Gymnasieskolans matematik (främst NV)

Material och uppslag


Teori

Algebra och talteori

Del I: Polynomuttryck
Del II: Rationella uttryck
Del III: Potenser och logaritmer
Del IV: Trigonometriska uttryck
Del V: Komplexa tal

Basic algebra

Geometri

Mandelbrotmängden - deep zooming

Funktionslära (analys)

Ordinära differentialekvationer
Partiella differentialekvationer

Repetitionsmaterial

Övningsuppgifter/Problem


Internetlänkar

Algebra

History of Mathematics - Al'Khwarizmi & Al Jabr
Mathematics - Algebra - Fractals and Chaos - Web Index - Bengt's Home Page
Mathematics Archives - Topics in Mathematics - Abstract Algebra
Quintic Equation -- from MathWorld
Solving the Quintic with Mathematica

Analys

IRA: Interactive Real Analysis
Lambert W-Function -- from MathWorld
Trigonometry and Basic Functions - Numericana

Geometri Topologi

A Gallery of Interactive On-Line Geometry
*** ArtByMath Gallery ***
Byrne's edition of Euclid
An unusual and attractive edition of Euclid was published in 1847 in England, edited by an otherwise unknown mathematician named Oliver Byrne. It covers the first 6 books of Euclid, which range through most of elementary plane geometry and the theory of proportions. What distinguishes Byrne's edition is that he attempts to present Euclid's proofs in terms of pictures, using as little text - and in particular as few labels - as possible. What makes the book especially striking is his use of colour.
Directory of Computational Geometry Software
Euclid's Elements, Table of Contents
Euclid's Geometry: History and Practice
Famous Curves Index
Hypercubes
Mathematics Archives - Images and Mathematics
National Curve Bank
The National Curve Bank is a resource for students of mathematics. We strive to provide features - for example, animation and interaction - that a printed page cannot offer. We also include geometrical, algebraic, and historical aspects of curves, the kinds of attributes that make the mathematics special and enrich classroom learning. - We welcome participation. We encourage you to submit your best web animation as a "deposit" in the National Curve Bank.
NonEuclid - Hyperbolic Geometry Article & Applet
NonEuclid - Hyperbolic Geometry Article + Software Applet
The Four Color Theorem
The Geometry Center Welcome Page
TRIANGLE CENTERS
Unlike squares and circles, triangles have many centers. The ancient Greeks found four: incenter, centroid, circumcenter, and orthocenter. A fifth center, found much later, is the Fermat point. Thereafter, points now called nine-point center, symmedian point, Gergonne point, and Feuerbach point, to name a few, were added to the literature. In the 1980s, it was noticed that these special points share some general properties that now form the basis for a formal definition of triangle center. - The Encyclopedia of Triangle Centers lists many centers, but without pictures. The purpose of this page is to introduce a collection of individual pictures, showing constructions of selected triangle centers. The selections are in two groups: Recent Triangle Centers and Classical Triangle Centers.

Diskret matematik Experimentell matematik Sannolikhetslära Talteori Konstanter Primtal

Almost Integer -- from MathWorld
An almost integer is a number that is very close to an integer. - A surprising example involving both e and pi is e^pi - pi = 19.999099979...
Chance Welcome Page
The goal of Chance is to make students more informed, critical readers of current news stories that use probability and statistics.
e -- from MathWorld
Experimental Mathematics
Exp(Pi*Sqrt(n)) Page
Some of these values are very close to integers.
ISC
The ISC is the Inverse Symbolic Calculator, a set of programs and specialized tables of mathematical constants dedicated to the identification of real numbers. It also serves as a way to produce identities with functions and real numbers. It is one of the main ongoing projects at the Centre for Experimental and Constructive Mathematics (CECM).
JavaScript Turing Machines
Mathsoft Constants - Mathcad Library
NUMBER THEORY WEB (AUSTRALIAN SITE)
Maple Programs by Doron Zeilberger
Automatic theorem proving.
Mathematical Constants
Mathematics Archives - Numbers
Number Recreations by Shyam Sunder Gupta
On-Line Encyclopedia of Integer Sequences (Look-Up)
PI
Pi and Other Constants
Pi and the Fibonacci Numbers
Pi -- from MathWorld
Ramanujan Constant -- from MathWorld
e^(pi*sqrt(163)) = 262537412640768743.9999999999992500...
Random Number Generators >> Home
Record for pi
Resources
This page contains links to sites that are similar, or complementary, to the material of the Inverse Symbolic Calculator.
six
Some Thoughts on the Number 6
The Irrationality of Pi
Elementary proof
The Mathematics of Fermat's Last Theorem
The Paule/Schorn Implementation of Gosper's and Zeilberger's Algorithms
Automatic theorem proving.
The Pi Pages
The Prime Pages (prime number research, records and resources)

