virtual Library [FSU Math]
Information, links. From bibliographies to software.
Mathematics Prizes
Listing of, and links to, prizes and awards in Mathematics.
- Fields Medal
Summary of the award. Listing of many winners of the premier Mathematics award, the equivalent of a Nobel Prize. - Mathematics Prizes
Listing of Mathematics prizes. Specific links and links to other sources. - Mathematical Societies, Medals, Prizes, Other Honours
Includes links to Mathematics Prizes. - The Fields Medal
Information about the Fields Medal Won by an Australian in 2006.
S - Z
Software
- GAMS Guide to Available Mathematical Software
‘Cross-index and virtual repository of mathematical and statistical software components of use in computational science and engineering’. Search engine. - GAMS - Other Sources of Math Software Information
6 major directories. - SAGE
‘Sage is a Free open-source mathematics software system licensed under the GPL. It combines the power of many existing open-source packages into a common Python-based interface’.
Specific Mathematical Areas
- Cryptography A - Z
Introduction, algorithms, protocols and standards, access references, resources. - EqWorld
‘Solutions to various classes of ordinary differential, partial differential, integral, functional, and other mathematical equations. Outlines some methods for solving equations, includes interesting articles, gives links to mathematical websites, lists useful handbooks and monographs, refers to scientific publishers, journals, etc.’. - Geometry
‘Several hundred links in 30 directories from Algebraic Geometry to Trigonometry. Each further subdivided and explanations, references, etc., provided’. - Xah Visual Dictionary of Famous Plane Curves
Methods of generating new curves, special plane curves, definition, graphics, formulae, properties, web links, curve family system. - Probability Web
‘Probability resources on the World Wide Web. Designed to be especially helpful to researchers, teachers, and people in the probability community’. - The Integrator - Power To Do Integrals
History of Integration, enter and compute Integrals. - Visual Calculus
‘Designed for instructors to give some ideas how technology, in particular, computers, can be used in the teaching of calculus. Detailed instructions on implementing these ideas with various public domain, shareware and commercial software packages are provided. Tutorials, interactive modules [LiveMath, Java, and Javascript] which can be used by either students or faculty and includes detailed instructions for TI™ and TI™ graphing calculators. Modules containing quizzes and drill problems have also been added’. - Wolfram Functions
Information , examples for some 87 000+ formulae, 10 000+ have visualisations to help understanding.
Symbols, Mathematical
Includes mathematical notation.
- Earliest Uses of Symbols of Operation
Begins with addition and subtraction symbols and extends to more complex mechanisms with relevant examples. Bibliography. - Mathematical Symbols
‘Mathematical symbols and links to definitions of what they represent’. Table lists the symbol, what it is, how it is read, how it is used, sample expression[s]. Links to greater explanations of particular concepts. - Notation
Listed alphabetically from Almost All to Wythoff Symbol. Each has a descriptor, links to related sections, author of the contribution, references, correct method of citing the contribution.
Tutorials
-
ARC Links
‘Internet links for tutorials and other resources in various academic subjects’. Select Links > Mathematics > Topic desired from those listed. These include Calculus & Differential Equations, Tertiary Algebra … , Mathematics Advanced, Mathematics Developmental and more. - Internet Mathematician
Tutorial to practise internet information skills based on Mathematics. Links to Mathematics sites. -
MIT OpenCourseware - Mathematics
Lists all the units available online for Free. From Calculus and Algebra to Matrix Theory and The Art of Counting. - Oxford - Mathematics Course Material
‘Courses offered by the department. Not all can be used freely. For Free materials see OpenCourseWare courses’. - S.O.S. Maths
‘Free resource for math[s] review material from Algebra to Differential Equations. The perfect study site for high school, college [university] and adult learners’.