Abstract Algebra
Abstract algebra Online from Mathematics Archives contains large hypertext lecture notes for abstract algebra 1 and 2, based on John A Beachy's books.
Maple worksheets for abstract algebra by Mike May, St. Louis University
Analysis
Interactive real analysis- real analysis lecture notes by Bert G. Wachsmuth.
Analysis Webnotes - this is university level math! by John Lindsay Orr, University of Nebraska, Lincoln.
Calculus & Differential Equations with Maple V North Carolia State University's page. The pages have dozens of Maple-worksheets, and they cover indtroductory differential and integral calculus. The definitions are included in the Worksheets, and they have lots of examples and exercises.
Georgia Tech's Calculus I - IV Additional Maple worksheets and Java applets. they include for example Newton's method, finding roots, Newton's law of cooling, tecniques of integration, curves and surfaces.
Maple worksheets for Integration topics: numerical methods of integration, calculating e, Taylor's polynomials, methods of integration. More from the same site: double and iterated integrals, visualizing integration regions by Scott Thatcher in Northwestern University
Worksheets for numeric integration and Taylor polynomials from St. Louis University.
Multidimensional calculus: lines in spce R3, tangent planes, finding maxima and minima, Lagrange multipliers. Northwestern University
Double and triple integrals plotted in different coordinate systems
Manipula Math with Java - a collection of Java applets. For example Rolle's theorem, mean value theorem, nice applets related to teh geometry of complex functions and applets for trigonometry.
University of Carolina Maple worksheets, topics are: Taylor polynomials animated, numerical integration methods and comparison of convergence rates, convergence of series and sequences, convergence of power series, plots of curves in polar coordinates, curves and parametric equations, geometric visualization of divergence in 2-D, gradients and contours.
Connected Curriculum project Maple worksheets and Mathematica notebooks for multivariable calculus.
Connected curriculum project again, materials for precalculus, calculus, linear algebra, engineering mathematics
Gallery of Famous plane curves
Animation of Epitrochoid (in Finnish): a html-document Maple-worksheet
Complex analysis
Manipula Math with Java- a collection of Java applets. For example Rolle's theorem, mean value theorem, Nice applets on geometry of complex functions and trigonometry.
Complex Function viewer - a nice Java applet which shows you how complex functions z -> sin(z), z-> cos(z) and z-> exp(z) map a point and a square grid around it.
Graphics for Complex Analysis - Douglas N. Arnold. A collection of graphical demonstrations of concepts in complex analysis developed for a course at McAllister. Most are animated so that the original curves are continuously deformed into the image curves, and the eye can follow which points move where, and colors are used to distinguish different points and curves. Contents: The squaring map; The exponential, sine, and cosine; Conformality; Möbius Transformations.
Differential equations
Ordinary Differential Equations
using MATLAB or Java applets. John C. Polking's Matlab functions and
corresponding Java implementations
dfield: drawing direction fields of ordinary first order differential
equations and numerical solutions of initial value problems; with many
features
pplane: drawing phase planes of systems of two ODEs and numerical
solutions of initial value problems; with many features
Differential equations worksheets from university of Illinois, Chicago.
Calculus & Differential Equations with Maple V from North Carolia State University. Sivut sisältävät kymmeniä Maple-worksheettejä, ja ne kattavat differentiaali- ja integraalilaskennan alkeet. Worksheetit sisältävät käsitteiden määritelmät ja paljon esimerkkejä sekä harjoitustehtäviä.
For ODEs Slope Fields, Numerical Solutions, Forced Oscillations, Linear Systems of Differential Equations, Series Solutions for Variable Coefficient equation. Northwestern University
University of Carolina Maple worksheets for differential equations. Topics are Direction fields via DEplot, Picard iterates and existence, Discontinuous coefficients, Boundary value problems, Laplace transforms, Systems of ODEs, by Robert Murphy, Douglas Meade, & Matthew Miller.
Rensselaer Polytechic Institute's Maple worksheets for teaching elementary differential equations
Maple tutorials for ODEs, by Archie G Gibson, University of New Mexico.
Connected Curriculum project Many Mathematica notebooks for ODEs
Maple worksheets on partial differential equations and heat transfer from Mechanical Engineering Department at the University of Waterloo.They've done with Maple V Release 3 and might need some upgrading.
On-line module on heat equation, Connected Curriculum Project
Dartmouth College Lots of Java-applets concerning ordinary and partial differential equations and related stuff.
Differential geometry:
Differential geometry at Geometry Center
CurvesSurfacesKnots by C.T.J. Dodson, Department of Mathematics, University of Manchester Institute of Science and Technology.
Introduction to Differential geometry - many worksheets by Matt Kawski from Arizona State University
Some Maple
worksheets I've done for differential geometry
Discrete math: graph theory
Online tutorial by Chris K. Caldwell, Mathematics and Computer Science, University of Tennessee at Martin
MahtMania tutorial and activities.