Datorprogram Datoralgebra/Automatisk symbolbehandling Superdatoranvändning

Automated Deduction Systems and Groups
CalculationCenter: Wolfram Research's accurate, easy-to use, equation solver software
Garbo Anonymous FTP Archive
Joey_21's Scientific Calculator
Maple Programs by Doron Zeilberger
MIT Artificial Intelligence Lab
RIACA: Research Institute for Applications of Computer Algebra
Solving the Quintic with Mathematica
SymbolicNet -- Information Center for Symbolic and Algebraic Computation
The Paule/Schorn Implementation of Gosper's and Zeilberger's Algorithms
Automatic theorem proving.
TOP500 Supercomputer sites
Wolfram Research, Inc.

Fraktaler och kaos Komplexa system

Center for Complex Systems Research
Chaos at Maryland
Chaos Downloads from Rudy Rucker's Wesbsite
Dynamical Systems and Technology Project
This project is a National Science Foundation sponsored project designed to help secondary school and college teachers of mathematics bring contemporary topics in mathematics (chaos, fractals, dynamics) into the classroom, and to show them how to use technology effectively in this process. At this point, there are a number of Java applets available at this site for use in teaching ideas concerning chaos and fractals. There are also several interactive papers designed to help teachers and students understand the mathematics behind such topics as iteration, fractals, iterated function systems (the chaos game), and the Mandelbrot and Julia sets.
fractalus home
FRACTINT Deepzooming With Bengt
Graphics Archive - General Interest:Fractals
Mandelbrot Set -- from MathWorld
The term Mandelbrot set is used to refer both to a general class of fractal sets and to a particular instance of such a set. In general, a Mandelbrot set marks the set of points in the complex plane such that the corresponding Julia set is connected and not computable.
Mathematics - Algebra - Fractals and Chaos - Web Index - Bengt's Home Page
Mathematics Archives - Topics in Mathematics - Fractals
Spanky Welcome
THE SPANKY FRACTAL DATABASE. This is a collection of fractals and fractal related material for free distribution on the net.

Matematiska problem och problemlösning Tävlingar

Crux Mathematicorum with Mathematical Mayhem
The digital supplement to the Canadian Mathematical Society's Problem Solving Journal
Högstadiets Matematiktävling
Interactive Mathematics Miscellany and Puzzles
Mathematics is the only deductive science. The peculiar beauty of Mathematics lies in deduction, in the dependency of one fact upon another. The less expected a dependency is, the simpler the facts on which the deduction is based -- the more beautiful is the result. - Learning starts from wondering, and [another] purpose of this site is to serve as a resource for things, simple but curious, related to Mathematics.
Internet Center for Mathematics Problems
Math Problem Directory
Månadens problem
Number Recreations by Shyam Sunder Gupta
Olympiad Math Madness
Visit my hall of fame - those who have solved at least one problem.
The Norwegian Mathematical Olympiad
Thunderstone's Webinator: Search: problems [FSU Math]
Unsolved Problems -- from MathWorld

Matematikens filosofi och historia Logik

Alan Turing - Home Page
Alan Turing Scrapbook - Turing Machines
Archimedes Home Page
Archimedes Palimpsest
Automated Deduction Systems and Groups
Bruno Kevius
Earliest Uses of Various Mathematical Symbols
Euclid's Geometry: History and Practice
Goedel, Escher, Bach
Greek Mathematics and its Modern Heirs
Hilbert's Problems
Hilbert Tenth Problem: database index
History of Mathematics - Al'Khwarizmi & Al Jabr
History of Mathematics Links: Electronic Texts
History of Mathematics - Table of Contents
History Topics Index
JavaScript Turing Machines
Logic Software from CSLI
Matematik
MIT Artificial Intelligence Lab
Principia Cybernetica and Principia Mathematica
Teaching with Original Historical Sources in Mathematics
Turing's World: More Information (1)
In Turing's World, a collection of graphical tools lets you design Turing machines by directly drawing their state diagrams.
Unsolved Problems -- from MathWorld
Websites relevant to the History of Mathematics

