# External Study Resources

### Tutorials

- Visual calculus
- Featuring online tutorials on Pre-Calculus; Limits and Continuity; Derivatives; Applications of Differentiation; Integration; Applications of Integration; Sequences and Series. Developed by the Department of Mathematics at the University of Tennessee.
- Rigid Transformations
- Visualise the key concepts through interactive Java applets. Developed by the University of Tennessee at Chattanooga.
- Graph Theory Lessons
- 23 lessons with interactive Java applets. Developed by the University of Tennessee at Chattanooga.
- Fluid mechanics
- Online tutorials on Aurora; Bernoulli Eqn; Lubrication; Raindrops; Sound Barrier; Water Waves. Developed by M.S. Cramer, Engineering Science and Mechanics, Virginia Tech.
- Abstract Algebra
- Online study guide based on the textbook
*Abstract Algebra*, by John A. Beachy and William D. Blair. Online materials include definitions and review of the main theorems , problems and solutions.

### Books (freely available)

*Calculus*, by Gilbert Strang (MIT)- Made available through MIT's OpenCourseWare electronic publishing initiative.
*Topology without tears*by Sid Morris, School of Information Technology and Mathematical Sciences (ITMS) at the University of Ballarat. Freebly readable online. The author also provides free access to a printable pdf version.*Introduction to Probability*, by Charles Grinstead and J. Laurie Snell.- Published by the AMS and now freely available. The website includes Mathematica, Maple, and TrueBASIC programs that go with the book with experimental versions of the programs as Java applets. The answers to the odd-numbered problems are also available from this website.
*An Introduction to Probability and Random Processes*, by Gian-Carlo Rota and Kenneth Baclawski.- Freely available for viewing and printing.
*Euclid's Elements*- This HTML edition of Euclid's Elements uses a Java applet called the Geometry Applet to illustrate geometry interactively. Developed by D.E.Joyce, Department of Mathematics and Computer Science, Clark University, USA.
*The Hyperbook of Combinatorics*- This is a project to cover major topics in combinatorics with high quality expositions, the latest developments, and up-to-date references. Developed by The Combinatorics Net.

### Book repositories (freely available)

- The Trillia Group self study books
- Freely available undergraduate textbooks. Titles include
*Basic Concepts of Mathematics*;*An Introduction to the Theory of Numbersand Mathematical Analysis I.* - The Math Books Archive
- Freely available volumes (mostly in pdf) on Mathematics, Physics and Computing. Also provides links to lecture notes and other repositories. Maintained by Bhargav Bhatt, Princeton University.
- AMS books online
- All books are freely downloadable in pdf format and subjects include: Algebra and Algebraic Geometry; Analysis; Applications; Differential Equations; General Interest; Geometry and Topology; Logic and Foundations; Mathematical Physics; Number Theory; Probability.
- The Cornell University Library - Historical Mathematics Monographs
- Features more than 500 digital volumes accessible page-wise through an on-line reader. The archive is searchable by keywords and can be browsed by author and title.

### Mathematics portals

- The European Mathematical Information Service
- Supported by the European Mathematical Society (EMS).
- MathGuide
- The MathGuide is an Internet-based subject gateway to scholarly relevant information in mathematics - including Universities, Data Collections, Bibliographies, Journals, and Software. Hosted by the University Library, Göttingen (Germany).
- The MacTutor History of Mathematics archive
- Currently listing more than 1300 biographies of mathematicians; 30 articles on the history of various topics in mathematics and more than 60 curves with their history and properties. Searchable.

### Miscellanea

The Mathematical Quotations Server

"The mathematical sciences particularly exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful.", Aristotle, *Metaphysica*, 3-1078b.

- Gallery of fluid mechanics
- Provides a collection of pictures, movies, and sounds which illustrate a great variety fluid flows. Developed by M.S. Cramer, Engineering Science and Mechanics, Virginia Tech.

### Other collections of links

- Online Mathematics Textbooks by George Cain
- Lecture notes collected by Bhargav Bhatt
- Textbooks in Mathematics by Alexandre Stefanov
- Wikibooks:Mathematics bookshelf
- A Catalog of Mathematics Resources on the WWW by M. Maheswaran Department of Mathematics, University of Wisconsin Marathon County