Frank Potter's Science Gems - Mathematics

Mathematics Categories

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• NANOWORLD HOME PAGE - D. Waddell @ Univ. of Queensland, Australia Electron microscope images in abundance: select Image Gallery to see insects, blood cell, cement, polyp skeleton, crystals, bread mold, rat hair, egg shell, pollen, etc. Also a wonderful section on scale size examples from the atomic & molecular to the cellular and macromolecular. [If you have a slow connection, turn off auto-images and select later.]
  
  
• ASK DR. MATH by the SWAT TEAM - Drexel University Elementary, Middle, High, and College levels: 100's of problems, favorite problems, and Problem of the Week, Problem of the Month.
  
  

• ASK DR. MATH by the SWAT TEAM - Drexel University Elementary, Middle, High, and College levels: 100's of problems, favorite problems, and Problem of the Week, Problem of the Month.
  
  
• Quandaries and Queries - Math Central, University of Regina Variety of problems and their solutions.
  
  

• MOLECULAR MODELING - New York University [SELECT Quicktour, or, Modules, or Software] In MODULES ones finds: Water Module (labs, simulations, activities, challenges, reviews); Carbon Chemistry (bonding, compounds, diamond, graphite, Buckyballs, kevlar); Photosynthesis (under development); Molecules of Life (access to protein molecules in archives at other sites); 3-D Modeling of Molecules (tutorials); Ask-a-Scientist Page. Also tutorials in 3-D imaging of geometrical solids.
  
  
• ASK DR. MATH by the SWAT TEAM - Drexel University Elementary, Middle, High, and College levels: 100's of problems, favorite problems, and Problem of the Week, Problem of the Month.
  
  

• Quandaries and Queries - Math Central, University of Regina Variety of problems and solutions for the high school studdent.
  
  

• Geometry Java Applets for Euclid's Elements- D.E. Joyce, Clark University Dynamic interactions with the geometrical renditions of the propositions. Author is setting up all the propositions in Book 1 of Euclid's Elements via Java script!
  
  
• Mathworld- E. Weisstein & Wolfram Research Definitions, equations, and examples.
  
  

• Available when verified.
  
  

• Graphing Vector Calculator (Java Applet) - P. Flavin Practice vector operations.
  
  

• Available when verified.
  
  

• GRAPHICS FOR THE CALCULUS CLASSROOM - Douglas N. Arnold Collection of graphical demonstrations for first year calculus. MPEG Animation, text, etc.
  
  
• Interactive Real Analysis/ - B. Wachsmuth, Seton Hall University "Interactive Real Analysis is an online, interactive textbook for Real Analysis or Advanced Calculus in one real variable. It deals with sets, sequences, series, continuity, differentiability, integrability (Riemann and Lebesgue), topology, and more. The text is changing constantly."
  
  
• Mathworld- E. Weisstein & Wolfram Research Definitions, equations, and examples.
  
  
• Calculus Examples - K.S. Brown Limit paradox, functions with nozero derivatives, high order integration schemes, etc. - explanations and answers to questions.
  
  
• Online Integral Calculator - Wolfram Research Integrates practically any combination of functions!
  
  

• Bayesian Network Tutorials Links to resources.
  
  
• Probability & Statistics Examples - K.S. Brown Poisson, collector's problem, lottery, barrel of colors, etc. - explanations and answers to questions.
  
  
• Prisoner's Dilemma (Java) "This game is an implementation of the Prisoners' Dilemma, a classic problem in which competition between players is structured in such a manner that when decisions are made based on individual self-interest, the result is likely to be less than optimal for each player."
  
  
• Combinatorics Examples - K.S. Brown Polynominos, permutations, partitions, etc. - explanations and answers to questions.
  
  

• GANG Geometry Archive - UMass/Amherst Surface lib, knot lib, research papers, quicktime movie lib, software lib.
  
  
• Pavilion of Polyhedreality - G.W. Hart Pavilion of practical polyhedra.
  
  
• Geometry of Surfaces Archive - UMass/Amherst GANG - D. Oliver Surfaces, Knots, quicktime movies of surface deformations.
  
  
• Geometry Examples - K.S. Brown Tringles, spheres, tangents, etc. - explanations and answers to questions.
  