Arkiv Böcker Frågelådor Institutioner Tidskrifter

American Mathematical Society: Mathematics Research and Scholarship
*** ArtByMath Gallery ***
CalculationCenter: Wolfram Research's accurate, easy-to use, equation solver software
Chance Welcome Page
Crux Mathematicorum with Mathematical Mayhem
CSC
Mathematical visualizations and animations
Directory of Mathematics Preprint and e-Print Servers
Elektroniska tidskrifter Matematikbiblioteket Chalmers
Front for the Mathematics ArXiv
Fråga Lund om matematik
Gallery of Mathematics
Garbo Anonymous FTP Archive
KaBoL
KaBoL is a "cool math site of the week" service to the mathematics community provided within Camel by the Canadian Mathematical Society.
Matematik
Matematik minimum - Terminologi
Math art gallery
MathGate | UK Mathematics Projects using Teaching and Learning Technology
Math Forum: Ask Dr. Math - College Level Archive
Math Forum Internet Mathematics Library
MathPages
MathWorld
Mathematical Association of America: MAA Online
Mathematical Atlas: A gateway to Mathematics
This is a collection of short articles designed to provide an introduction to the areas of modern mathematics and pointers to further information, as well as answers to some common (or not!) questions. The material is arranged in a hierarchy of disciplines, each with its own index page.
Mathematical Quotation Server
Mathematics - Algebra - Fractals and Chaos - Web Index - Bengt's Home Page
Mathematics Archives - Images and Mathematics
Mathematics Archives - K12 Internet Sites
Mathematics Archives - Numbers
Mathematics Archives - Topics in Mathematics - Abstract Algebra
Mathematics Archives - Topics in Mathematics - Fractals
Mathematics Archives WWW Server
Mathematics for Students and Teachers
Mathematics on the Web: Books
Mathematics Online. Scientific Magazines and Journals Online.
Mathematics Resources on the Internet - (Math Links by Bruno Kevius)
mathstore | LTSN Maths, Stats & OR Network
PlanetMath
PlanetMath is a virtual community which aims to help make mathematical knowledge more accessible. PlanetMath's content is created collaboratively: the main feature is the mathematics encyclopedia with entries written and reviewed by members.
PSU Math - Mathematics Websites
Question Corner
Resources for Teaching Complex Analysis
SUNET - Swedish University Network's FTP-archive
SUNETs Webbkatalog: Matematik
Svenska och Nordiska Matematiklänkar
The EMS Home Page
The European Mathematical Information Service
The International Study Center at Boston College
The KnotPlot Site
Here you will find a collection of knots and links, viewed from a (mostly) mathematical perspective. Nearly all of the images here were created with KnotPlot, a fairly elaborate program to visualize and manipulate mathematical knots in three and four dimensions. You can download KnotPlot and try it on your computer...
The Mathematical Foundation; free mathematics books, tables and texts
The Math Forum Home Page
The Pacific Institute for the Mathematical Sciences
The Pi Pages
The Prime Pages (prime number research, records and resources)
Wolfram Research, Inc.
Yahoo! Directory Mathematics
Yahoo! Directory Education


Böcker

Aritmetikens grundvalar (Frege)
Turing's World 3.0 for Mac: Introduction to Computability Theory
Boken om tal
Stora matematiker
Diskret matematik
Problemlösning (Polya)
Den fantastiska matematiken
Diskret matematik och diskreta modeller
Matematik inför högskolan - repetition
Algebra och analys med Mathematica
Diskret matematik för gymnasiet
Människorna bakom matematiken
Experimentell matematik med DERIVE (Månsson)
Matematiken i historien (Thompson)
Matematiken i historien - övningsbok (Thompson)