A very good Java applet by which you can draw graphs, and then find shortest paths between vetrices, convert them to matrices, draw graphs from matrices etc.
A Java Applet that animates some algorithms (finding shortest path, breadth-first search, depth-first search, minimal spanning tree) with the help of graphs
Dynamical systems and fractals
Dynamical systems and fractals lecture notes
Interactice Java applet iterating the logistic map x -> ax(1 - x) by Andy Burbanks.
Geometry
Euclid's
Elements , the totality of these magnificent books online. All the
figrures are illustrated with the Geometry applet, by which the user can
often drag the (randomly chosen) points or lines in the constrcution and
so 'see' how the proof works. Excellent tool!
Geometry center - geometristen objektien visualisointeja. Mm. applet, joka piirtää ja laskee kolmion alan hyperbolisessa tasossa
Cabri Geometre home page, a software tool that is extremely useful when studying geometrical objects.
The Living Mathematics Project, Java applets demostrating for example Kepler's laws, proofs of Pythagora's theorem, Bezier curves.
High school math
CyberCalc - limits and derivative for those who need some revision
California State University, San Bernardino An interactive algebra course for high school. Topics include functions, drawing graphs, matrices, sequences. Includes many nice interactive Java-applets.
The Atlas of high school math by Simo Kivelä Iso-M (in Adobe Acrobat form)
http://www.geom.umn.edu/education/calc-init/
Calculus projects from University of Minnesota Calculus project : Rainbow,
Numerical integration,
Beams, Bending, and Boundary Conditions, Modelling population growth.
Finite Mathematics and Applied Calculus home page - on-line lecture notes on calculus and probability, exercises, some Java and Java-script programs.
History of mathematics
Yahoo -collection of links on mathematics history
Introductory university math
Johdatus korkeakoulumatematiikkaan
-
lecture notes for introduction to univeristy mathematics - in Finnish.
Produced by Hypermedialaboratorio, Matematiikan laitos ja Tampereen teknillinen
korkeakoulu
Notes on set theory, logic and proof - on-line notes, dealing set theory, prof techiques, groups, binary operation, function and relation concepts from California State University at San Bernandino
Linear algebra
Johdatus matriisilaskentaan
- luentomoniste (In Finnish).
Linear algebra Webnotes by Mark V. Sapir
Maple workhseets for linear algebra
http://www.ms.uky.edu/~carl/linalg.html Applications and models where one can use linear algebra. Vectors and angles, drawing lines, Inverses of Bidiagonal and tridiagonal matrices, Hilbert matrices and finite presicion arithmetic, ...
University of South Carolinan Maple worksheets. Topics are: Eigenvalue and eigenvector calculations, Example of singular value decomposition and Hilbert matrices and complications due to ill-conditioned matrices and finite-precision arithmetic, Geometric programming example (unconstrained), Homework solutions for least squares and data fitting, Comparison of iterative methods for the minimization of nonlinear functions (Newton, steepest descent, Broyden), Constrained geometric programming.
Maple materials from Connected curriculum project
Metric spaces
Hyperbolic
geometry using Cabri Here you can download a menu file to Cabri Geometre
- program by which you can then draw and study geometrical objects in the
hyperbolic plane H2.
Rice University Java-applet about hyperbolic geometry.
Analysis Webnotes - includes also chapters of metric spaces. By John Lindsay Orr, University of Nebraska, Lincoln.
Number theory and cryptography
Cryptography Maple worksheets by Mike May, St. Louis University
Numerical analysis
Course notes using Maple for numerical analysis from Laurentian University. Topics such as roundoff errors, Taylor series approximations, stable and unstable recurrence relations and other numerical pathological examples, Maple programs for the solution of linear systems of equations using gaussian elimination and the LU decomposition, Runge Phenomenon...
Practicum in Numerical Analysis (for Maple V) by Gleb Beliakov. This site has a zip file that includes many Maple worksheets. Practicum in Numerical Analysis (PNA) is a set of laboratory tasks designed to be a supplement to the course of numerical analysis. The exercises illustrate the basic numerical methods, show their advantages and limitations and help to understand the behavior of numerical solutions.
Maple Worksheets contributed by G.Keady This site includes routines and worksheets especially for ODEs.
Probability theory
A simulator
of Markov chains
A Monty
Hall -simulator (There is a treasure behind one door. When you
choose one door out of three, the leader shows you the other of those you
didn't choose and where the treasure is not. Now you may change your selection.
Should you?) , both programs are from Finite
mathematics & Applied Calculus page.
Maple handbook - includes an introduction to Maple + worksheets from topics of calculus, eg differentiation, integration, Taylor series. Inverse functions, Center of Mass. As a zip file.
University of Carolina Links to tutorials and Maple sites.
Mathematics
Archives - interaktiivisten sivujen kokoelma
Megamathematics
- some fun stuff with real mathematics about map coloring, concept of infinity,
algorithms, graphs.
CRC concice Encyclopedia
of mathematics