  
• Millefiori Quilted Patterns - Geometry Examples - D.E. Joyce, Clark University You can set some of the parameters for the quilt pattern.
  
  
• Mandelbrot Set - Geometry Examples - D.E. Joyce, Clark University You can set some of the parameters for the images.
  
  

• Mathematical Constants and Sequences - S. Sykora All numbers are not created equal; that certain constants appear at all and then echo throughout mathematics, in seemingly independent ways, is a source of fascination. Just as physical constants provide "boundary conditions" for the physical universe, mathematical constants somehow characterize the structure of mathematics.
  
  
• Inverse Symbolic Calculator - CECM at University of Newcastle 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 projects presently ongoing at the Centre for Experimental and Constructive Mathematics (CECM). There are over 22 million constants as of Jan. 15 1996.
  
  
• Number Theory Examples - K.S. Brown Primes, sequences,congruences, Marsenne Coincidence, etc. - explanations and answers to questions.
  
  

• To be added when verified.

• To be added when verified.
  
  

• Amazing Mathematical Object Factory - F. Rushkey, University of Victoria, Canada Information about and amazing dynamic generation of these objects: Subsets; Permutations; Combinations; 8-Queens problem; Pentominoes; Permutations of a Multiset; Partitions; Fibonacci sequences; Magic Squares.
  
  

• To be added when verified.
  
  

• Set Theory & Foundations - K.S. Brown Fuzzy logic, implicit means,consistency, Brouwer, etc. - explanations and answers to questions.
  
  
• LOGIC CALCULATOR - A. Yavuz Oruç, Department of Electrical Engineering, University of Maryland "This simple calculator computes the truth value of a logic expression comprising up to four variables, w,x,y,z, two constants, 0,1 and sixty symbols (variables, constants, and operators)."
  
  

• Matroid Theory - S. Kingan "A matroid is a mathematical construct, just as a group, a field, or a topology is a construct. It has a somewhat surprisingly large number of associated operators or special collections of subsets, and perhaps just as surprisingly, one can use any one of these to "define" what a matroid actually is...."
  
  
• Test data for comparative studies - NIST "A visual repository of test data for use in comparative studies of algorithms for numerical linear algebra, featuring nearly 500 sparse matrices from a variety of applications, as well as matrix generation tools and services. "
  
  

• Our Mathematical Universe: I. How the Monster Group Dictates All of Physics - F. Potter "...if a 4th quark family exists, the physical rules of the Universe follow directly from mathematical properties dictated by the Fischer-Greiss Monster Group via the Monster’s j-invariant function and the Mo ̈bius transformation in discrete spacetime, with everything related to the Golay-24 information code for the Leech lattice."
  
  
• ATLAS of Finite Group representations - R.A. Wilson, University of London "Representations of many finite simple groups and related groups such as covering groups and automorphism groups of simple groups."
  
  
• Mathematics of Rubik's Cube - Think Maths U.K. YouTube video and instructions
  
  

• Geometry and the Imagination in Minneapolis - J. Conway, P. Doyle, J. Gilman, W. Thurston Handouts from their workshop.
  
  
• Level Set Methods- J. A. Sethian, UC Berkeley "Level Set Methods are numerical techniques which can follow the evolution of interfaces. These interfaces can develop sharp corners, break apart, and merge together. The techniques have a wide range of applications, including problems in fluid mechanics, combustion, manufacturing of computer chips, computer animation, image processing, structure of snowflakes, and the shape of soap bubbles."
  
  
• KNOTPLOT site (Knot theory) - R. Scharein
  
  

• To be added when verified.

• Unsolved Mathematics Problems - S. Finch at Wolfram Research "This evolving collection of unsolved mathematics problems is not systematic or complete; it is only an eclectic gathering of questions and partial answers which have come to my attention over the years. In particular, I am less interested in reporting the latest incremental advances on well-known problems than I am in publicizing little-known problems."
  
  
• Mathematical Physics Examples - K.S. Brown [Select physics] Interpretations of gravity, retrograde motion, accelerated frames, shortest paths, etc. - explanations and answers to questions.
  
  

• Quotations of Mathematics - M. Woodard, Furman University "Life is good for only two things, discovering mathematics and teaching mathematics"-- S. Poisson.
  
  
• Alan Turing and the Turing Machine - A. Hodges, Oxford History and ideas.