Euclidean and Non-Euclidean Geometries
Abstract Algebra and Solution by Radicals
Fractals Everywhere
Beauty of Fractals: Images of Complex Dynamical Systems (Peitgen)
The Banach-Tarski Paradox
A History of Mathematical Notations
Mathematics : Its Content, Methods and Meaning
Theory of Sets (Kamke)
Foundations of Geometry (Hilbert)
On Gödel
Table of Integrals, Series, and Products (Gradshteyn m fl)
The Fractal Geometry of Nature (Mandelbrot)
The Science of Fractal Images
Integral Equations
Turbulent Mirror: An Illustrated Guide to Chaos Theory and the Science of Wholeness
Flatland : A Romance of Many Dimensions (Abbott)
Prelude to Mathematics (Sawyer)
Chaos: Making a New Science (Gleick - äv på sv)
What Is Mathematics, Really? (Hersh)
Encyclopedic Dictionary of Mathematics: The Mathematical Society of Japan
A=B (Zeilberger m fl - även på nätet)
Foundations of Analysis (Landau)
Symmetry (Weyl)
Geometry : A Comprehensive Course (Pedoe)
Non-Euclidean Geometry (Coxeter m fl)
Essays on the Theory of Numbers (Dedekind)
Lectures on Classical Differential Geometry (Struik)
Euclid's Elements (Heath, Densmore)
An Investigation of the Laws of Thought (Boole)
Contributions to the Founding of the Theory of Transfinite Numbers (Cantor)
The Joy of Pi
Journey Through Genius: The Great Theorems of Mathematics
A Mathematician's Apology (Hardy)
On Formally Undecidable Propositions of Principia Mathematica and Related Systems (Gödel)
A Primer of Infinitesimal Analysis
Div, Grad, Curl, and All That: An Informal Text on Vector Calculus
Proofs without Words : Exercises in Visual Thinking
A History of Pi
How to Solve It : A New Aspect of Mathematical Method (Polya)
Regular Polytopes
Abel's Proof : An Essay on the Sources and Meaning of Mathematical Unsolvability
Concrete Mathematics: A Foundation for Computer Science (Knuth m fl)
Hilbert's 10th Problem (Matiyasevich)
Elementary Concepts of Topology
Gödel, Escher, Bach: An Eternal Golden Braid
What Is Mathematics? : An Elementary Approach to Ideas and Methods (Courant, Robbins)
The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography (Singh)
The Penguin Book of Curious and Interesting Numbers
Engines of Logic: Mathematicians and the Origin of the Computer (Davis)
Men of Mathematics (Bell)
Recreations in the Theory of Numbers
How to Solve It (Polya)
Computability and Unsolvability (Davis)
The Emperor's New Mind : Concerning Computers, Minds, and the Laws of Physics (Penrose)
Greek Mathematical Thought and the Origin of Algebra
Counterexamples in Analysis
An Introduction to the Theory of Numbers (Hardy, Wright)
Gamma : Exploring Euler's Constant
The Honors Class: Hilbert's Problems and Their Solvers
A Course of Pure Mathematics (Hardy)
An Essay On The Foundations of Geometry (Russell)
Mathematics and Plausible Reasoning (Polya)
The Book of Numbers (Conway m fl)
The Development of Mathematics (Bell)
Proofs and Refutations : The Logic of Mathematical Discovery (Lakatos m fl)
A Profile of Mathematical Logic
Complex Variables Problem Solver
Number Theory and Its History (Ore)
Visual Complex Analysis
The Continuum : A Critical Examination of the Foundation of Analysis (Weyl)
A History of Vector Analysis : The Evolution of the Idea of a Vectorial System
The Principles of Mathematics (Russell)
Introduction to Mathematical Philosophy (Russell)
Three Pearls of Number Theory
A Concise History of Mathematics
Godel's Proof
A Source Book in Mathematics
Foundations of Galois Theory
Nonstandard Analysis
Disquisitiones Arithmeticae (Gauss)
The Higher Arithmetic : An Introduction to the Theory of Numbers
The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time
The Thirteen Books of Euclid's Elements
The Bones: A Handy, Where-to-find-it Pocket Reference Companion to Euclid's Elements
A History of Greek Mathematics (Heath)
The Geometry of Rene Descartes
The Works of Archimedes
The Mathematical Experience (Hersh)
Functions and Graphs (Gelfand)
Algebra (Gelfand)
The Method of Coordinates (Gelfand)
Trigonometry (Gelfand)
Sequences, Combinations, Limits (Gelfand)
The Man Who Knew Infinity: A Life of the Genius Ramanujan
Infinitesimal Calculus
Axiomatic Set Theory (Suppes)
The History of the Calculus and Its Conceptual Development (Boyer)
Mathematical Theory of Communication (Shannon)
The Skeleton Key of Mathematics : A Simple Account of Complex Algebraic Theories (Littlewood)
Fundamentals of Number Theory
The Decomposition of Figures Into Smaller Parts
Complex Dynamics
Five Golden Rules : Great Theories of 20th-Century Mathematics -and Why They Matter
Five More Golden Rules: Knots, Codes, Chaos, and Other Great Theories of 20th-Century Mathematics
Continued Fractions
The USSR Olympiad Problem Book : Selected Problems and Theorems of Elementary Mathematics
100 Great Problems of Elementary Mathematics
An Introduction to Lebesgue Integration and Fourier Series
Metamagical Themas: Questing for the Essence of Mind and Pattern (Hofstadter)
Geometry Revisited (Coxeter)
Fermat's Enigma : The Epic Quest to Solve the World's Greatest Mathematical Problem
e: The Story of a Number
Mathematics : The Loss of Certainty
Famous Problems of Geometry and How to Solve Them
Euler: The Master of Us All
From Here to Infinity
Foundations and Fundamental Concepts of Mathematics
Fifty Challenging Problems in Probability with Solutions
The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems (Gardner)
The Prime Numbers and Their Distribution
The Mathematical Universe: An Alphabetical Journey Through the Great Proofs, Problems and Personalities
Geometry
Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics
The Beauty of Geometry (Coxeter)
Prime Numbers: The Most Mysterious Figures in Math
Challenging Mathematical Problems with Elementary Solutions
My Best Mathematical and Logic Puzzles (Gardner)
Entertaining Mathematical Puzzles (Gardner)
The Moscow Puzzles: 359 Mathematical Recreations
Challenging Problems in Geometry
A History of Mathematics
The Divine Proportion: A Study in Mathematical Beauty
Mathematical Recreations and Essays
Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace
Language of Mathematics
Challenging Problems in Algebra
Adventures in Group Theory: Rubik's Cube, Merlin's Machine and Other Mathematical Toys
Introduction to Geometry (Coxeter)
Mathematical Modelling Techniques
Introduction to Mathematical Modelling
A Passion for Mathematics: Numbers, Puzzles, Madness, Religion, and the Quest for Reality (Pickover)
A Mathematical History of the Golden Number
The Foundations of Mathematics (Stewart, Tall)
Mathematical Thought from Ancient to Modern Times
Zero: The Biography of a Dangerous Idea
To Infinity and Beyond: A Cultural History of the Infinite
Dr.Riemann's Zeros
Winning Ways for Your Mathematical Plays
1089 and All That - A Journey into Mathematics
Projective Geometry
Mathematical Fallacies and Paradoxes
The Mathematical Career of Pierre de Fermat, 1601-1665
Concrete Abstract Algebra : From Numbers to Gröbner Bases
Mathematica by Example
Stability, Instability and Chaos : An Introduction to the Theory of Nonlinear Differential Equations
An Introduction to Algebraic Structures
Logic: A Very Short Introduction
An Introduction to Non-Classical Logic
Forever Undecided: A Puzzle Guide to Godel (Smullyan)
The Ancient Tradition of Geometric Problems
The Elements of Non-Euclidean Geometry
Five Equations That Changed the World : The Power and Poetry of Mathematics
The Shape of Space
The Mathematics of Soap Films: Explorations With Maple
Discovering Curves and Surfaces with Maple
Geometry of Curves and Surfaces with MAPLE
The Mathematics of Oz : Mental Gymnastics from Beyond the Edge
Using History to Teach Mathematics
The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry
Analysis of Numerical Methods
Mathematical Methods using Mathematica
Classics on Fractals (Studies in Nonlinearity)
Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities
The Joy of Sets : Fundamentals of Contemporary Set Theory
Experiments in Topology
Diophantus and Diophantine Equations
The Beginnings and Evolution of Algebra
Mathematical Constants
A Concept of Limits
101 Great Ideas for Introducing Key Concepts in Mathematics
The Music of the Primes : Searching to Solve the Greatest Mystery in Mathematics
When Least Is Best : How Mathematicians Discovered Many Clever Ways to Make Things as Small (or as Large) as Possible
PI in the Sky : Counting, Thinking, and Being
Classics of Mathematics
Mathematics in the Time of the Pharaohs
Experimentation in Mathematics: Computational Paths to Discovery (Borwein m fl)
Mathematics by Experiment: Plausible Reasoning in the 21st Century (Borwein m fl)
Kepler's Conjecture: How Some of the Greatest Minds in History Helped Solve One of the Oldest Math Problems in the World
Modern Differential Geometry of Curves and Surfaces with Mathematica
The Golden Ratio and Fibonacci Numbers
Circles : A Mathematical View (Pedoe m fl)
Fermat's Last Theorem for Amateurs (Ribenboim)
The Calculus Gallery : Masterpieces from Newton to Lebesgue
Euclidean and Non-Euclidean Geometries

Historiens matematik (Thompson)
Fördjupad linjär algebra och matematisk analys för gymnasieskolan (Jansson, Matsson)

Structural Stability and Morphogenesis (Thom)
Ars Magna or The Rules of Algebra (Cardano)
The Mandelbrot Set, Theme and Variations (Tan Lei, ed)
From the Calculus To Set Theory 1630-191 (Grattan Guinness, Iv)
Mathematics: The Study of Axiom Systems. (Witter)


Övrigt

"Math Page"

Delta-X

Diverse dokument:

DERIVE-seminarium
Extremvärdesproblem mm utan derivator
Chalmers material för IMO-deltagare

Bengt Månsson 2006-04-05